[TRINPsite/MVVM, 59.04.7-59.04.7, mvvm.net/En/MNI/BoI1-3.txt ] [Plain text file of section files at www.trinp.org/MNI/BoI/1/(*/)*.HTM to 3/(*/)*.HTM. Additions and revisions in the original *.HTM files have been incorporated until 59.04.7. This file is not part of the digital Model, as it may not be up to date and does not contain special symbols and fonts.] MODEL OF NEUTRAL-INCLUSIVITY by Vinsent Nandi, 41 aSWW BOOK OF INSTRUMENTS, PART I [chapters 1-3] 1 HAVING AND THINGNESS 1.1 HAVING COMPONENT PARTS, ATTRIBUTES AND RELATIONS 1.1.1 HAVING CONCRETE AND ABSTRACT THINGS 1.1.1.1 ---------------------------------------------------------------------------- TO THE EARLY READERS Once the wheel of the Norm, the new doctrine, the new paradigm, has been set in motion, there is then no way anymore to stem the anabasis, the advance of the neutral-inclusive movement. It may go faster, it may go slower sometimes, but it will never return to its original position of nonhaving, of nonbeing. ---------------------------------------------------------------------------- There is something remarkable about having a pen, paper and a table, having a hand with fingers, having a will and thoughts of your own, and having the intention to write down these particular thoughts. By itself there is nothing peculiar in saying that you have an instrument for writing, like a pen, or that you have some paper, or a table. In theory you could have any kind of concrete thing in the sense of being close to it, in the sense of controlling, keeping or using it, or in the quite different sense of owning it. By itself there is nothing peculiar either in saying that you have a body, in saying that you have a hand, and in saying that you have a number of fingers. You could mention any other bodily part or organ you have, or your body has, that is, has as a component part or element. It is of some interest, however, that both you and your body seem to have that hand, and that you, your body and your hand or your body's hand all have the same fingers. Yet, even by itself there is something noteworthy about saying that you have a will (of your own), or that you have certain thoughts and an intention to communicate them thru the medium of paper as it carries the implicit presupposition that wills, thoughts and intentions are entities which exist like a pen and paper. Of course, this does not prove the existence of abstract entities like wills, thoughts, intentions, or other attributes and relations, mental or not. It merely shows that in the language which is our present means of communication existence and being also cover abstract entities. If there were no freedom of the will, it is not because freedom is or would be something abstract. And if perfect harmony did not exist, it is not --again-- because perfect harmony is or would be an abstract entity. Another thing to bear in mind with respect to having a mental attribute or relation is that it is you who does have a will, a thought, or an intention, not your body. (Note the difference with having parts of the body.) Many attributes and relations belong to you and not to your body: it is not your body which is intelligent, middling or unintelligent, and it is not 'your body which is someone else's friend'. What is especially remarkable about all aforementioned sorts of 'having' is that they are relations of quite dissimilar types. The first sort of having is a relation between a person or an object and another object which is usually extraneous to it, that is, neither a component part nor an attribute or relation of it. The second one is a relation between a person or an object and a component or 'proper' part it has as an element. If you mention your whole body, you are referring to the sole component part you have in a strict sense. The third and fourth relations of having apply between a person or an object and the attributes and relations this person or object has. In the language we communicate in at the moment every object in our environment, whether a human being or a house, a virus or a body cell, has both component parts and one or more attributes as elements, and as entities of which the existence is taken for granted. A table, for instance, may have a board and four legs, but this is never everything. It must also have one or more properties and relations, properties and relations which its parts do not necessarily have as well. (As a matter of fact there is nothing remarkable about having a pen, having a hand and having thoughts. What is remarkable is something with regard to the expressions of what it is to have one or more of these things. This distinction, which is crucial, will always be indicated here by means of italics or angle brackets. In general "the ... < * >", or briefly "< * >", may be read as "the ... of what is * ". Thus good or is usually the predicate, word or notion good. The predicate good is, then, the predicate of what is good, that is goodness; the word good, the word for everything that is good; and the notion good the notion of goodness. Unlike a change of font from regular to italic (or from italic to regular) or angle brackets apostrophes on both sides of an expression, like in <'having'>, can always be deleted without change of meaning. They may emphasize that there is something typical of the word or choice of words, for example because the term plays a special part in the context, or because it has different meanings, or because the whole expression has been used by others before.) Once many people were taught (or, perhaps, many people are still taught) that 'the world' would consist of human beings, animals, plants and so-called 'things', that is, all the rest. This was a conception exclusively suited to the human, material environment. All people or persons were of necessity, human beings and vice versa, and these human beings were first of all separated from all other animal beings, and with them from 'the' other living beings, that is, plants. And as living beings the human beings were again separated from 'the things' (not from all other things). This, however, was by no means a universal conception independent of the position of the conceiving object, even not when exclusively considering the material world. To be universal both the material and the nonmaterial have to be included in one system (a system which must not assign an exclusive status to life on Earth and which must refrain from anthropocentrism or any other kind of speciesism). In a universal, conceptual structure we are all objects, whether independently moving and growing or not. What counts is that all these objects can be defined in two basically different ways: (1) by the parts they consist of, and (2) by the attributes and relations they have. When defining objects by the parts they consist of, someone who would be unfamiliar with the culture of human beings on Earth might regard a house as merely a collection of construction materials skilfully attached to each other. Such a person would not be that wrong, for a house is indeed a whole of certain materials put together in a certain way. On the other hand those who have to live in such a house themselves may rather see it as a place with a conditioned microclimate, a place in which it is warm, dry, and also safe (or in which it is or can be made warmer, drier and safer than outside). They might also speak in vaguer terms, suggesting that a house has to provide shelter. Thus, instead of a house having certain materials (or rooms for that matter) of which it is composed, they would speak of its being warm, dry and safe, and of its providing shelter. The structure and idiom of the language spoken should not confuse us when not to have is used, but to be or some specific (nonprimitive) verb like to provide. (Compare to have a thought / intention with to think / intend .) It may not be clear that there is a question of having an attribute or relation until the original sentence is replaced with a sentence of the same meaning in which the (primitive) verb to have is used. For example, the following sentences on the same line have the same, or nearly the same, meaning. (Some of them may be too formal, literary or technical to be used in ordinary language, yet all of them are fully intelligible for someone only speaking an everyday conversational variant of this language.) WITH TO HAVE WITH TO BE WITH A SPECIFIC VERB ONLY I have the (relation I am desirous of I desire something of) / a desire something / that.. I have the attribute of I am hungry (for I hunger for something hunger / the relation something, if no food) (else than food) of hunger for something (else than food) You have work / the You are working / You work attribute of working a worker That person has the That person is honoring That person honors (A) attribute of honor(ing) / the relation of honoring something That person has (the) That person is (being) -- (P) honor / the attribute / honored relation of (being) honor(ed by someone) It has the attribute of It is following It follows (A) following / the relation of following something It has the attribute of It is (being) followed -- (P) being followed / the relation of being followed by something It has (a) color It is colored -- (Note: in (A) the active, and in (P) the passive form of the same verb are shown.) Altho it may not be an example of colloquial language to say that your table has the property of heaviness, there is no reason why such a proposition would contradict the conceptualization implicit in the language we are using here: every table has a weight after all. Weight is something every table must have as an object or concrete thing, heaviness is something it may have. The pattern (or lack thereof) exhibited in the above table of examples is not typical of the present language. It is a general pattern in many other languages as well, altho there may be variations to it. Thus, while the construction i have hunger may not be employed in this language, it is correct in other languages. (Compare i feel hunger.) The difference between the use of a specific verb or to be and the use of to have typifies a linguistic structure and must not be taken to reflect any analogous distinction in (nonpropositional) reality. We can always refer to the attributes or relations (and parts) a thing has instead of expressing ourselves in terms of specific verbs, or with the verb to be. 1.1.2 ONE RELATION OF HAVING-AS-AN-ELEMENT There is no need to distinguish the having of parts from the having of attributes and the having of relations. (If it is believed that attributes or relations do not exist, then the having-of-attributes-or-relations does not exist either, and also then the result is still one type of having: having-as-an-element.) This having is purely factual and in this sense not different from the having in having a pen, having paper and having a table where these objects are actually near at hand, or used. A fundamental difference lies in the logical necessity to have something one is made up of, that is, a body or (if preferred) a mind. In the sense of having-as-an-element one must have something, if not a part, then at least one attribute or relation; otherwise one would not even be identifiable. In the sense of being-close-to, owning, and the like, having is a contingent matter: one need not have anything in anyone of these senses. If both types of having were not distinguished, one could not even tell anymore who you were. Are you a set of which a pen is an element, or are you a whole which consists of a piece of paper among other things? The table you have has four legs, but do you have these four legs in the same sense as you probably have two legs? The answer is no, because whereas all these objects (other than your two legs) may be owned by you, or had in some other sense, they are not elements of yourself. Maybe one also feels 'physically close' to one`s body or its parts, and to the attributes and relations one has; maybe one 'controls', 'keeps' or 'uses' them in a sense; yet, this would all be in addition to having them as an element (of oneself). Furthermore, one may feel that one has one`s (own) body in the sense that one owns it, that it is one`s personal property. This use of having lays claim to a cultural or subcultural norm or law, or to a normative institution believed in, such as that of natural or human rights. But then --again-- one does not only 'have' one`s body in the factual, noncultural (and nonlegal) sense of having as an element, one also `has` it in the logically contingent, normative, cultural or legal sense. The conceptual framework we shall use as the supporting structure of our thought will allow for one relation of having-as-an-element, that is, for things having both parts and attributes and relations. We shall also employ the term existence (or being) in such a way that attributes and relations exist, or rather can exist (but not necessarily as things). For those speaking the language which is our present means of communication here this may all sound very trivial. However, it is philosophical analyses and formal systems which exclusively recognize the having or possession of (component) parts, or exclusively the having of attributes or properties (whether or not in addition to two- or more-place relations) which force us to state our basic assumptions explicitly. Altho we did try and shall try to avoid deviating from traditional language and its presuppositions as much as we can, traditional language is never an argument by itself, because it may be incoherent, ambiguous, wrong or immoral in its terminology and assumptions (as it not seldom is). Thus we shall accept the having of parts, attributes and relations as one kind of having, but we shall not consider the having of extraneous objects, or things looked upon as being extraneous, to be identical to it. And altho we do recognize abstract entities as existing besides concrete ones, we shall later reject as pseudo-entities many (if not most) attributes and relations implicitly recognized in ordinary or traditional language. It cannot be proved that a certain ultimate conceptual framework --or 'ontology' for short-- is the best one, or the sole adequate one, as an ontological framework is itself a prerequisite for any logical proof. It can be illustrated, however, that constructional systems which only recognize the existence of wholes and parts, or only that of attributes or relations, suffer from the conflation of having-parts and having-attributes-or-relations just because they neglect the presence of the one or the other category. The illustration of this shortcoming can only be done within our own frame of reference tho, and could therefore be consistently dismissed by others. Whatever the disadvantages of our own conceptual supporting structure, it will show to be very useful. In spite of this, the edifice we are going to construct can stand without it, and could also be erected with the help of a different scaffolding. There are hardly any logical objections which can be made to our constructional system, but some might reject our choice from an ontological or some (other?) metaphysical point of view. And while we have no absolute pretensions with respect to our ontology, we must be prepared to meet the criticisms of those who have. 1.2 THE CHOICE OF ONTOLOGICAL INSTRUMENT 1.2.1 SENSIBLE AND NONSENSICAL QUESTIONS OF ONTOLOGY Theories propounded under the heading of ontology have often been full of whimsical, metaphysical inventions and the source of much confusion. Ontology has been defined as the study of what is the case as contrasted with epistemology: the study of what one can know to be the case. It has also been contrasted with axiology or normative philosophy: the study of what is the case versus of what ought to be the case. 'Ontological' problems of that sort have thus been posed on the same level, and side by side, with those of epistemology and axiology or normative philosophy. Considering themselves 'specialists in the nature of being' the 'ontologists' concerned purported to be searching for what there (really) is, as opposed to what can be known to be the case, and to what should be the case. Antimetaphysicians who have always repudiated the belief in some 'nature of being' or an 'ultimate reality' have indicated that this kind of 'ontology' is an exercise in futility. With it, however, they have traditionally also repudiated all theories about kinds of existence or about the ontological status of existents. It seems like they have wrongfully equated the idea of an ultimate reality with the idea of an ultimate conceptual framework or constructional system used when speaking or thinking about reality. But it is exactly this which is the primary task of a sensible ontology: to make explicit the fundamental, conceptual or constructional categories and presuppositions of a particular system of language or thought, and to examine what are the primitives and hypothetical entities in this system. Ontology in this sense is, then, concerned in the first place with the question whether such a system does indeed make a distinction between: * what is the case, and what is known to be the case; or * what is the case, and what is believed to be the case; and * what is the case, what can be the case, and what should be the case; and * what was, what is, and what will be the case. The subject of ontology is therefore not what is the case as distinct from what is, can, or should be known or believed to be the case, or as distinct from what ought to be the case, but the subject of ontology is first of all the question whether the distinction between the factual and the epistemic or doxastic, and between the factual and the normative, is actually drawn in a particular system. Some of the above distinctions correspond to a difference in ontological status, some do not, but also in 'one and the same' sphere of what was, is and will be the case some entities may have another ontological status than other entities. Immediately following is therefore the question of what is explicitly or implicitly taken to be existing in a certain language or system of thought: * only 'i' or 'my' mind (in solipsism)? * only mind (or the human mind), or only matter, or * only abstract entities such as attributes, or only concrete things, or both? * sets, classes, functions and/or numbers (in logics and maths)? * one or more gods, demons and/or other supernatural entities (in religious thought)? * (a) supreme being (in denominational thought)? The crux of the matter is, of course: what does existence mean? If we do not make use of a synonym like being , it is not possible to define this term (or these terms) without referring to entities whose (purported) existence is required for the definition itself, if only by means of giving examples of existence. This implies that the term existence may have different meanings in different systems, dependent on what kind of entities are said to 'exist' in these systems. (Compare the meaning-variance thesis in logics: the meaning of logical constants wholly depends upon the axioms or rules of the system in which they occur.) Thus solipsists who believe that they only exist themselves, or idealists who believe that only mind exists (that is, who use the word exist so that only mind 'exists') give another meaning to existence than materialists who believe that only matter exists. The same does not apply to the existence or nonexistence of the supreme being and entities with supernatural qualities like gods and demons, because the suggestion is that they have the same ontological status as human beings or people and the other things of the 'natural' world. After having made these inventories the next step is to study the possible inconsistences in the constructional or ontological system, and the possible elimination of certain categories, postulates, primitives or hypothetical entities. Underlying this activity is the conviction that every theory or conceptual system must be free from superfluous conceptual ballast. The criterion of consistence is an essential element of the coherentist theory of truth, the criterion of simplicity or parsimony is a principle of conceptual minimization, that is, of fewest conceptual entities (categories, postulates, primitives, and so on). A problem with regard to the latter criterion is that it is not that simple to determine the general, formal simplicity of an ontological system (if possible at all), even not in only one respect. For example, the simplicity of the basis of primitive predicate expressions is not fixed by merely counting the number of primitives, or of primitive predicate places (because --as has been argued-- predicate expressions can be compounded into other predicate expressions having more places, or can be replaced by other predicate expressions having fewer places). Another question is the number of nonprimitive expressions. We shall see that our own ontological system has many more individual expressions, because it accepts the names of attributes, such as happiness, as individual expressions where other, formal systems have only -- is happy as a predicate expression. On the other hand, the latter systems need many more predicate expressions, and the total number of individual and attributive expressions remains the same in both types of system. If individual expressions should not be multiplied 'beyond necessity', then neither should attributive expressions. And altho -- is happy and the other expressions designate only one-place predicates or attributes, the primitive two-place predicate expression -- has .. needed in addition to the individual expressions is always the same one, and cannot be dismissed anyhow in any system which recognizes the relation of having-as-an-element or being-an-element-of (which is its inverse). As to relations it is inevitable that we must use individual expressions besides the relational ones. These individual expressions are reduced or 'derelativized' one-place predicate expressions of the two- or more-place corresponding ones. (In combinatory logic such 'derelativization' is done by means of a predicate operator 'Der'.) Friendship in the sense of having (someone as) a friend, for instance, corresponds to the one-place -- has (someone as) a friend which is a reduction of the two-place -- has .. as a friend (the inverse of -- is a friend of ..). This recognition of individual relations is necessary, because when relations become the focus of attention, and when we start talking about their attributes and/or relations (with other attributes and/or relations), they become things themselves, albeit in a different domain of discourse. Relations (such as friendship) cannot have the same ontological status as the things (such as friends) they relate to each other, otherwise we would be stuck with a loose, unconnected set of objects with parts and purely nonrelational attributes at the most. Thus, when we talk about relations, we make use of individual expressions corresponding to reduced, one-place predicates, and when we talk about the things being related, we make use of two- or more-place predicate expressions. Attributes are limit cases of relations: one-place predicates as it were. They have the same ontological status and behave very much like them, especially when looked upon as things in a separate (the so-called 'secondary') domain of discourse. This is the reason that we shall employ the term predicate as common denominator of both attributes and relations, while using the phrase predicat(iv)e expression for an expression which designates an attribute or relation. (In other systems such an expression itself is often termed "a predicate", while attributes may be called "internal" or "intrinsic properties" and relations, "relational" or "extrinsic properties".) 1.2.2 ON NOMINALISM, PHENOMENALISM AND THEIR ANTITHESES Real existence of predicates or universals, or of all abstract entities, is denied by nominalists. They do not want to commit themselves to (the existence of) 'something which all gray objects have in common', or to any other attribute or relation. According to another definition of nominalism they admit solely the existence of particulars and eschew all reference to nonindividuals such as classes or sets of particulars. Also numbers as classes of classes do not exist, then, in the nominalists' eyes. However, this respectable sobriety may not preclude these same nominalists from recognizing as an individual any sum of two arbitrary individuals, even if they have no property in common whatsoever, or even if no general term is applicable to both of them (while not being applicable to other possible candidates). Should the legs of your body and the legs of your table be individuals in such a nominalist 'calculus of individuals', the sum of one of your legs and one of the table's legs will be an individual as well. Nominalists who do not want to recognize the existence of classes or sets may thus in the end hardly be more sober than nonnominalistic realists who recognize at least some nonindividuals (such as classes of particulars) as existents, or as values for predicate variables. Our recognition that abstract entities 'exist' and can be 'things' in a world of their own, not in space and time, is a kind of realism, and is contradictory to the form of nominalism founded upon a rejection of all abstract entities. On the other hand, we will not admit sets of particulars as existing just because one can theoretically construct such sets. (If a set exists, then it has one or more attributes, not only nonattributive members.) Not admitting this kind of nonindividuals, our system could be called "nominalistic" in this respect. Perhaps conventionalism would better describe our position, for we consider the calculus of classes or functions, or set theory, as a 'creation of the mind' good for a convenient interpretation of the world. But then, we will not adopt the kind of conventionalism according to which all formal and scientific theories are nothing else than systems of linguistic conventions. What complicates matters is that we need to make a distinction between existence and thingness, and that we will recognize the existence of relations, but not their thingness when talking about physical reality (in what will turn out to be the primary domain of discourse). Traditional philosophical distinctions like the one between nominalism or 'antirealism' and (nonnominalist) realism, may just not be applicable anymore to novel conceptual structures, or at least not unequivocally. Moreover, there are good reasons to avoid terms like nominalistic and realistic altogether, because of the dissimilar meanings they both have been given. The term realistic is not only opposed to nominalistic or antirealistic, and not only to unrealistic, but also to particularistic, in which case it refers to a different interpretation of phenomenalist systems. The distinction between phenomenalist and physicalist systems is, then, itself one in addition to the distinction nominalism versus (logical, nonnominalist) realism. If physical entities such as objects or processes are chosen as the basic units of an ontological, constructional system, then it is called "physicalistic"; if phenomenal entities such as qualia or presentations are chosen, then "phenomenalistic". (A quale is a property which is considered an object of experience rather than the physical entity itself which has that poperty: it is the characteristic presented by that physical entity.) In both systems the basic units are individuals which can be perceived by one of the senses. Physicalists and phenomenalists both claim epistemological priority for their own basic units, but it has been demonstrated already by theorists with less absolutist pretensions that it is hard to understand what such would mean in the first place. Now, if the basic units of a phenomenalist system are nonconcrete, qualitative elements, then it has also been called "realistic"; if they are spatiotemporal particulars like phenomenal events, then "particularistic". Those free from metaphysical, ontological or epistemological absolutism have also made clear before, that when choosing between these different systems, it is most of all the way in which they deal with the relationship between qualities and particulars which matters (and not so much the metaphysical priority of either qualities or particulars). Thus a particularist theory is faced with a problem of abstraction: how to obtain repeatable, abstract universals from concrete particulars; but an (antiparticularistic) realist theory is faced with a problem of concretion: how to obtain unrepeatable, concrete particulars from abstract qualities. Attention has already been drawn to the fact that every perceptible object can be described in two different ways, namely (1) by the parts it consists of -- as such it is conceived of as a whole of component parts -- and (2) by what it looks like, what it does, how it relates to other objects, how it is changing or not, and so forth. The latter thing is done by mentioning the object's inherent characteristics, its actions, its relations, and its changes or lack thereof. All these latter elements of the object, whether 'essential' or accidental, are attributes and relations, that is, predicates, of the thing in question in a broad, but strict sense. By speaking of these elements the object is conceived of as something which has a collection of attributes, and a number of relations with other objects. But while every object presents itself in this view as a whole of component parts and/or by the attributes it has, the parts themselves are in their turn also presented by their parts and the attributes (and relations) they have. This pattern can be pursued until those objects emerge which cannot be described by mentioning their parts any longer, but only by referring to their attributes (so far as the internal elements are concerned). We are assuming, then, that there is an end to this process of dissection -- an assumption necessary to arrive at the basic elements of this ontological system: the attributes. On this construction every object is a more or less complex system of attributes, a structure of which the 'materials' (the minimal basic units) are the attributes. (Relations exist between things and are in this domain of discourse no material of any of the discrete things they relate to each other.) Altho an attribute is a nonphysical entity -- and therefore our system not physicalistic -- it need not be a phenomenal entity either. It may be or cause single phenomenal colors, sounds, tactual sensations, and so on, but it may also be a mental or other nonphenomenal (and nonphysical) entity. Insofar as our system is phenomenalistic, however, it is also realistic (in a nonparticularist sense). 1.2.3 SPECIES ESSENTIALISM ON SPEC Until now we have been thinking about objects as if they were givens, that is, immediately present in our personal, or some communal, experience. But what is it which is given ? One particular, concrete thing? (The problem is then abstraction.) A particular color? (The problem is then concretion.) Or a human being? It is essentialists of the metaphysical persuasion who believe that objects (or at least objects of a 'natural kind') have real essences, and that those essences are a prerequisite for identifying them as separate objects. In their view an object is not only always of some particular kind, but 'essentially' always of that one particular kind, normally the species it belongs to if it happens to be a living being. The emphasis on species membership forces metaphysical essentialists to adopt a naively absolutist conception of the notion of species, because each species must be as fixed and as detached from other species as each corresponding 'real essence'. As soon as objects are not of a natural kind (for example, artifacts or even not that), their metaphysics immediately runs short of essentials. (In spite of this, some essentialists maintain that the discovery of real essences would be the ultimate goal of all scientific investigation.) The metaphysical essentialists' belief in fixed, specific quiddities -- not generic or other superspecific ones, and not racial or other subspecific ones -- may be preposterous or nonsensical, there is another element in their belief for which we have to be even more on the alert. It is the underlying supposition that there is merely one way, or merely one adequate way, of describing reality, namely by referring to the fixed essence or essential properties of an object or kind. Describing reality is therefore presented as if it were relevancy-independent, that is, independent of the purpose of describing it. In fact, however, it is the context or the goal(s) of the description which determine which predicates are accidental or not in those circumstances. This is not to say that given a certain description of an object (for example, the natural kind it belongs to) certain attributes are essential whereas others are not. Yet, such a form of essentialism is only of some conventionalist type: all it claims is that if an object is classified in a certain way, it is a convention of language that it must have certain attributes and/or relations and/or component parts which are essential elements of each member of the class mentioned. Thus a human being has certain essential parts and characteristics, and all other parts and predicates are contingent, but nothing forces us to classify an object (even if it is a human being) as a human being: we might classify the thing concerned as a living or sentient being, as a male or female mammal, as a person, as a member of a particular ethnic group, and so on and so forth. Which description we should or should not use, and which properties are essential is, then, context- or relevancy-dependent. While the metaphysical, 'specific' form of essentialism is too implausible and too deceptive to deserve further consideration here, the problem remains how things are distinguished as separate entities. It seems that we must at least accept some notion of substance from which a thing derives its more or less discrete existence. Attempts to explain objectual existence in the physical world on a phenomenalist basis have failed, but mainly because of a one-sided emphasis on phenomena which are visual. Confining oneself to visual sense experiences exclusively, it is indeed impossible to distinguish spatially discernible individual things. The identification of individual objects in the environment surrounding them is obviously not a question of visual perception in isolation, but rather of intersensory conformity, particularly conformity between visual sensations and simultaneous tactual ones so it seems, and particularly after many repeated experiences in that environment. That is why a fata morgana is not an object in the sense a pen and a finger are objects: altho it may visually be a discernible phenomenon, there is never a tactual, or other nonvisual, sensory experience accompanying it at the same moment as we see it. (This is also why we should not call anonymous phenomena "unidentified flying objects" when people have only 'seen' them and not experienced them in any other way.) As a matter of fact, this hypothesis of intersensory object identification is more of an empirical(-scientific) nature than ontological. It is not the place here to work it out further and to defend it, but it is definitely a more sober and fertile hypothesis than the quasi-explanation of metaphysicians groping for ghostly 'whatnesses'. 1.2.4 AN INSTRUMENTALIST ATTITUDE TO ONTOLOGY Ontology or the development of an ontological system is not an end in itself: an ontological system is usually an instrument for other theories or doctrines. Only if a theory or doctrine could not be developed by means of any other ontology would this ontology be basic to it, or an integral part of it. Normally, however, one can translate the one ontological language into the other; for example, realist language into nominalist language, or phenomenalist language into physicalist language, and vice versa. If such a translation is available and does not result in a change in the body of (nonontological) principles of the theory or doctrine itself, then the ontology employed is not fundamental to it. Moreover, the kind of ontological instrument chosen may itself not be appropriately classifiable anymore in traditional terms. As already pointed out, and as will become clearer later, our own ontology is realistic in a sense, but nominalistic in another sense. And as explained above: altho it is certainly not essentialistic in the metaphysical sense, it is fully compatible with a conventionalist form of essentialism, or a form of essentialism in which the notion of an essence would not be more specific than that of a thing. Since our ontological, conceptual framework is regarded as a mere instrument, not fundamental to the doctrine to be developed, and especially not fundamental to the normative aspects of this doctrine, our attitude towards ontology (and also logics) is instrumentalistic. This does not mean that the system's usefulness would determine some kind of absolute truth; it rather means that the idea that there is and can be only one correct ontological system is rejected altogether. (Strictly speaking, this is a kind of nonmonism which might also be called "pluralism".) We still have to continue our investigation tho in order to make sure that we are not going to work with an inadequate instrument, or an instrument (much) more inadequate than other conceptual tools. It cannot be denied that many specialists in the fields of constructional ontology, logics and related disciplines have wholeheartedly supported other systems or other interpretations of systems for a long time. 1.3 THE ATTRIBUTIVE VERSUS THE OBJECTUAL VIEW 1.3.1 LOGICAL DOMAINS OF DISCOURSE The prime task of logics is to supply precise, purely formal standards of validity to distinguish valid from invalid arguments. While the domain of discourse which may be selected in logics is always restricted in some sense, one may pick out any kind of thing (perceptible, fictional or potential) one likes or believes in, and one may construct whatever fancy predicate or predicate expression one feels desire for. So far as formal logics is concerned logicians normally cannot and do not bar any entity or type of entity people wish to include in their domain. This does not mean, of course, that individual logicians may not be interested in ontological questions. (Such a logician may personally dismiss names as strictly redundant, for instance, but at the same time have no scruples about artificial solutions like rendering every a= 'simply' as a predicate expression A which would be true solely of the object named "a".) The fictitious objects or things logics allows us to talk about are not necessarily beings created out of the imagination with some fancy combination of brilliant and/or gaudy attributes as we so often find in religious ideologies, in fairy tales, or in other supernatural thought. Such fictitious things may also be conceptual constructions, like sets or collections, soberly and coherently represented in a formal, philosophical or mathematical system. In logics a domain of discourse may encompass all these fictional entities besides (really) existing ones. What is even more interesting from the systematic point of view is that such a domain may include both discrete individuals and the parts of those individuals, from which they are not distinct (so long as all these individuals are definite, distinguishable objects or things). And it is logically also quite as acceptable --without making existential presuppositions-- to take in attributes as elements in a logical domain besides the things themselves and besides the parts of those things. Having done this it is only a question of translation to adequately write down in the logical calculus that a thing has parts and that it has attributes, using the same two-place relation of having. 1.3.2 THE CHARACTERISTICS OF TWO DIFFERENT INTERPRETATIONS Technically speaking, the interpretation of a formal system is determined by the domain itself and a function assigning elements of this domain to singular terms and n-tuples of elements of it to n-place predicate expressions (and functions to function symbols as well). (One-place predicate expressions are often said to refer to classes of entities rather than the singletons thereof or the subclasses collectively.) The singular terms are proper names, definite descriptions, pronouns or demonstrative phrases. An interpretation function thus assigns entities of the domain to singular terms; entities or singletons to attributive expressions; pairs to two-place relational expressions; and so on. The question which is important for us now is what 'kinds' of thing are chosen as elements of the domain in the ontological sense of kind. In the standard, 'objectual' interpretation of formal systems the elements of a domain are interpreted as objects which are not attributes themselves, which bear relations to one another, and which --expressing it in extrasystematic language-- 'have properties'. The particular in the domain assigned to a basic, singular term is a (nonattributive) object. (Note that an 'object' need not be a concrete thing in this terminology but it has to be of the same ontological order if it is abstract.) The two- or more-place predicate expressions to which n-tuples of particulars are assigned correspond to n-place 'relations between them'. This objectual interpretation is nominalistic in that it does not treat attributes as individuals; it is realistic in that it does admit sets of particulars, and in that it does not reject other abstract entities than attributes or relations. Furthermore the objectual interpretation of formal systems tends to be physicalistic. If it is of a phenomenalist nature, it may be expected to be particularistic (and in this sense definitely not realistic). The ontological position we will adopt ourselves fits in best with an 'attributive' interpretation of formal systems. This means that we take the elements of the domain to be attributes which belong to (nonattributive) things, and which also bear relations to one another. The specific element in the domain assigned to a basic, singular term is now an attribute (a 'property' if belonging to a concrete thing or 'object'). In this interpretation the basic two- or more-place predicate expressions correspond to relations between attributes, not to relations between objects (or things) which have properties (or attributes). The difference between the two interpretations of formal systems is schematically represented in figure I.1.3.2.1. (In both interpretations a set of elements is ontic, that is, an existing thing, if between all the elements of the set the relation of belonging to the same thing holds, as designated by a two-place predicate expression. Every object which has other objects or properties as elements should in the first instance also be represented by a dot in addition to the dots representing the basic objects or properties it has. Such objects are shown as a closed curve around their elements because this considerably facilitates the reading of the diagrams.) In terms of systematics the things in the figure given are simple, being either basic themselves, or a set of basic things ('objects' in case of the objectual interpretation). In physical terms the things of the objectual interpretation may be extremely complex tho: what they are may vary from an 'elementary' or smaller particle to a galaxy or bigger whole. In this interpretation one elementary particle and one galaxy might be taken as separate entities side by side, and shown as two separate dots in a diagram; in the attributive interpretation they could at the most be shown as vague assemblages of dots or of dots and closed curves (properties or properties and parts) surrounded by a (bigger) closed curve. Of course, neither interpretation would in this way represent the structure of the physical universe in which elementary particles do not exist beside galaxies but in galaxies as part of them (or part of a part of them, and so on). A truly ultimate constituent of matter is in the 'objectualist' scheme a dot and in our 'attributivist' scheme a closed curve encompassing a number of dots representing properties (which may be derelativized relations as well). Such a truly elementary particle is a thing of the first type in the nonattributive and a thing of the second type in the attributive interpretation, the properties themselves being things of the first type. (In the attributive interpretation there are not 'objects' of the first type, since 'objects' are defined as 'material things', and properties are not material themselves.) We shall call an element of a domain of discourse "a thing of the first type", an ontic set of two or more of these elements "a thing of the second type", an ontic set of two or more things of the second type "a thing of the third type", and so on. According to this systematic typification of things, the elements of a thing of type n are things of type n-1 or of a lower type. There is no reason why a thing with an element of the second type, that is, an element which is a thing of the second type, could not have an element of the first type as well, that is, an element which is a thing of the first type. It should be kept in mind that a thing of type n-1 which belongs to a thing of type n is not a subset of that thing, even not an 'ontic subset'. This is because the elements of the type n-1 thing are not elements of the type n thing. Distinguishing elements on a different level of typification may be unimportant in the objectual interpretation, it is crucial in the attributive interpretation. Here it allows complex things to have attributes which are elements of the domain of discourse, while at the same time having things as constituent elements which are not elements of the domain of discourse, that is, not attributes (or relations) themselves. Moreover, the attributes of a component part of such a complex thing are not elements of the complex thing itself either, which makes it possible to distinguish between the attributes (and relations) of a whole and the attributes (and relations) of a part. It is only in this way that we can obtain an insight into the structure of the concrete world, and also --as we will learn-- an easier and clearer insight into the structure of the world of attributes and relations. Figure I.1.3.2.2 shows the difference between the objectual and the attributive representations of complex objects (ontic collections of things) . By a whole of nonbasic things/ (component) parts/ objects we shall mean an ontic set of which all these things are members, while no other nonbasic thing is a member, but --and this is important-- of which basic things, that is, attributes, are elements as well. The mere collection of component parts (nonbasic things) is called "the extensionality of the whole", while the collection of attributes, that is, predicates, which are an element of the whole is called "the predicament of the whole". Both these sets are purely conceptual constructs and do not really exist: solely their elements exist in (nonpropositional) reality. Extensionalities cannot exist because, if such sets were ontic, they would be the sole component part of the whole, and this part would still not be the set of which it were the only element. (Set-theoretically one must distinguish a singleton from the only element it has.) Predicaments (in the sense used here) cannot exist either because, if a collection of attributes existed, it would not exist besides the extensionality but belong to it. Objectualists have no systematic criterion to distinguish the sets of objects which exist themselves as objects from those sets which are extensions of a predicate expression, but can never be objects themselves. (If a set of objects was an object itself, it could not be an extension, because even a predicate expression which is true of one object only would have at least the singleton of this object as its extension.) In the attributive interpretation such a criterion can easily be provided: to be an object a set must have at least one attribute (as an element), that is, the set should also 'be' something, possibly in addition to having component parts. The analog of this criterion in the objectual interpretation would be that an ontic set needed a basic object as an element to exist. This seems rather odd tho from a structural point of view. For example, a material thing, however complex, would only exist if it had an elementary particle in the direct sense, that is, a particle which did not belong to any of its component parts. Being is having, that is, having an attribute in the attributivist ontology. (We shall see that existing attributes also have attributes.) But having is also being, since it is either having an attribute and therefore being right away, or having a component part, and therefore being an existing whole. Also the whole of one thing (a 'singleton' in some objectualist sense) must have at least one attribute, or one other attribute, in order to exist. Hence, such a whole has at least two elements, and singletons as such do not exist in the attributivist system. Just as pure collections of nonattributive things are conceptual constructions which do not exist in reality, so extensions as sets of objects, or n-tuples of objects, do not exist 'de re' either; only 'de dicto' may they play a role. In the objectual interpretation an attribute is instantiated as it were by the system of things which is its extension. However, this extension does not determine the meaning of the corresponding predicate expression, since two or more different expressions may have the same extension without being synonymous. Apart from this problem, a result of the objectualist position seems to be that one first has to know, say, all gray objects in the universe before one can know what grayness is. And another problem is that of attribute identity or the identity of predicate expressions: the objectualist must explain what happens when one or more temporal objects enter or leave the predicate extension. These problems cannot be adequately dealt with without making a distinction between the extension (or reference or denotation) and the intension (sense, connotation) of an expression. Being forced or willing to acknowledge the existence of intensions, intensionalist objectualists might as well recognize attributes and relations right away. (If extension is distinguished from denotation, the former term refers to all the subclasses of the property class collectively, and the latter one to its members collectively.) In the attributive interpretation a thing is, roughly, an instance of a system of attributes. The things are determined by the attributes which they have themselves or which their component parts have, or ultimately have. Normally tho, one does not have to know all attributes of a thing before knowing, or being able to identify, the thing itself. It depends on the uniqueness of attributes or of certain combinations of attributes. As regards concrete things, their spatiotemporal position is probably one of the most important means of identification. A special problem the attributivist faces is that of object identity thru time: the question whether the object is still the same when it loses or acquires a certain attribute in the course of time. This is first of all a problem for an ontology in which perceptible objects would solely have attributes, and no component parts as in our own conceptual framework. To overcome this difficulty a distinction between essential and accidental predicates might have to be drawn, but only in a conventionalist sense. A different problem of object identity arises when two objects would have exactly the same properties and no component parts. But as speaking of "an object" or "something" itself presupposes the presence of substance or existence, speaking of "two objects" itself presupposes that these objects must be distinguishable in some way. If they cannot be told apart by the attributes they have (and not by their parts either), then by means of one or more relations they bear to each other and/or to other objects. Usually the relationship one has in mind when speaking of "two objects" is a spatiotemporal one. This being the case two objects which are 'entirely the same' (with regard to attributes and parts) will have at least one different relation with a third object or thing, for example, the person speaking about these 'two' objects. It is clear that in the attributive interpretation objects with exactly the same attributes need not be identical, so long as relationships between objects are recognized as well. On the other hand, for 'two' conceptually distinguished objects to be identical 'they' must have the same attributes, the same component parts (or none in both cases) and the same relations. Objectualists who do not attempt to cling to pure extensionalism say that the extension of the predicate expression < -- is gray > is something else than its intension. Instead of this we will say ourselves that the collection of gray things, or of classes of gray things, is something else than grayness; or rather that grayness itself is not a gray thing. In this way we do not only capture the significance of the distinction, but we also do not unnecessarily deviate from ordinary language, for we can express ourselves very well in this language in this case. It is precisely one of the distinctive advantages of the attributive interpretation of formal systems that the way of formulating the object/property or thing/attribute relationship directly mirrors the way of talking about this relationship in extrasystematic discourse. Objects are not elements of a property or of a fictional singleton or subclass belonging to a property or one-place predicate extension: A is strong means A has strength; strength is a property (or fully derelativized relation) and thus A has the property of strength is true. Some confusion might arise sometimes, because things with a certain quality may on occasion, informally or figuratively, also be given the name of this quality, for example, beauty for somebody or something that is beautiful itself, or neutrality for something that is neutral itself. Yet, even then it is only the single things (beauties and neutralities) which have that name, not the set of all things having the quality in question, let alone the set of all singletons or subclasses of those things. 1.3.3 SECOND-ORDER PREDICATES ON THE OBJECTUAL VIEW Until now we have only looked at one domain of discourse in isolation, namely that of objects, or of objects and attributes of objects. We have confined attention to the attributes and relations of these objects, and we have compared the capacities of the objectual and the attributive interpretations of formal systems to deal with the possession of these attributes and the existence of these relations. We have not yet considered the attributes and relations of these predicates themselves. Doing this will open up a new field, or even a second domain of discourse. In the predicate calculus predicates of predicates are called "second-order". In principle this hierarchy of orders of predicate expressions is unlimited. An example of a predicate expression which is taken to be second-order is < (-- is a) color > 'because green is a color' and green [] itself is a first-order predicate expression, 'because grass is green' and grass is chosen as an entity (or collection of entities) in the domain. An expression like unhealthy may be treated as a compound second-order predicate term which results when a productive process is applied to the second-order predicate term healthy, like in exercises are healthy. Unhealthy is then analyzed as if it would mean not healthy. The first flaw in this approach is that the prefix un- in unhealthy, like in unhappy or unwise , does not simply mean not. For example, something that or someone who is unhappy is not happy, but something that is not happy is not necessarily unhappy at all. As we will see later (in 2.3.2) no fewer than three possibilities' of not being happy must be distinguished instead of one.' There are other objections that can be made against the above approach, such as treating the same term both as a first- and as a second-order expression, even tho it looks like this is done in everyday discourse. While words like healthy are also applied to attributive expressions, no-one could understand their meaning if one did not first understand what a healthy living being or person is. And in the latter usage healthy is not of the second but of the first order. That exercising is healthy should therefore be read as there is a causal relationship between somebody's exercising and somebody's being healthy/becoming healthier. In this way we still speak of a relation between attributes of the first order which is second-order itself. The difference is that causality is, then, always a second-order relation and health(iness) always a first-order attribute. In a hierarchy of orders it is important that expressions or entities of a different order have different names (something that does not apply to entities without order such as having-as-an-element or being-an-element-of and existing). If we look upon grass as a basic object, then grass is green (assuming that this is true), grass is colored and grass has a color. This means that, if color is an attribute, it is just a first-order attribute but an indefinite one. Color is certainly not an ontic property beside being green, being red, and so on. It is rather a conceptually produced property: if something is green or red or .., then it is (said to be) colored, and then it has a color. Hence, being-green or greenness, being-red or redness, and so on, is having-a-color. Now, green is also said to be a color, but then green is considered a basic object in a domain of discourse, not a first-order attribute in such a domain. Treating color simply as a second-order predicate expression therefore passes by the tendency in everyday language to treat phenomena of perception, or objects of experience, as basic entities of the or a domain of discourse. Thus we speak of colors, sounds, feelings, smells and flavors as particulars and not as intensions of first- or second-order predicate expressions or something of that nature. In this respect everyday discourse seems to be phenomenalistic (and realistic) instead of physicalistic. The objectual interpretation of formal systems is just not very well suited to handle such an ontology in which both physical things like grass and phenomenal things like greenness or the color green are recognized as real entities. The objectual and the attributive views are, strictly speaking, not dissimilar logical views. Yet, it is not impossible that the development of certain logical theories only makes sense in an objectualist frame of mind or, for that matter, in an attributivist frame of mind. Nevertheless, everything that can be formulated in attributivist terms can be formulated in objectualist terms, and vice versa, at least so far as the essentials of our conceptual framework are concerned. Given our ontological presuppositions, and in view of the constructional, normative doctrine to be expounded in due course, the attributivist instrument is much more adequate, however. Hence, we will use this tool from now on and look how it works in more detail. 1.4 ATTRIBUTES AS ULTIMATE CONSTITUENTS 1.4.1 SIMPLEX AND COMPLEX THINGS IN DIFFERENT DOMAINS It has been pointed out (in 1.2.1) that for every relation there are one or more derelativized one-place predicates. If A looks at B, there is a relation of looking between A and B, directed from A towards B. Thing A, then, has the property of looking-at-something, or simply looking, and B has the property of being-looked-at. A is at the fundament of the relation and performs the act of looking. (Looking is something else than receiving reflected beams of light.) We shall assume that the active form looking(-at-something) represents a real attribute. B, which is at the terminus of the relation, does not perform anything, and there is no need to assume that it has any real attribute because of its being looked at. Being-looked-at and other passive forms stand as such for pseudo-attributes. In diagrams where we show nonprimitive relations between things as lines connecting these things, there is no need to show the corresponding, existing one-place predicate(s) separately (inside the closed curve): altho not wrong, it would be superfluous. It has also been pointed out that a relation between basic things is a relation between attributes in the attributive interpretation of formal systems. If there is such a relation, then at least one of these related attributes must have a derelativized one-place predicate itself. But in the first domain of discourse such an attribute has no elements because it is a basic thing in this domain. Therefore it cannot be at the fundament of a relation with something else at all. It could be at the terminus of a relation tho as this does not require the attribute to have a real one-place predicate itself. When an attribute is said to have attributes itself, and when an attribute is said to have relations in which it is not just at the terminus, it is treated as a nonbasic thing, a thing with several elements itself, in another domain of discourse. The relations between those attributes belong to that domain of discourse too, that is, not to the domain in which one speaks of relations between nonattributive objects. Whereas the latter relations are primary, the former are secondary. And whereas attributes which are not attributes of any other (kind of) attribute are primary, the attributes of those attributes are secondary attributes. All of them are primary and secondary predicates. Just like in the objectualist interpretation, a predicate of a predicate of order n is itself a predicate of order n+1. This does not apply to the primitive having(-as-an-element), because this is a 'relation' inherent in the hierarchical structure itself. Like being and existing it is of all orders, or rather of no order in particular. The same applies to the primitive 'relation' of identity, which is purely conceptual and neither ontic nor of any particular order either. Identity solely plays a role in the description of reality, not in nonpropositional reality itself. Identity statements cannot express a relation between different things in reality, because, trivially, everything is identical to itself and to nothing else. Predicates have only higher-order (nonprimitive) predicates. They do not have component parts, of whatever order they might be. So every predicate of order n is an ontic set of predicates of order n+1. In the same way as a 'really elementary', that is, simplicial, particle is a set of primary attributes, a primary attribute is itself a set of secondary attributes, a secondary attribute a set of tertiary attributes, and so on. And like in the objectualist interpretation there is in principle no end to this hierarchy. Those who despise infinity should bear in mind that this hierarchy is an abstract, conceptual structure and in no way forces us to accept the existence of infinite sets of concrete things. As a basic thing a predicate belongs to one domain of discourse, and as a set of predicates to another one, that is, the next domain. Thus there are (basic) things in the one domain which are identical to (nonbasic) things in the next domain. This identity of things across the border of domains can be represented by means of a line interrupted by a special identity symbol (=), as indicated in figure I.1.4.1.1. It is now clear why it may seem that a relation between primary attributes exists in the first domain of discourse. The explanation is that the relation exists between two nonbasic things of the second domain which are both found as basic things in the first domain as well. The relation itself is secondary, however, and corresponds to a secondary one-place predicate found inside at least one of the primary attributes in the second domain of discourse. Figure I.1.4.1.2 gives some examples of primary, pseudoprimary and secondary relations between and with primary attributes. (By way of clarity the relational attributes are shown extra as a separate attribute besides the relations themselves.) In the attributivist terminology a universe of discourse is the totality of all hierarchically ordered domains involved in a particular communication. The ultimate constituents of the first domain of this universe are primary attributes, those of primary attributes and all other things of the second domain secondary attributes, those of secondary attributes and all other things of the third domain tertiary attributes, and so on. Hence, the ultimate constituents of all domains are attributes, and those of a particular universe of discourse the attributes of the highest domain in the hierarchy. The simplex particles and the predicates in a universe of discourse are all simplex things, that is, things which have no extensional elements and which cannot present themselves by means of component parts. They are sets of predicates which exist in reality as a thing -- according to our typification in section 1.3.2 as a thing of type 2. All things of a higher type we shall call "complex things". Simplex and complex things belong to the same domain as the attributes of the highest order they have belong to. (Attributes of a lower order are components.) Hence, a simplicial particle belongs to the first domain, altho it could be represented as a set of sets of secondary attributes in a universe of discourse which would include the second domain too. If we allowed this, however, only its 'parts' would have attributes and relations, not the thing itself. Since a simplicial particle must have attributes and relations of itself, it does not belong to the domain of secondary attributes. On the other hand, a complex thing with a primary attribute does belong to the second domain, if it contains one or more secondary attributes as well. Its primary attribute is, then, not an attribute in the sense of a basic thing, but a component part. Some might have expected that our distinction between parts (as nonpredicative elements) and attributes (as basic, predicative elements) is a distinction only to be found in the physical world. They might have believed such a distinction to be inappropriate to the general framework of an ontology. But our example of a complex thing in the domain of secondary attributes proves that this objection is wrong, for complexity of this sort exists as much in the abstract world as it exists in the concrete or physical world. The very recognition of this complexity is an absolute prerequisite to understanding the structures in both these worlds. It is of paramount importance to realize at this stage that the universe does not only encompass material things, with or without related things and attributes, but that it also encompasses complex systems of nonprimary attributes. The development of one of the two paradigmatic components of our weltanschauung itself will depend on this insight. 1.4.2 ABSTRACTION AND CONCRETION As the ultimate constituents of our universe of discourse are attributes, we are formally faced with a problem of concretion. (See 1.2.2) But, actually, we have started the other way around, namely with the assumption that complex, concrete things have both component parts and attributes, and those parts in turn also parts and attributes. We have thus considered complex things and their parts to be of the same ontological category, since they all have parts and attributes as their elements. Yet, whereas complex things have attributes, attributes never have things of that same category: a table may have a weight, but (a) weight cannot have a table. (It may belong to one at the most.) In subdividing complex things into smaller things (parts of a lower type) we have first formed a picture of abstraction which looks like the one in figure I.1.4.2.1. The crucial theoretical question is now whether we do arrive in this way at components which are mere sets of attributes (but which have relations as well). Without such an end to the abstraction process one might object against the 'categorical' discrepancy between things as parts and attributes and maintain that this discrepancy remains, however far down the components are subdivided into their elements. But then, one should bear in mind that the question whether the difference is categorical from any ontological point of view is the very matter at issue here. If parts and attributes can never be taken as ultimate elements of one and the same thing, the aversion of this sort of combination may be the very reason to postulate that there is an end to the abstraction ladder so that all parts, that is, all things, only have attributes as their ultimate factors, tho certainly not as their elements or components. A second point to take into consideration is that in the beginning the things of our domain were phenomenal or material things such as pens and fingers, but if there is an end to materiality when subdividing these things, there should be borderline cases. And indeed, there are such borderline cases: elementary particles do not have 'material', that is, constituent parts, and fail to count as bodies in this respect. They are not material in that they are not decomposable into matter, and yet they are material in that they are components of matter. It is here where we have arrived at a level where we can merely speak of an object's purely physical attributes and relations. And it is here where mass and energy become one and the same, where the material world transubstantiates to become immaterial. At this level objects are purely 'intensional', precisely like attributes, in that they have no extensional elements anymore. If this is not correct for particles such as neutrinos, one may assume that it still applies to 'truly' elementary particles, unless one is absolutely unwilling to ever accept the existence of such simplex objects. By choosing attributes as the ultimate constituents of the first and all other domains of discourse we have implicitly postulated that there is an end to the abstraction ladder. That there is, then, a beginning of a concretion ladder amounts to the same: to approach the problem of concretion we are faced with we reverse the picture of abstraction. In general, every realist constructional system needs at least one primitive relation which will make it possible to differentiate systematically between those abstract qualities (such as attributes) which form concrete things and those which do not. As the basic concreting relation one might choose togetherness, in our case among attributes, which obtains between any two attributes belonging to some one concretum or thing in general. (Choosing having as primitive does not make a difference: two qualities are 'together', if they are 'had' or possessed by the same thing.) If the relation of togetherness did not hold between any two attributes of a set (that is, if they did not belong to one and the same thing), the set in question would simply not be ontic, that is, (trivially) would not exist as a thing. The notion of togetherness can subsequently be extended to obtain not only between distinct, atomic qualities, qualia or elements but between every two discrete elements of a concretum or other thing. The elements may be component parts or attributes of the whole. In our constructional system a concretum may be conceived of as a single physical body with all its parts and its (whole-)attributes. All the elements of such things 'are together', that is, bear the relation of togetherness to each other, but the whole itself is not a part of another thing in which it bears the same relation of togetherness to other things. In a biological or physical sense human beings, for instance, are concretums but humankind is not a concretum. An old metaphysical issue is that of the distinction and relation between instance and quality. But as the 'atoms' of our constructional system are attributes we have no problem since they are 'fully repeatable, universal individuals'. The instance/quality distinction is in our case an instance/element distinction. Whether we regard a whole as an instance or as an element (component) simply depends upon whether we are concerned with its relationship to its attributes (those belonging to its predicament) or to a whole of which it is itself a component part. In our system instances of a property or attribute are never entirely separate. They may be discrete in space-time and in every other respect, yet they still have at least one common element: the common attribute itself. As has already been rightly argued before, attributes are not metaphysical sums of various particles which would occur in several instances. When concrete individuals which are believed to stand wholly by themselves 'participate in' a single property, their similarity is due to identity between at least one of their predicative elements. This could be shown diagrammatically by having the predicaments of the things in question overlap, by drawing the identity relation between one or more predicative elements of these things or by giving identical and unique names to identical and unique elements. 1.4.3 CONCRETE AND ABSTRACT If we compared the ultimate factors of a system to physical atoms, then concretums could be compared to molecules. And --as has been argued too-- as no fragment of a molecule of water is water, so no fragment of a simplicial concretum is concrete. Moreover, since a glassful of water is water, but not a molecule of water, it has been suggested that individuals of which a concretum is a proper part be called "concrete", altho they are not concretums themselves. Concrete would, then, mean that the individual's extensionality were exhaustively divisible into concretums. Thus, because human beings and their parts are concretums, humankind would be 'concrete' in the terminology of such a constructional system. We will not adopt this terminology. Instead of it we will later define concreteness in such a way that a concrete thing must be either in motion or at rest. (Abstract things are neither in motion nor at rest.) Furthermore, one concrete thing must in this view have one velocity with respect to a certain frame of reference. Hence, a glassful of water may be considered to be a concrete individual in this sense but humankind is not, since it is not part of the meaning of the term humankind that all humans always have the same velocity. (The simile was therefore not valid.) Humankind is either the whole of all human beings with its own attributes, or it is the collection of all human beings, the extension of being human. In the first case humankind would exist as an abstract entity, assuming that its predicament contains attributes which characterize it in a way logically independent of (the predicates of) its components. (The number of humans or some human average will therefore not do as a characteristic.) In the second case 'humankind' is a conceptual construct denoting the set of all things that have a certain characteristic combination of properties in common. In neither case humankind is concrete itself in our manner of speaking, but it or its extensionality is exhaustively divisible into concretums nevertheless. For each spatial dimension concrete things have a negative velocity ('the' property of moving in a negative direction), a neutral velocity (the property of being at rest) or a positive velocity ('the' property of moving in a positive direction). We will use the word object only for those things which have one of these properties. (To be more precise, they are derelativized relations: something 'is at rest', if it does not change place with respect to a particular, other object or frame of reference.) The properties of motion and rest or motionlessness are primary attributes which belong to concretums but the negativity and positivity of certain kinds of motion and the neutrality of motionlessness are secondary attributes. The attributes of primary attributes are never primary and therefore the properties of velocity (of motion and motionlessness) do not have a velocity themselves. Negative, neutral and positive velocity are abstract entities tho they are things in the first domain of discourse. (We thus employ abstract in the sense of not having any neutral or unneutral velocity, which is roughly synonymous to immaterial or intangible.) Altho objects are solely found in the primary domain, it follows that it would be a serious mistake to believe that all things in the primary domain were objects, that is, concrete. Whereas some primary things, like properties, are abstract entities which do not even have a concrete component, other primary things, like humankind (if existing as a whole), are abstract entities which do have components which are concrete. Secondary things and things of a higher order, however, are always abstract. If they are wholes consisting of one or more component parts, they are abstract wholes of abstract entities. 1.5 WHOLES 1.5.1 THEIR WHOLE-, PART- AND PSEUDO-ATTRIBUTES To exist, a whole of things must have at least one real attribute in addition to its parts. (See 1.3.2.) Not only should such an attribute not be a pseudo-attribute, it should also be an attribute of the whole itself rather than of one or more (or even all) of its component parts. (It may be a derelativized relation tho.) So far as such a whole-attribute is a prerequsite for the existence of the whole, it must be logically independent of the part-attributes. In other words, a whole is a gestalt, that is, a unit with attributes in addition to and not derivable from its parts in summation. It is in this literal sense that a whole is 'greater' than the sum of its parts. If whole-attributes could be derived from part-attributes, every set or 'sum' of concrete individuals could pop up as an entity, since one can always conceive of a physical attribute which would correspond to the 'sum' of the part-attributes. Thus, the volume of the whole, which is the total of the volumes of its parts, would be a characteristic of the whole, however far separated from one another its parts. Another such 'improper' whole-attribute would be the one relating to the average value of its component parts. The difference between attributes of a (whole) thing and attributes of its parts is often crucial and has but too often been blurred, for example, in discussions on individuation and identity thru time. Somebody who has brown hair first and gray hair later in life does not have any different property at all later on. Instead, such a person('s body) has a component part or parts (the person's hair) which were brown first and gray later on. It is this part or these parts which change properties. Strictly speaking, a whole consisting of several phenomenal parts actually never has any color of its own. If it is said to be parti-colored or to have one or more colors, these colors are the qualia, qualities or attributes of its parts. Only if all parts have, or seem to have, the same color, may this color, for the sake of convenience, be attributed to the whole consisting of these parts. Now, some predicate expressions precisely refer to the having of parts with certain characteristics or of a certain kind. In the above example one might come up with having brown hair (or <-- has brown hair>) and having gray hair as predicate terms designating a property of somebody considered as a whole. Such predicate expressions have to be devised in an objectualist ontology which cannot handle the part-whole relation very well. On the attributivist construction, however, it is evident that such constructions are completely artificial and do not denote any real attribute of the whole itself. Particularly notorious expressions of this ilk are being cordate and being renate, because they happen to have the same extension, so far as known. Cordateness is having a heart; renateness is having kidneys. As hearts and kidneys are organs or parts of the animal beings which have them, to say that an animal being is 'cordate' or 'renate' is nothing else than to say that it has parts of a certain type. Such expressions could be constructed for any type of having parts, for example, for a table which would be 'legged' or 'four-legged'. But of course, this would in no way force us to accept as real attributes like 'leggedness', 'four-leggedness' or, for that matter, quadrupedality. Cordateness is having a heart, not the property of having a particular part which is a heart or which has the property of being a heart (provided there is such a unitary factual attribute). If it were a question of having one particular thing which is a heart, there would be as many cordateness properties as there are hearts and mammals. Each such property would, then, be a haecceity predicate of the mammal concerned, that is, a predicate which no other thing has or can have as well. To avoid this consequence the predicate being a heart must be brought in, or a combination of predicates necessary to keep the same total meaning of (being a) heart. Cordateness is then the property of having something as a part that is a heart. 'Cordateness' and also 'renateness' are therefore pseudo-attributes. It is easy to understand why they are not synonyms altho cordate and renate are true of the same things: being a heart is just not the same as being a kidney, even tho one might have thought that having a heart would amount to the same as having a kidney. The ontological heartiness of logicians with kidneys has allowed some theoreticians to array their body of thought with the most fancy of predicate terms, also where the structure of wholes and parts is concerned. From a constructional point of view, however, it remains important that attributes of parts (such as being a heart) can be clearly and distinctly told apart from attributes of the whole (other than pseudo-predicates such as being cordate or having a heart). It is on this distinction that the existence of wholes or gestalts depends. Without the recognition of this distinction one will never gain a full insight into the configuration of these wholes. 1.5.2 EXTENSIONAL MEREOLOGY We have rejected both the idea that all things would be nothing else than collections or sums of component parts and the idea that all things would be nothing else than collections or sums of attributes (leaving aside the relations they may have). Insofar as we have chosen attributes as the ultimate factors in a structure of sets interpreted in the line of the sober ontology of a nominalist calculus of individuals, we are much closer to the latter view than to the former. We do recognize some sets of attributes as entities, whereas we do not recognize any pure set of 'parts' as an entity. Nevertheless, sets of parts do play a role as the extensionalities of wholes, and thus it may be worthwhile to have a look at theories which deal with wholes in a purely extensional way. A constructional theory which solely recognizes parts is mereology. It treats a physical aggregate as a 'sum' or 'fusion' of all elements of the class of parts of the object in question, so that all elements of the class of parts of the object are part of the fusion and no proper part of the fusion is disjoint from all parts of the object. Others have already argued against mereology that an object like a jug cannot be a mere collection, or even a mere 'fusion', of its proper parts. The reason is for us that such an object must have properties as well, in particular those bearing on its own integrity or function. Only because of those properties is the object under consideration a jug. None of its component parts is a jug on its own. Suppose that merely a heap of fragments is left of a certain jug; and suppose that these pieces are subsequently put together again to make a certain kind of pot. The pot is then made of the same collection of pieces as the jug was, but it has taken on quite a different shape and function (as we assume). Hence, the object is another one, tho the mereological sum has remained the same. To solve this analytical identity problem it has been suggested that is would be used in two different senses in this sort of context, namely in a sense pertaining to the object's constitution and in a sense pertaining to its identity. In the first sense the jug and the pot are, then, the same (made of, or constituted of, the same bits of clay, for instance); in the second sense they are not the same (not identical). This rather drastic cleavage in the meaning of the monosyllabic is provides too easy a way out tho and is not required in our system. We must, to make it work, not apply the mereological conception to the whole things themselves but only to their extensionalities. The jug character of a thing belongs to the attributive predicament of the whole and it is this which disappears or changes when a jug is dropped or badly damaged. The extensionality of the jug remains, if we interpret it not just as a set (as we have done hitherto) but rather as a 'fusion', so that it is a collection of all component parts of the whole however specified, thus including the collections of parts and the parts of parts. In this mereological sense the extensionality of the pot is the same as that of the original jug, and in this respect they are the same or constituted of the same matter. It should be kept in mind tho that the extensionality is not an ontic set, that is, not a real thing itself. From the point of view of strict identity, that is, sameness in all respects, the jug and the pot are different, albeit merely because of their disparate predicaments (attributive but also relational). This does not mean, of course, that the two objects could not be the same in some other than extensional respect as well. Furthermore, it is worth noting that one does not (necessarily) damage the (proper) parts of a jug, or affect them as severely, when the jug itself is damaged -- as has been confusedly suggested. Just as somebody who paints a little figure on the jug does not (necessarily) paint this figure on every part of the jug, so somebody who damages the jug does not (necessarily) damage every part of it; if so, then this is an additional, contingent fact. Damaging the jug is affecting the predicament and extensionality of the jug; damaging a part of the jug is affecting the predicament and extensionality of that part. It is obvious that not only the attributes of the whole and those of its parts are to be distinguished, but also that the relationships with the whole may be quite different from those with the parts of that whole. Altogether a thing may have a relation with a whole, with one of its parts and with one of its attributes. And as regards a thing which has one or more parts itself, one of its parts may have a relation with another whole, with a part of another whole or with an attribute of such a whole. These different types of relations are shown in figure I.1.5.2.1. In the diagram of this figure one does not find any truly reflexive relation, that is, a relation between 'two' things which are identical in the strict sense. There is no problem with accepting reflexivity with respect to (nonpropositional) things in a loose sense, but the strict interpretation of the notion remains obscure. To prove that things can have (nonpropositional, nonultimate) relations which literally turn back upon themselves, one must either give plausible examples of such things which are not wholes, or which are wholes, but which definitely do not have a relation with one, or between two, of their own (proper) parts instead. The so-called 'reflexivity' does not seldom concern such a relation between a whole and one of its parts or (in an even looser sense) between two different parts of the same whole. 1.5.3 HAVING AND PART IN A STRICT AND IN A LOOSE SENSE A table is not simply the set of a number of particular legs, or a particular stump and a particular board, altho it is made up of them. Three or more legs at one place and a board somewhere else do not yet constitute a real table; maybe they can or could constitute one. To actually be a table, more is needed and this more of every table is, or is found in, its attributive predicament. 'Mereologists' may talk about the different parts of the table and even wonder whether they are essential or not, while at the same time defining this table as a mere extensionality. (Mereological essentialists claim that all or certain parts are always essential to their whole.) When running into difficulties they may distinguish 'popular parts' for the ordinary or loose sense of part from 'philosophical parts' when speaking of "parts" in a strict sense. In a 'creative' bout of supernaturalist elation a realm of 'entia successiva' (things which are such that at any moment of their existence something other than themselves serves as their stand in and does duty for them), 'entia per alio' (things which derive all their attributes from other things which do duty for them) and 'entia per se' ('real things') may be hypostatized. But ordinary talk about wholes and parts cannot be that inadequate, even tho one of the issues, that of things remaining the same (or identical) thru time, is a delicate one. Theories which cannot tackle the ordinary language of wholes, parts and attributes without taking refuge in a thicket of ethereal entities just don't ring true. This is not to say that they would be wrong or uninteresting in every respect. For example, it does turn out very fruitful to draw a distinction between a strict and a loose sense of the words part and having, also in our nonmereological framework. The difference is that it is a very straightforward distinction here which can be easily defined in set-theoretical terms. For a clear understanding we must in the first instance reject in our case the axiom that if X is a part of Y and Y is a part of Z, then X is also a part of Z. If parts are genuine wholes themselves (and recognized as 'individuals'), then a part X of Y is, strictly speaking, no part of Z, even if Y is part of Z. (The axiom itself is the expression of a mereological conception of wholes and parts.) A part of a part of Z is something else than a part of Z, just as a parent of a parent of P is not (necessarily) a parent of P, and just as an utterance about an utterance about a fact F is not (necessarily) an utterance about F itself. At the same time it cannot be denied that one often calls a part of a part of A also "a part of A", or an utterance about an utterance about B also "an utterance about B" (and a friend of a friend of C also "a friend of C"?) in a loose sense. Especially when the division into parts, and also subjects, is vague or quite arbitrary the loose usage may suffice for the purpose of the conversation. But whether the term part is employed in a strict or in a loose sense, Y is never a part of X, if X is a part of Y (as another axiom reads). This is because in both cases part only refers to proper parts, not to wholes which would be 'their own part'. The appeal of the distinction between the strict and the loose meanings of part and having is that it provides us with an alternative to extensional mereology (having refused to accept total mereology in any case). The distinction allows us to do away with the very complicated 'fusions' to which not only the parts of the whole belong but also the parts of parts and collections of parts, or of parts of parts, and so on. This is not a very practical, accurate picture because, for example, somebody does not have a hand and five fingers in addition to that hand; that person('s body) has a hand and that hand has in turn five fingers (granted that the number is correct). It follows from this that also that person has those five fingers, but then in a looser sense of having. The part-whole configuration and the transition from a strict to an ever looser sense of having can be well demonstrated particularly with regard to persons. It is therefore high time now to see how these peculiar entities which no adequate ontology may ignore or neglect can be portrayed by means of our own conceptual apparatus. 1.6 PERSONS 1.6.1 SPEAKING PERSON-TO-PERSON Let us agree that all persons are living beings, but that not all living beings are persons. One way of subdividing living beings is, then, into personal and nonpersonal, living beings. Another way of subdividing living beings is into species, but from the point of view of personhood this categorization is not essential, as we shall not assume that all persons (or 'people') are human beings, nor that all human beings (in the zoological sense) are necessarily persons. Altho the distinction between person and human being may often not have been made at all, this is an anthropocentric fallacy we can dismiss immediately. A third way of subdividing living beings is into sexual and asexual beings. This is an aspect we must take into consideration for a moment before turning to the issue of personhood itself. Speakers of the traditional variants of the present and of many other languages, but also many speakers of languages which were never genderized, have always convulsively clung to the discrimination between male and female persons. Yet, the factor on which this distinction is based actually concerns living beings in general and not especially persons. A particular living being which is asexual (1) belongs to an asexual or metagenetic species which reproduces without sexual differentiation or alternatingly with and without, (2) lacks functional sexual organs, or (3) is not interested in sexuality. If, on the other hand, a particular living being is a sexual being, then it does belong to a species which reproduces sexually or also sexually, altho it may not be able (anymore) to reproduce itself in this way and altho it need not itself be interested in sexual matters. Sexual beings are either unisexual or hermaphroditic. In the former case the plant or animal has either male or female reproductive organs; in the latter case it has both. This conception is based on the kind of sexual differentiation, or lack thereof, as found on Earth. Logically speaking, however, there is no reason why the sort of generative reproduction in which two sexes are involved (the female and the male sex) should be the end to the possibilities of the types of reproduction. If reproduction is 'asexual', it is said that there is 'no sex' involved, but it might as well be said that there is only one sex or reproductive division involved; if it is sexual, then there are two sexes or reproductive divisions involved. But theoretically one could conceive of a form of life which depends for its direct reproduction on the union of the genetic material of three or more individuals of the same number of three or more different reproductive divisions. In the sense of complexity or natural, bodily development such a species would be of a 'higher' level than the one to which human and other living beings on this planet belong. (By way of illustration one may think of a planet Hyperyinyang with many asexual species and sexual species whose members have only male and/or female sexual organs, chromosome combinations and/or hormones. Assume, furthermore, that there is a species of 'jumans' on Hyperyinyang which can be divided into three sexes: 'cemales', 'demales' and 'eemales'. Should some jumans of Hyperyinyang now discover Earth, they will probably declare that 'humans', among others, are a genetically less-developed species with only two sexes: 'aemales' and 'bemales'.) While living beings may be asexual, female, male, hermaphroditic or something else, they belong to one of these sexual categories on account of their body, whether it be its parts or its general physical characteristics. No living being is male, female or something else as a person, because many sexual living beings simply are not persons. (Plants are an example.) Reproduction and sexuality are entirely irrelevant with respect to personhood proper. When referring to persons it is therefore wrong to use the masculine singular pronoun he or the feminine singular pronoun she. Only when referring to male or female bodies, and only when sex is relevant, is it correct to say "he" or "she". In all other cases nongenderized or 'gender-transcending' pronouns should be employed. (Just like she and he themselves are species-transcending, race-transcending, age-transcending, and so forth.) To refer to things, whether living or lifeless, whether concrete or abstract, the pronoun it may be used. But while it is traditionally also used for persons whose sex is unknown or disregarded, it is employed in particular when speaking of lifeless things, plants and abstract entities. In traditional language people would not say "it" of a person whose sex was known, even if this person's sex was of no import at all. If somebody's sex was unknown, or could be either one, the traditional speaker used --and may still use-- the masculine he to refer to a person. He would thus be employed to refer both to males and to people (irrespective of their gender), whereas she would refer to females exclusively. Some of the pioneers in the fight against androcentrism, also in the language, have proposed that she should include both female and male persons but they merely substituted gynocentrism for androcentrism. Most of the pioneers combating sexism decided to write the cumbersome "he or she" or "he/she", but altho this usage was gender-neutral, they were not conscious enough that they were still --and may still be-- caught in the same web of sexual irrelevantism (and moreover, it was never done consistently). The distinction between female and male as such has no bearing on personhood whatsoever, even not on being a living being. To refer to persons with he, she or he/she only depersonalizes them. It makes them into males and/or females on the grounds of characteristics which are basically biologic, material and physical, that is, their bodies'. (Of course, in practise sexual irrelevantism, especially a long history of sexual irrelevantism, may result, or have resulted, in many profound mental differences as well.) The tendency to always refer to persons by means of he or she in traditional language may cause and/or be caused by sexism or sexual irrelevantism, this does not mean that the availability of a pronoun other than it is not very convenient when speaking about persons. People do play a significant role in this world; in a way they are the only ones 'playing a role'. It is therefore very helpful to be able to easily distinguish these people from the nonpersonal things surrounding them in a domain or universe of discourse. The great advantage of the use of she or he for persons rather than it was (or still is) that one would know immediately that the thing referred to was a person and not some nonpersonal being. The importance of the person-nonperson distinction in our discourse does justify the introduction of a special pronominal device to refer to a person (not a male or female being or human being) -- a person named or described in a particular context. A language which does not have such a third-person pronoun (instead of or besides a third-male pronoun like he and a third-female pronoun like she) is less efficient in this respect. In line with the general pronominal pattern of inflection in the present language, in view of the phonological variants of pronominal terms starting with h and of the historical development of the nonpersonal hit to it in this language, and taking into consideration the advantage of having different words for genderized and nongenderized pronouns, and for the objective case and the pronominal adjective, we shall therefore henceforth refer to a person by means of 'e (subjective case), 'im (objective case) and 'er (pronominal adjective). (One may also simply spell "e", "im" and "er".) This pronominal series is the 'personal', singular analog of the plural they, them and their, the nonpersonal analog being it, it and its. (Traditionalists should be aware that the question is not whether this usage is good or not in some absolute sense, but whether any other usage or proposal is better -- and no traditional usage or proposal is, as examples like a person who denies himself or herself and a person who denies or deny themselves testify.) We are now able to relate to and speak about people regardless of their being female, male, hermaphroditic, asexual or something else of that ilk. Solely when gender is (believed to be) relevant, and if a male person or living being is concerned, is it alright to say "he"; and if a female person or living being is concerned, "she". By using 'e in a nonerotic, nonreproductive context the alternative use of he or she will automatically acquire an erotic or sexual significance where it may or should have such a significance. As sure as Nature makes numberless apples year after year, this will render a lovable language only richer. 1.6.2 THE PERSON AS A PAIR OF OBJECTS OR OBJECT OF A PAIR The classical idea that a person is nothing else than a soul, separate from and independent of a body, was already entertained and believed to be 'amply proved' at least two to two-and-a-half thousand years ago. The argument is founded upon the premise that 'man' is the user or ruler of 'his' body and that 'he' must be either soul, body or both together as one whole. Yet, since the body is not ruling but ruled, the combination of both entities could not be ruling either, and thus it must be the soul which rules where a person rules. In this reasoning it is taken that a soul stands to its body as a user to a thing used, or a ruler to a thing ruled. This however, is a treacherous simile which not only presupposes implicitly that 'the soul' is an entity like a ruler is, but also that the soul and the body it is supposed to rule are entirely separate individuals. (Individuals in an ontological, not necessarily a physical, sense.) Moreover, it is not unimportant that historically the 'thing ruled' is in the first place another person like the ruler `imself. If body and soul belong to one whole at all on this view, then merely as two different, individual parts. The dualism of body and soul, or 'mind', is a fallacy which readily results from an objectualist ontology. It starts with the correct recognition that there is a distinction between a person and `er body, that a person and `er body are two 'irreducible' entities as it were. No person can be identified with `er own body as the behavior of people is or can be purposeful or intentional, whereas the actions and reactions of mere bodies can be explained in terms of causes and effects. These observations themselves are very plausible, but it is a grave mistake to subsequently treat a 'soul' and a body both as entities and to put them apart in an objectualist frame of reference with all other souls (or 'persons') and bodies. First of all, there is then no way anymore to conceptually determine which body belongs to which soul, because every body is conceptually as much separated from each soul as every other body. This requires the special introduction of some nonultimate relation like 'using' or 'ruling'. Only such a relation can still determine by whom a particular body is possessed, but then a soul is not necessarily the possessor of merely one body anymore. Many classical or traditional, supernaturalist doctrines could, of course, not care less about this possibility because their souls do indeed change bodies as slaveholders change, or used to change, slaves. (The dualist-objectualist world-view of the consubstantiality of body and soul, or 'mind' or 'person', is shown in figure I.1.6.2.1.) If a dualist of the slaveholder type does admit that every soul has or can have only one body at a time, then `e is apt to speak of composites of one soul or mind and one body, at least in `er subjects` 'earthly' life. Such pairs are either sets of attributes which do not exist on our attributivist construction or wholes of two parts, but then it is these wholes which become the persons rather than the nonbodily parts. If persons were wholes of one body and one soul or mind, however, they would have their own whole-attributes in addition to the attributes of their soul and their body, and they would not rule their bodies anymore; or, if they would, they could rule their soul as well. Thus the soul which started out as the ruler of matter has on this account come down to the level of just another entity like a body or any part thereof. And also a part of a body may in some sense 'use' or 'rule' another part of the same body. Not only has the objectualist dualist of mind and body not explained, nor clarified anything, `e has merely left `er disciples with more problems. The most tricky of these metaphysical (pseudo-)problems are, firstly, what a soul or mind is as a whole (if it is distinguished from the person-whole having it); secondly, why such a whole as a soul or mind could only 'rule' one body during its life or at any particular time; and thirdly, what that peculiar nonultimate relation of 'ruling' is, and what determines conceptually which body or bodies are to be 'ruled' by which soul. All this metaphysics or supernaturalism has led people but too far astray from insight into the nature of a distinction which is itself genuine, namely that between a person and `er body. 1.6.3 AS SOMETHING HAVING BOTH A BODY AND MENTAL PROPERTIES I have a body and there is no body which has me (in the same sense of having as an element and of body as in i have a body). That is why i can speak of 'my body' instead of 'the body which has me'. Thus i am a whole of which my body is a component part, and --i must assume-- the sole component part, because there is nothing that forces me to believe that i have other parts which do not belong to my body. Being a whole, and having rejected the objectualist conception, i do not merely have my body, i also have my own whole-attributes as a person. These attributes are my 'personal' or 'mental' properties, whereas my physical characteristics are, strictly speaking, only properties of my body, that is, part-attributes. It is my behavior, not my body's, which is purposeful. I intend to write things down, not my body; and i have a will and thoughts, not my body. If my body shows tendencies to something, and if my body has a 'will', it is in addition to the tendencies and will i have in a strict sense. And this is true of all of us, of every person. As everyone is the whole of 'er body, the extensionality of a person is 'er body and the predicament a set of nonphysical whole-attributes which the person has 'imself in the strict sense of having. A person has 'er nonphysical, or not purely physical, properties as a gestalt, since they are not logically derivable from the only part 'e has: 'er body. What, then, ordinarily is called "(a person's) mind" is a person's predicament (or attributive predicament) and what ordinarily is called "(a person's) body" is a person's extensionality. Hence, the mind or soul is no whole whatsoever, but the set of a person's not purely physical (whole-)attributes. And these properties, which may be called "mental" or "psych(olog)ical", are not parts or elements of parts; they are attributive elements of the whole itself, of the person 'imself. A person's body, however, is in turn a whole itself, and has parts and attributes of its own. This configuration of persons is illustrated in figure I.1.6.3.1. A person's body may be made up of, let's say, a trunk, a head, two legs and two arms (leaving the discovery of these wholes and the need to have them to empirical scientists). The trunk in turn may be made up of a heart, kidneys and other wholes, like sexual organs. Because of this the body, or person having it, may be called "cordate", "renate" or "sexual". In a strict, primary sense, a person does not have a heart or kidneys or genitals: 'er trunk or maybe 'er body has. In the same, strict sense 'e does not have a left or a right arm: 'er body has. It is only in some loose, secondary sense that a person (instead of 'er body) 'has' a trunk and arms; and it is only in some tertiary sense that 'e 'has' a heart and hands. When 'finally' a hand has fingers, it is only in some quaternary sense that the person 'has' these fingers. It depends on the definiteness of the position of an extensional element whether the use of having is secondary or even looser. If this position is not clear at all, every use of having may be regarded as secondary in the case of a person having bodily organs or parts. 'Having a hand with fingers' does seem to be for a human person a kind of having of the third or fourth degree, while 'having mental characteristics, such as a will or intentions,' is definitely a kind of having of the first degree. Altho these mental predicates which may determine a person's utterances on paper are located a long way up from the fingers writing them down, they are all elements in the same realm nevertheless. A person's physical characteristics are the elements of 'er body's predicament. Hence, a person has 'er body in a primary sense but 'er physical properties only in a secondary sense. A person's mental characteristics are the elements of 'er (very own) predicament, 'er properties in the strict, primary sense of having. It is this set of predicates which is often called "mind", "soul" or "spirit". Yet, this set is merely a theoretical construct and does not represent any really existing entity at all. (Predicaments are not ontic sets as we have seen in 1.3.2.) The mind does not exist as a whole or thing, since it is itself the predicament of a whole of which a body is a part, the sole part. The mind is a collection of nonphysical predicates. The only thing that distinguishes it from a mere collection is that all its elements are had by one and the same person or mental being. Some might now wonder whether a number of mental attributes could not form a thing themselves just as a number of physical attributes can form a thing in the process of concretion (yielding a simplex thing with an attribute of velocity). But again, so far as the collections of mental attributes of individual persons are concerned this is even conceptually impossible, because it would make those collections into simplex things, and the persons having no attributes anymore (but things instead) would lose their personhood. (In this respect the situation is not dissimilar for physical attributes: the collections of the physical attributes of concrete, complex things cannot form a thing either.) The idea of the mental attributes of individual people being a thing collectively would merely lead us back to the dualistic objectualism we were forced to dismiss. For the sake of completeness it must be noticed however, that it is indeed possible on our attributivist construction that sets of mental, or at least nonphysical, properties do exist as abstract, simplex things. Just as in the physical world, it is furthermore also conceptually possible that there exist more complex, abstract things of which the ultimate constituents are nonphysical properties. But none of those abstract things --even if they exist at all-- is a person, or can ever be part of a person. In our terminology bodies do exist and are concrete things. Persons exist too but are not concrete things in a strict sense, for they do not have an attribute of velocity or any other physical attribute. Hence, in a strict sense, persons are abstract entities with a concrete object as the sole component part. It is only in a little bit looser usage that we may say that a person is something concrete with physical properties. The (personal) mind is an abbreviation for mental property A, and mental property B, and mental property C, and so on or for all a person's (whole-)attributes or for all a person's nonphysical characteristics. Thus, paradoxically as it may seem, the mind is no thing and does not exist, whereas all 'its' elements do exist. But what is presented theoretically as 'its' elements is in reality the person's elements. As a set of a person's mental predicates (or attributes only) no personal 'mind' can exist independently of a body since a person is 'imself a whole with a body as part, a whole of one body. On the other hand, a personal body always exists with mental characteristics called "a mind" conjunctively. As soon as a body is not part of a whole with a mental predicament, it simply is not a person's body. And, of course, there are many bodies without a person. There is no need tho to hypostatize persons (or other entities which have mental properties) without a body. On the contrary, it entirely passes over the configuration of personal beings and it detaches what belongs together, however different in nature. 1.6.4 THE FOURTH OF FOUR LINES OF THOUGHT In our brief survey of body and mind we have not examined the materialist view according to which mental entities do not exist. Being convinced that an adequate ontology must be able to distinguish persons from mere bodies, we have supposed that the difference lies in a mental being having nonphysical properties which a mere body by its very nature cannot have. Secondly, we have not examined either the idealist view according to which material, concrete or physical entities do not exist. We have supposed that there are 'material' bodies and that there are people who have bodies of this kind. The existential postulates of both (exclusive) materialism and (exclusive) idealism are just too farfetched to leave us with any useful notion of existence. In not taking the objections of this materialism and this idealism seriously, we follow the ordinary way of speaking about physical and mental properties, or about concrete and abstract things, because we have no reason to deviate from that usage in this respect. We have investigated the position of those who hold body and mind to be two existing things, and two separate things. We have in line with this view identified the concept of person with that of mind or soul, and also with that of the whole or combination of body and mind or soul. In both cases this position turned out to be untenable. Instead of proceeding along one of these three traditional ways, we have chosen and prepared a fourth way by founding our concept of personhood on the attributivist interpretation of set structures, in particular those structures which are whole/part configurations with one part only. It is on this view that bodies and persons both exist as entities, albeit not as separate entities since each body of the type concerned is part of a person or mental being. And it is on this view that minds (in the sense of nonpredicative things) do not exist, whereas mental properties and relations do. 1.7 EXISTENCE AND THINGNESS 1.7.1 THE VOIDNESS OF THE METAPHYSICAL EVERYTHING When someone says that (literally) 'everything' is and only can be thus or so, 'e often does not say anything more or else than someone saying that 'nothing is or can be thus or so'. If everything is (pre)determined, then 'nothing is (pre)determined'. (This everything is to be everything, not everything minus our feeling that we are responsible for something or not minus our feeling that someone else is responsible for something or not minus people's belief that someone who has committed a serious crime should be punished for it. And if literally everything is determined, then both the belief in determinism and in the doctrine of free will are determined, and so is neither one.) If everything is and must be material, then 'nothing is or can be material'; if everything is and must be ideal or mental, then 'nothing is or can be ideal or mental'. If everything is created (any 'creator' included), then 'nothing is created'; if everything is divine (that is, if one god is everything, or if gods are everything), then 'nothing is divine'. And if everyone has a right to everything, then 'no-one has a right to anything'. All these kinds of metaphysical everything are void. Worlds proposed by these universal statements are 'as replete as they are empty'. Thought and the ability to express thought solely exist because of distinctions made within reality, that is, by pointing out that some entities are of type T and that other entities are not of type T. (Even those believing in many-valued logics have to distinguish every single value from the other values which are not that value.) It has to be borne in mind, however, that this 'reality' is not necessarily a factual, momentary reality but that it must be looked upon from a temporal angle, that is, thru time, and from the point of view of 'possible worlds', that is, taking into account what is possible and impossible as well. For example, before the coming into being of persons or beings with mental characteristics --if there ever was such a moment-- there were only 'material' (in the sense of nonmental) beings, but this does not mean that the proposition everything (in the first domain) is material did not make sense at that time. (It could only never have been uttered by a person.) There was at that time already the possibility of being nonmaterial, that is, mental. It is void, metaphysical verbalism tho to say that 'everything (in the first domain) is material' with respect to the past, the present and the future, and with respect to the actual and all possible worlds. Then someone else might, metaphysically speaking, as well assert that 'nothing is material' or that 'everything is ideal'. Some theoreticians have claimed, too, that 'everything is real', others that 'everything is a dream'. But also the distinction between dream and (what is called) 'reality' can only make sense if it is somehow made within reality itself. The former people either say something as meaningless as nothing is real or something that is a tautology or analytical truth adding nothing to what we did already 'know' or could 'know'. The latter people parasitize our (fore)knowledge of a distinction between what is 'real' and what is 'only a dream'. That we have this knowledge, or this faculty of discerning the 'real' from the 'oneiric', entails that there is or could be such a difference. In the first case the contention that everything is a dream is false; in the second case everything is either 'real' in the sense of nononeiric or a dream. Now, the latter people's suggestion was that our world would always be and remain a dream. If it would not always remain a dream, then, in the course of time, 'everything' is nononeiric (that is, 'real') or oneiric (that is, 'a dream'). Well, this is an experience we --supposedly-- all have had, and in this sense the statement would be banal. If our world was always a dream, and if there still was a real distinction between the oneiric and the nononeiric, one or more possible worlds would have to be nononeiric or partially nononeiric. But if our world is supposed to be (necessarily) a dream forever, there would not (and never) be a relation of accessibility to any other (possible) world. (The difference between oneiric and nononeiric would be that between saying "actual at this and every moment or impossible" and "impossible forever, whatsoever".) There would not even be a possibility of our (actual) world being nononeiric. The claim that everything is a dream would, then, amount to the same as saying that 'nothing is a dream'. Is everybody is an egoist as meaningless as nobody is an egoist? Someone maintaining that it is not could argue that everybody is an egoist is a statement like everybody has a heart. This is a meaningful, contingent proposition, because, logically speaking, mammalian beings or at least people could do without a heart. Rather than to logical necessity it would refer to a kind of biological necessity (whatever that may be). Similarly, it would be a biological necessity for everyone to be an egoist, altho not strictly logically speaking. But then, biological necessity (if there is such a thing) may apply to mammalian or human bodies; it has no immediate bearing on persons as they are not mere (biological) bodies. While there is already no proof as yet that all people in the universe are cordate, altho all mammalians are, it is even not plausible that all persons would be egoists at all times. The idea that everybody is an egoist is parasitic on the distinction between egoism and nonegoism (not necessarily altruism) and on our foreknowledge of this distinction. The suggestion is, in spite of the distinction within factual and/or modal reality parasitized, that every person or human being would always be egoistic, and would have to be egoistic, because 'e could not be different. If this were really the case, the distinction itself could never have been drawn and the word egoist could never have acquired its present, everyday meaning in the first place. (If there still is someone who maintains that 'everyone is an egoist', ask 'im to compare 'egoists' who often derive their pleasure from helping others and 'egoists' who never derive their pleasure from helping others.) Somewhat paradoxically one might say that material entities solely exist if mental entities exist or can exist, and vice versa; that dreams solely exist if (nononeiric) 'reality' exists or can exist; that egoists solely exist if there are or could be people who are not (always) egoists. It is certainly possible to pronounce that 'everything or everybody is material, or ideal, or a dream, or egoistic' -- metaphysicians and exclusivist ideologues but too eagerly do this and have done this. Even in the context of purely formal, logical systems there is little or nothing against all entities always being of a certain type, and not being able not to be of this type. The crux of the matter is that such statements and doctrines keep us wholly entangled in purely theoretical or linguistic affairs which do not lead to any insight into reality itself whatsoever. If matter exists in a world in which only matter exists and can exist, then the notions of existence and of having an attribute --that kind of attribute-- become themselves devoid of any meaning, at least devoid of having some meaning. One definition of attribute is: nonextensional element which is common to all members of a certain group and which is not common to anything not belonging to that group. On this definition nonextensional elements which were, are, will be and must be common to all things in the world are not attributes; at the most they are universal (pseudo)predicates. Of course, it is not totally incomprehensible that, for example, all things of the first domain have and must have one or more elements in common, elements which are not logically derivable from their belonging to the first domain. The point is that we could never know these elements as such knowledge presupposes the actual or potential existence of a difference between having and not having these elements. Stating that being material or being ideal is such an attribute, while still suggesting that we know what material or ideal is then to signify, amounts to denying the possibility of a distinction on which one epistemologically depends. (It would be something else to refuse to make a distinction which one cannot or does not understand, like one between the 'divine' and the 'nondivine'.) 1.7.2 PSEUDOPREDICATES A predicate which a thing would not have, if it were not thought, talked or written about by the person(s) thinking, talking or writing, does not determine its character in any way. Such a predicate is merely a product of the person's or our conception (perhaps even of our imagination) and must not be considered a determinative predicate of the thing in question. So far as the relation of conceiving between a person and the thing itself is concerned, this is an asymmetrical relation with the person thinking, talking or writing at the fundament, and with this person having the attribute which results from derelativizing the relation. Quite a few traditional languages distinguish feminine, neuter and masculine genders, but this does not mean that any of these genders is determinative for the thing it is attributed to. Also the mere fact that a thing is thought, talked or written about now, does not mean that it does exist now or did ever exist at all, for being thought about, being talked about and being written about are purely conceptual predicates. When people are 'macarized', that is, called "happy", they do not have or get any determinative predicate on the basis of being macarized, and it certainly does not make them happy. It is solely the people macarizing who have a real, determinative predicate in this way. (Altho for certain religious devotees dutifully macarizing themselves both assertions may seem to hold.) Predicate expressions which do not designate any existing attribute or relation but which are determinative nevertheless refer to '(determinative) pseudopredicates'. If P is a determinative predicate which is no pseudopredicate, then not having P is a privative (pseudo)predicate. Privative expressions predicate privation or absence of an attribute or relation and thus stand for nothing. They replace a certain expression or part thereof in the particular language applied. When we define abstract as not concrete, for instance, the statement that a certain thing is abstract replaces the statement that it is not concrete, that is, that it lacks the attribute of being concrete. Being abstract is, then, not a proper attribute. Similarly, when something is dead, it does not mean that it has a proper attribute of being dead, it means that it does not have the attribute of living, that it is deprived of life. Being-dead is therefore a pseudo-attribute and, strictly speaking, death does not exist. In the same way, blindness is a privative pseudo-attribute where blind is a synonym of sightless. Altho prefixes like a-, non- and un- may be called "privatives" by linguists, predicate terms which begin with one of these affixes need not refer to privative predicates by any manner of means. For example, unhappiness has the same ontological status as happiness: they are opposites of each other. The one predicate is not 'more privative' than the other, just like hatred is not 'more privative' than love, and vice versa. The fact that unhappiness was not given a positive or affirmative name in this language, like happiness or hatred, does in no way determine its existence or nonexistence. Certain predicates designated by predicative expressions are improper, not because the expression does not denote any existing predicate, but rather because it does not denote one particular, existing predicate. A class of such improper predicates we have already been confronted with are compositional predicates. Thus cordateness and renateness are improper attributes as the terms cordate and renate do not refer to real attributes but to the fact of having component parts as a heart and kidneys. X is cordate if X has a part Y (in a strict or looser sense of having) which has the (proper or improper) attribute of being-a-heart. Another kind of compositional predicate is being-a-grandparent. If X is a grandparent of Z, there is not really a direct relation of 'grandparenthood' between X and Z (altho there may in practise be all kinds of other direct relations between grandparents and their grandchildren). There is a relation of parenthood between X (the fundament) and a living being Y, and also a relation of parenthood between Y (the fundament) and Z. It is these two relations which exist (unless they happen to be no proper predicates themselves), not the single relation of 'grandparenthood'. Especially when attributed to people who are dead, (still-)having-a-great-influence is also a compositional predicate. If X (still) has great influence (even tho 'e is dead), then, for example, X created something Y --'e wrote a book or painted a picture, for instance-- and many people who have come into contact with this creation Y ('er book or painting, or any copy thereof) are (still) very much influenced by it now. The composition of having-a-great-influence or fame, or for that matter infamy, may be much more complex, but it is essential that it can always be reconstructed in such a way that it consists of relations between terms which exist or existed at the same moment or in the same period. Hence, there is nothing mysterious about someone becoming famous or infamous long after 'er death because (this kind of) fame or infamy itself does, strictly speaking, not exist. X is famous or X is infamous is in this case merely an abbreviation for a long conjunction of propositions. Predicates like cordateness, 'grandparenthood' and famousness are conjunctive predicates: propositions in which they are mentioned can be replaced by a conjunction of several propositions in which only proper or more basic predicates are mentioned. Compositional predicates for which this is not possible might be called "sortal predicates". Some people, especially metaphysical essentialists, maintain that species membership is not just a question of having certain attributes and/or relations in combination. They believe that sentences with sortal predicate expressions such as <-- is a human being> cannot be replaced by a conjunction of sentences with several proper predicate expressions in them. Being-human would, then, imply the presence of a certain specific structure of the body called "human". Maybe, a being with predicates or parts A, B and C would be human, but also a being with predicates or parts B, C and D, and one with C, D and E. Solely having predicate or part C would, then, not suffice to be called "human". (We shall neither assume nor deny here that so-called 'sortal predicates' are in fact a kind of conjunctive predicates.) Instead of compositional, an improper predicate may also be disjunctive. If X is p or X has (the attribute) P means X has (the attribute) Q or (the attribute) R, then P is a disjunctive attribute. An example of such an improper attribute is concreteness if concrete means moving or at rest. Being-at-rest or motionlessness is itself a proper predicate but motion is in turn a disjunctive, improper predicate as there is not just one predicate of motion but as many as there are speeds. While we have been willing to accept the existence of abstract entities such as attributes and relations, our realism now turns out to be quite sober, for a great number of attributes and relations for which there are names in everyday language are not proper predicates and will not be regarded by us as existing in reality. These nondeterminative, privative, disjunctive, conjunctive or sortal 'predicates', which do not represent one particular, existing attribute or relation at all, are mere pseudo-entities. 1.7.3 FOR AN EXISTENCE WHICH MAKES SENSE A whole of things exists only if it has one or more proper attributes of its own. On our attributivist construction a set of things which are not attributes never exists (as a thing or whole) because it does not have attributes, let alone proper attributes. And even a set of existing attributes (such as mental properties) which is the predicament of a whole (such as a person) does not exist. Now, some logicians, set-theorists, mathematicians and other theorists are 'infinitely' more realistic than we are. They believe in every set that can be constructed theoretically, and in an abstract world which is at least partially incomprehensible to us 'finite creatures'. Not only would all cardinal numbers one can think of 'exist' but also every other 'real' number. For some of these 'real' numbers there are even no formulas for generating or defining them, which makes them truly incomprehensible. Since there is merely a denumerably infinite number of names and definitions in human language, it is impossible to comprehend every set, given the 'existence' of nondenumerably infinite sets. If this sounds too abstract, another realist infinity creator may take over and talk about physical space as having infinitely many 'concrete points' (whatever that may mean). And if this 'concrete' infinity is not nondenumerable too, there would be at least a nondenumerably infinite number of subsets of these points. 'Thus' even not in the 'concrete' world could every subset of points be defined and comprehended. (This should consequently make us believe that there is necessarily something incomprehensible, and therefore something maximally incomprehensible. The climax of the argument is then reached, when it is 'proved' that a being named "God", and defined as maximally incomprehensible, necessarily 'exists'.) By way of stipulative definition any abstract construction or infinite sequence, or any factual or potential result of a theoretical exercise, may be called "existing" or "concrete", so long as the theory within the bounds of which it is done is free from contradictions or from proved contradictions. The result, however, is merely the greatest possible exhaustion of the notions of existence and concreteness. Underlying this 'infinite' eagerness of set-theoretical realists is basically the idea that coherence (or the absence of incoherence) would be a sufficient (not just a necessary) condition for truth, and that the 'truth' thus generated would also somehow correspond with reality; or, that it would have something to do with existing things. According to the meaning-variance thesis mentioned in section 1.2.1 existence means something else in a system in which incomprehensible, nondenumerably infinite sets 'exist' (and maybe also a maximally incomprehensible, partially abstract, partially concrete devil) than in a system in which only things such as the bodies of living beings and artifacts 'exist'. So the belief that gods or unicorns 'exist' will have a different meaning too in the two systems. The very function of the notion of existence, however, is precisely to provide a theory-independent link between a particular theory and that what the theory is about (nonpropositional reality if the theory is of the first order). Its function is definitely not purely theoretical like that of a criterion of validity or consistence. Furthermore, the meaning of existence is also different from that of concreteness, given the vocabulary of the present language which requires, or at least enables, us to make this distinction. It is for these reasons that we reject both a notion of 'existence' which remains entirely intratheoretical and a notion of 'existence' which is superfluous given the concepts of the 'concrete' and the 'material'. 1.7.4 THE DOMAIN OF A THING We use the word existing in such a way that at least some predicative expressions of the language we communicate in here do designate an 'existing' or 'real' attribute or relation. Hence, attributes and relations, or --to be precise-- proper attributes and relations, do exist. (In other words, there are attributes and relations, namely proper attributes and relations.) Moreover, given the special function of existence, the existence of these predicates is language-independent. It does not matter whether the language we use has a name for the predicate in question or not, and it does not matter whether it has a name for the predicate itself or for the (privative) 'fact' of not having the predicate in question. It is not important either whether the predicate is mentioned in the first or any higher-order domain of discourse: existence per se is existence in the universe, and if mentioned, being mentioned in the universe of discourse. We may only say that a certain thing or predicate which exists, that is, exists in the universe (of discourse) does not exist in a particular domain (of discourse). Unlike existence, thingness is inherently domain-dependent in that there is no thingness per se. For example, a primary relation is no thing in the first or third domain of discourse, whereas it is a thing in the second domain. Of course, one will be tempted to say that a relation is always something, that is, a thing, if it is existing, but this is only because by focusing attention on the relation itself it is automatically located in the second (or a higher-order) domain of discourse, where it is indeed a thing. It is difficult, then, to transcend this secondary (or higher-order) position and to look at the role of primary relations in the first domain of discourse (or of any kind of relation in the domain where it does relate things to each other). Where a relation relates it is nothing, that is, no thing itself. In such a domain there is a relation between things or not, but --again-- this relation itself, altho existing, is not a thing. Only when the relation is derelativized does its existence turn into thingness in the same domain of discourse, but then it has become a kind of attribute. And when we subsequently talk about the attributes and relations of relations themselves, it is also in a derelativized form that they become things in the next higher-order domain. Primary relations are therefore things in the domain of which the basic things are secondary attributes, that is, in the domain where they themselves are related to other things by secondary relations. In the first domain of discourse a nonbasic, primary thing exists, is a thing ('something') and has a thing ('something': at least an attribute and perhaps a component part). A proper, primary attribute in this domain exists, and is also something, but has no thing ('nothing': no part or attribute). A proper, primary (nonderelativized) relation in this domain exists, but is no()thing and has no()thing. A secondary or higher-order predicate does not even exist in this domain, but as existence is language- and discourse-independent, it does exist nevertheless. The concepts of 'existing', 'being a thing' and 'having a thing' are schematically represented in figure I.1.7.4.1 with respect to their employment in the first domain of discourse. In the second domain proper, primary attributes and relations are nonbasic, secondary things which exist, which are something and which have something, namely secondary attributes, and also secondary relations with other secondary things. It is this domain of discourse which bespeaks our special attention now. 2 CATENAS OF ATTRIBUTES AND RELATIONS 2.1 BEYOND FORMAL CONNECTEDNESS 2.1.1 A MATTER OF BEING HEAVY, EQUALLY HEAVY OR LIGHTER Formal logic is the logic of validity in a chosen domain of discourse -- 'the logic of the chosen domain'. The choice of domain itself, and the translation from ordinary language or informal argument to formal symbolism is, strictly speaking, not a subject of formal logic. These are questions of interpretation, of fields of study like ontology and linguistic pragmatics. Yet, from a more general point of view, the 'logic of domain choice', which precedes the logic of the chosen domain, is not less important. This reflection on the choice of formal domain itself should give us more insight into the presuppositions made explicitly or implicitly, and into the relevance or irrelevance of the distinctions drawn thereby. The question of what is relevant or not we have to leave until later; suffice it to say at this place that someone's reasoning may be as valid as it ever can be within the formal logic of a chosen domain, but that this does not finally settle an issue if the scope of the domain itself is selected on the basis of an irrelevant factor. Objects or other things would then be taken in or left out which ought to be excluded or included for a proper argument. (Consider, for example, a utilitarian who proposes that a hedonic balance of good or pleasure over evil or pain should be maximized and who exclusively chooses human beings as the objects whose happiness is to be taken account of.) Some 'discoveries' of those working with formal logical systems depend entirely on the presuppositions made and the foreknowledge at hand before selecting the domain. Without such a priori knowledge, also if merely conventional or linguistic, it would not even have been possible to choose a domain of the kind in question. As an example, let us have a look at a formal analysis of the relations heavier than and as heavy as. The domain is said to consist of material objects only. The conversation is therefore about concrete primary things. Heavier than and as heavy as denote two-place relations and, moreover, are comparative notions. Such concepts enable us to order individuals on the basis of the relation concerned. Let Hxy be the relation heavier than and Exy the relation as heavy as. Hab means, then, a is heavier than b and Eab, a is as heavy as b. Now, to 'conclude' that b is as heavy as a if Eab is true, or that b is less heavy or lighter than a if Hab is true, already requires a certain foreknowledge. Logically speaking, it is first necessary to define E as an equivalence relation, that is, a relation which is symmetrical, reflexive and transitive: 'symmetrical' in that Exy implies Eyx and vice versa (if a is as heavy as b, then b is as heavy as a); 'reflexive' in that for every object x Exx is true (every x is as heavy as itself); and 'transitive' in that Exz is true if Exy and Eyz are true (if a is as heavy as b, and b as heavy as c, then a is as heavy as c). The logical properties of the relation H are that it is transitive as well, that it is irreflexive with respect to E and connected with respect to E: 'irreflexive' with respect to E in that Hxy is not true if Exy is true (if a is as heavy as b, then a is not heavier than b); and 'connected' with respect to E in that always Hxy or Hyx is true if Exy is not true (a is heavier than b, or b is heavier than a, if a is not as heavy as b ). If we take the relation R, heavier than or as heavy as, then there is a strong form of connectedness in that for every x and for every y of the domain concerned, Rxy or Ryx is true. (In a weak sense a relation R is connected over the class C of things if, and only if, whenever x and y belong to C, and are distinct, either Rxy or Ryx is true.) With these formal requirements for E and H it is possible to arrange all individuals to which they apply in a certain order -- a quasi-linear order in which there is exactly one place for every individual, but sometimes with several individuals (which are equally heavy) at one place. But what is the class of individuals to which these formal requirements apply? And what is the foundation of these formal requirements themselves? Have they been miraculously supplied to spiritually nourish the absolutely blank minds of logicians and scientists before they started to think of qualitative, comparative and quantitative notions at all? Of course not: before anyone had ever heard of notions like strong or weak connectedness in their logical sense, expressions like being heavier than, being lighter than, being as heavy as and being as light as were already intimately connected in common parlance. All the comparative notions of the same name are linguistically even unthinkable without the corresponding 'qualitative' (or 'classificatory') notions of heavy and light (even when heaviness and lightness are derelativized relations rather than genuinely nonrelative attributes or qualities). At least from the perspective of language, speaking of "heavy" and "light" precedes all speaking of "heavier than", "lighter than" and "as heavy as". Both the absolute and the relative conceptions apply to the class of all things that are heavy or light or something in between (namely medium heavy or light). Two distinct things of this class are either equally heavy (or light) or not, and if so, then both ways -- otherwise the word equal would simply not be appropriate. If they are not equally heavy, the one is heavier than the other, and the one which is not heavier is lighter than the other as long as the two things have some weight. Formal systems do not establish these trivial truths; they start from them. Now, we are going to choose a domain restricted to material things. What is 'material', however? There are two possibilities to be taken into consideration here: (1) material is defined in terms of weight; or (2) it is defined in other physical terms. In the first instance a material thing is a thing which has a weight. This, in turn, may be defined in an absolute (qualitative) or in a relative (comparative ) way. On the absolute account things which have a weight are light, heavy or something in between, and on the relative account they are things which are lighter than, as heavy as or heavier than other things. It is immediately obvious, when the relative approach is selected, that the connectedness of being heavier than or as heavy as (or lighter than) was presupposed or foreknown in the definition of materialness. The knowledge that the relation obtained by putting together heavier than and as heavy as in one disjunctive predicate (expression) would be connected over the class of material things and not over any class comprising immaterial things was a prerequisite to the very division between material and immaterial things itself. Weight is not a relative notion. Just as length must be read as longness rather than long-er-ness, so weight must be read as heaviness rather than heavi-er-ness. But also on the absolute interpretation one must have foreknowledge of the connectedness as somewhere in between cannot literally be read as neither light nor heavy, since immaterial things, too, are neither light nor heavy. Neither light nor heavy is to refer to the borderline, or rather the fuzzy zone, between the 'light' and the 'heavy', that is, to the 'medium light' or the 'medium heavy'. Yet, strictly speaking, this may imply the connectedness of the qualities or attributes but not the connectedness of a relation in the logical sense. Somehow it must also be given a priori that everything between light and heavy is heavier than light and lighter than heavy. Granted that things are as heavy as themselves or as other things belonging to the same set of the three qualitative sets distinguished, we have the same conditions as on the relative interpretation (assuming, again, that we allow ourselves to construct the disjunctive relation which is connected by now). Instead of in terms of weight, material may be defined as having a speed, as being at rest or moving (in a positive or negative direction) or in other spatiotemporal or physical terms. The crucial assumption is now that everything that is material in this sense (that is at rest or moves, for instance) is an object which is heavier than, as heavy as or lighter than other material things. It is implicitly taken for granted, then, that there could be no material object which is heavier than another one without there being any other material object being lighter than at least one other material object. Hence, also in this case the connectedness of the relation heavier than or as heavy as (or lighter than) over the class of all, and only, material objects is presupposed or part of our foreknowledge. Any 'discovery' of this formal connectedness in such a domain of material objects begs the question. (This is not to play down the issue of whether and why the class of all things that are heavier, as heavy as or lighter than one another is identical to the class of things that are, for example, at rest or in motion.) There is another, perhaps more serious, objection to overrating a formal, logical property such as connectedness and that is that it may be a necessary condition but that it is not a sufficient condition to express the typical 'connection' between notions like heavier than and as heavy as. Imagine a domain or a world in which all objects that are arranged in a quasi-linear order from 'light' to 'heavy' are arranged in a parallel order from 'fast' to 'slow': every object that is lighter happens to be faster (and necessarily faster if also dealing with modal conditions) and every object that is heavier happens to be slower (and necessarily slower). Our actual world is not like this, but one may think of other attributes or relations thus correlated. (The example is similar to that of all cordate beings that are renate, and vice versa, with the impossibility of identifying predicates on the basis of their extension alone, whether they are proper or improper.) On our assumption not only heavier than or as heavy as is connected over the domain in question but also heavier than or as slow as and faster than or as light as. Altho people are free to fabricate any fancy, disjunctive, or other, predicate expression they wish in formal logic, this certainly has no bearing on reality. If the (logically) informal language we communicate in is to mean anything, the concepts heavier than and lighter than are related to the concept as heavy as in a way they are not related to any other concept (whether it be as slow as or something else). The formal, logical requirements for H and E do not suffice: there must also be a special relationship between these relations which connects them in a way in which they are not or cannot be connected to any other relation. But the moment we recognize such a relationship (like that between heavier than and as heavy as) we do not need to emphasize the other requirements for our purposes anymore. 2.1.2 THE CONCATENATE PREDICATES OF A CATENA If a material thing is bound to be light, medium heavy (or 'medium light') or heavy, it is bound to have one of the properties of a certain set of properties which are inseparably connected with each other. And if it is bound to be lighter than, as heavy as or heavier than another material thing, it is bound to have one of the relations of a certain set of relations which are inseparably connected with each other. The set of properties is not a primary, simplex thing, for an object cannot be light (have the property of lightness) and medium heavy or heavy (have the property of heaviness) at the same time: it is the extensionality of a secondary thing. The properties in the first set are therefore to be conceived of as secondary things themselves, that is, as simplex things in the second domain of discourse. The relations in the second set can only be things in the second domain of discourse, but also the set of these relations is a mere extensionality belonging to a complex, secondary thing. Neither the set of connected properties nor the set of connected relations is purely conceptual, because then we would be faced again with the 'logical' predicament in which heavier than could turn out to be formally combined not only with as heavy as but also with as slow as or some other equivalence relation. The 'intensionally' connected series of lighter than, as heavy as and heavier than must distinguish itself from a mere set (such as that of heavier than and as slow as), because it is an existing whole with its own secondary predicates. The relationships between its constituent parts are now not merely conceptual or accidental any more: the primary predicates which constitute one and the same whole in the second domain of discourse are linked together or 'concatenate'. The connected series of related primary predicates itself we shall call "a catena", "a catena of attributes or relations". A predicate catena comprises all the, and only those, primary predicates that are inseparably linked together. Hence, the relations heavier than and as slow as do not constitute a catena, because talk of both relations presupposes the existence of other catenas before we can even speak of "heavier than" and "as slow as". But the relations heavier than and as heavy as do not constitute a catena either, since the relation lighter than is needed to complete its extensionality. (As light as may mean the same as as heavy as, lighter than certainly does not mean the same as heavier than.) The attributes light and heavy do not make up a catena, because they are inseparably connected with an attribute lying between lightness and heaviness: neither light nor heavy (but having a weight nevertheless) (if thinking of a borderline) or medium heavy (if thinking of a transitional zone). The terms light and heavy are so-called 'vague' predicate expressions in that it is not always evident when light becomes heavy, or conversely. It is therefore better to first illustrate the new concept of the catena by means of some other, clearer examples. The predicates of electropositivity, electroneutrality and electronegativity cannot exist without each other and make up the extensionality of --what we shall name after its positivity-- the 'electropositivity catena' (of which secondary predicates form the attributive predicament). The attributes of happiness, of the state of indifference between happiness and unhappiness and of unhappiness form extensionally the happiness catena. Increase, decrease and the concatenate neither increasing nor decreasing are together the component parts of an increase catena. (There is not one increase catena but there are many of them.) Rest, or being-at-rest, is itself a borderline predicate between motion in positive and motion in negative direction, and therefore rest and motion together constitute a motion catena without any third predicate or set of predicates. Just as increase catena is the common denominator of all increase catenas, so motion is the common denominator of all positive or negative velocities or degrees of motion, happiness the common denominator of all degrees of happiness; and so are unhappiness, electropositivity, and so on. What is special about heavier than and as heavy as is that they belong to the same catena of relations (together with lighter than). There is a real relationship of having between this one catena and the relation heavier than and also between this catena and the relation as heavy as. The so-called 'relationship' of catenation, that is, of belonging-to-the-same-catena, between heavier than and as heavy as themselves is therefore not ontic. Nevertheless it refers to the existence of a real, but abstract, whole with real, but abstract, components. What deserves our attention in particular is that this conceptual relation of catenation between primary relations is not at all different from the one between attributes as heaviness and lightness or, for that matter, happiness and unhappiness. It would therefore be a rather fragmentary approach to recognize a formal property like connectedness (our 'concatenatedness') only with regard to relations and not with regard to attributes, especially when the existence or recognition of the 'qualitative' attribute catena precedes or is presupposed by the existence or recognition of the comparative relation catena. 2.1.3 THE CATENA AND ITS PREDICATES AS SECONDARY THINGS Let us agree that material things must have one of the predicates of the motion catena, that is, that they must either be at rest or in motion, either in some (quasi-)absolute sense, or with respect to a certain frame of reference. Consequently they can have a negative velocity, a positive velocity, or a neutral one called "rest". But the predicate of positive velocity itself does not have a positive velocity because a set cannot be identical to one of its elements. As a matter of fact, it does not have any of the predicates of the motion catena, because a primary predicate cannot have a primary predicate as an element. Nevertheless, as a simplex, primary thing a primary predicate like positive velocity has attributes and relations of its own: it is positive, for instance. This is an attribute it has in common with other positive predicates such as electropositivity, happiness and increase. The secondary attribute of positivity itself, however, cannot be predicated to objects, or even not to immaterial or abstract, primary things. It can only be predicated of primary attributes and relations in the second domain of discourse. As secondary attributes positivity, neutrality and negativity do not constitute a catena, because the component parts of a catena are primary predicates like heaviness and happiness. Even as secondary attributes they are not (the intensional) whole-attributes of any catena either, for the catena itself is as a whole not positive, neutral or negative. At the most it might be said that positivity, neutrality and negativity are its part-attributes, or that they are the common denominators of all positive, neutral and negative predicates of the catena as common denominator of all catenas. What belongs to the predicaments of catenas is in the first place their relations with other catenas, like that between the heaviness catena and the catena of heavier than, as heavy as and lighter than. In general this relation is a relation between a catena and another complex, secondary thing. But also a relation with a simplex, secondary thing, or a secondary attribute, may be conceived of. The abstract world of catenas and related things in the second domain of discourse is structurally an exact copy of a concrete or abstract world of first- and higher-type things in the first domain of discourse. This parallelism is depicted in figure I.2.1.3.1. The attribute- or relation-catena is shown here to have three component parts. As we will see, this is the minimum number of parts it must have. To be a catena, a third-type, second-order thing must have at least one negative, one neutral and one positive attribute or relation. 2.2 CATENATED AND CATENARY PREDICATES 2.2.1 CATENATED AND NONCATENATED, PRIMARY PREDICATES The universe does not only 'contain' --if we may use this word-- objects, not only primary things and primary attributes and relations, but also more complex systems of nonprimary predicates. One of the latter systems is the catena, a whole of (con)catenated positive, neutral and negative predicates. Whereas attributes and relations are purely intensional, with no component parts, the universe is in a sense a pure extensionality recognized in ordinary language as a 'thing', but without any proper predicates which can be ascribed to it. Nevertheless, all things consist directly or indirectly of attributes on our ontological construction, and thus the universe comprises a theoretically unlimited number of parallel attributive systems, and therefore contains ultimately solely attributes itself (since also relations are, as things, sets of attributes). After having distinguished the different domains to which things belong, and the kinds of attributes which are the base-elements in those domains (primary, secondary, and so on), it is high time now to see how primary attributes (and relations) can be categorized. A systematic study of these atoms of the first domain of discourse, to which we belong ourselves as bodies and as persons, will at the same time tell us more about the character of their own, secondary attributes and relations. The first distinction to be made, then, is between primary predicates, looked upon as things in the second domain, which are and which are not part of a catena. The former predicates will be termed "catenated", the latter ones "noncatenated predicates". The following list is an example of predicates which are catenated, at least in a sense: electro-positivity electro-negativity directed towards directed away from happiness unhappiness more less elasticity inelasticity honoring dishonoring betterment worsening lightness heaviness acid basic thinness thickness hatred love shortness longness concavity convexity weakness strongness early late cheapness expensiveness goodness badness quickness slowness rest motion normality abnormality continuation change balanced unbalanced symmetry asymmetry harmonious unharmonious even uneven uncharged charged equality inequality centrality excentricity indifference difference For each pair of attributes or relations on this list, the left-hand predicate and the right-hand one are 'chained', catenated or inseparably linked together. (It is no coincidence that the original meaning of catena is chain.) Every extensional element of a catena exists because of the existence of the other constituents. No positive predicate can exist without the concatenate negative predicate, nor without the concatenate neutral predicate. For example, no love can exist where there is no hatred, no equality where there is no inequality, and conversely. Quite a few ideologues and others have said this before, while particularly emphasizing that no good or goodness can exist where there is no evil or badness. What they thus have often deluded people into believing is that there must somehow always be bad things (people, for instance) where there are good things. This, however, is existential rubbish. Badness is no 'bad thing' in the sense of an object, person or abstract thing which has the attribute of being-bad, nor is goodness a 'good thing' in an analogous sense. Badness is a primary attribute, that is, a simplex, secondary entity, whereas a thing which is bad is a primary (nonpredicative) entity. Hence badness would even exist (in the second domain) if nothing in the world (in the first domain) were bad, and even if nothing 'could' be bad. 2.2.2 THE TRIPARTITE STRUCTURE OF THE CATENA The concept of an attribute- or relation-catena looks very much like that of a dimension, scale, spectrum or factor. Yet, while there is much conformity, there are sound reasons to use the term catena where the concept of dimension, or a similar concept, would not be clear enough. One reason, of course, is that the catena is a thing, albeit abstract, with its own office in our ontological edifice: it is not a set of values, or something of that ilk, which would further force us to accept the existence of sets and of values. Another reason is that a number of different catenas may have the same dimension. And a third reason is that the components of a catena cannot only be ordered linearly but that they belong, and must belong, to one of three typical classes by definition. What are the characteristic classes or subsets making up the extensionality of a catena? Let us have a look: to the catena of electropositivity and -negativity also belongs electroneutrality; to that of happiness and unhappiness also being neither happy nor unhappy (but sentient nevertheless); to that of more and less also equally; to that of betterment and worsening also the continuation of the same goodness, badness or state of being-neutrally-indifferent; to that of acid and basic also neutral (in the sense of neutrally neither acid nor basic) ; to that of cold and heat also the normal or moderate temperature (being neither (too) cold nor (too) hot); to that of weakness and strongness also being neither weak nor strong (but something in between) ; and so on. As to rest and motion, we can subdivide motion into motion in positive and in negative direction (for each dimension concerned); as to continuation and change, change can be divided into decrease and increase; as to indifference and difference or not being indifferent, the latter one is positive (more or, for example, goodness, happiness or a liking for something) or negative (less or, for example, badness, unhappiness or a dislike of something); as to normality and abnormality, abnormality is positive or negative (for the factor concerned, if normal is taken in a statistical, or similar, sense); as to being-balanced and -unbalanced, the latter is a question of too large an amount or too small an amount; and so on and so forth. Electropositivity and -negativity, acidness and being-basic, happiness and unhappiness admit of degrees. Similarly, there are different intensities of weakness and strongness or strength, of the positive and negative forms of not being indifferent or difference, of friendliness and unfriendliness; and so on. There are therefore more than one, maybe many, electropositivity- and -negativity-predicates, happiness- and unhappiness-predicates, weakness- and strength-predicates, difference predicates, and so on and so forth. For each degree, for each intensity, there is a distinct (secondary) attribute, and a proper primary predicate can have only one of those attributes at a time. Heaviness, for instance, may denote each heaviness attribute separately if thought of as a proper attribute; it may also refer to all heaviness attributes together -- be their common denominator as it were. It is each heaviness attribute separately, however, which is an extensional element of the heaviness catena, not the set or totality of all heaviness attributes. The conceptual set of all heaviness attributes is a subset of the catena; and it is a 'positive' subset in that all its members have the secondary attribute of positivity, not in that it has this attribute itself (as it simply is not a thing with attributes as intensional elements). It follows that also neutral attributes like electroneutrality, the neutrality of the acidness catena or neither heavy nor light (but having a weight nevertheless) are elements of the catena themselves, and not their singleton, or some whole of which they would be the sole component part. Now it is evident that no fewer than three sorts of catenated attributes or relations belong to each catena, namely one or more positive predicates, one neutral predicate (with the catena value 0) and one or more negative predicates. Altho the number of extensional catena elements is not fixed, the extensionality of the catena has always three subsets (which are conceptual constructs however): (1) the subset of positive predicates, (2) the singleton of the neutral predicate, and (3) the subset of negative predicates. The predicate with the catena value 0 we shall call "a limit element" because it is a limit between the positive predicates on the one hand and the negative ones on the other. (We will see later that it is not necessarily the physical, chemical or other quantity which is 0 in the case of neutrality.) In a way neutrality is a limiting case of both positivity and negativity, the point where positivity and negativity could be said to overlap or meet. On the basis of its tripartite structure we shall define the catena as "a whole of catenated primary predicates of which the extensionality can be divided into three subsets so that the only element of one of these subsets is the limit element between the mutually opposite elements of the other two subsets". (Note that the requirement is that the extensionality can be divided in this way. In theory and in practise it may be divided in one or more other ways as well.) The neutrality of a catena must be a limit element between the subset of positivities and that of negativities. Electroneutrality, for instance, may be neutral and a limit element, it is not a limit element between happiness and unhappiness, and therefore happiness, electroneutrality and unhappiness do not constitute a catena. Similarly, altho electropositivity is a positive predicate and unhappiness -- let us assume -- a negative one, they still do not have a common, neutral limit element. So they are not each other's opposite and do not belong to the same catena: they are both catenated but not concatenated. Sets of extensional elements of one catena are closely related to sets of numbers. There is a one-to-one correspondence between catenated elements and the numbers associated with the degree of actualization. When we speak of "opposite predicates", however, we use the term opposite in a broader sense than a mathematician speaking about numbers might do. A mathematician may solely speak of "oppositeness" when the absolute values are equal. Only -1 would thus be opposite to +1, and not -2 or any other negative number. In the theory of catenas this conception would be too narrow for then happiness and unhappiness, for instance, could only be called "opposites of each other" if the respective intensities or degrees of actualization happened to be equal. But happiness and unhappiness are opposites regardless of the degrees involved; and so are love and hate, increase and decrease, highness and lowness, and so on. (Also etymologically it is justifiable to use opposite in this general way.) In accordance with this we shall call all those (catena) values "opposites" which differ in (plus or minus) sign. Hence, all negative numbers are 'opposite' to +1, and all positive numbers are 'opposite' to -0.5 or any other negative number. While referring to the corresponding set of degrees of actualization (interpreted as numbers) we may now say that a predicate is an opposite of or opposite to another predicate, (1) if its degree of actualization is opposite to that of the other predicate, and (2) if they belong to two subsets with a common, neutral limit element, or if they are elements of the same catena (the catena itself having already been established). And just as we may, loosely, call the subset of concatenate predicates itself "positive" or "negative", so we may call these subsets "opposites" as well, altho strictly speaking, it is only the predicative elements which are opposites. Thus deceleration, for instance, is the opposite of acceleration and a deceleration of -1 m/sec2 is opposite to all acceleration predicates. If the deceleration is -1m/sec2, this is its degree of actualization: negative in the case of deceleration, positive in the case of acceleration. The common limit predicate catenated to both deceleration (all deceleration predicates) and acceleration (all acceleration predicates) is the continuation of the same velocity. Since a proper predicate corresponds to one degree of actualization only, an object with an acceleration of +1m/sec2 has nothing in common with an object with an acceleration of +2m/sec2 (as far as this aspect is concerned). Only if they both have exactly the same acceleration (positive, 0 or negative), do they have a predicate of the acceleration catena in common. What is meant by saying that two objects 'have their (positive) acceleration in common' is that they both have a predicate belonging to the positive subset of the acceleration catena. It is, then, not the objects but their predicates which have something in common, namely the secondary predicate of positivity. Expressions like deceleration, weak and irrelevant are called "marked terms" because they are employed in only one, restricted sense, whereas the corresponding (but not necessarily opposite) 'unmarked terms' (acceleration, strong, relevant and the like) have both a specific meaning and a general meaning relating to the whole dimension in question. In terms of the catena (where applicable) marked terms refer to a proper subset of its extensionality (in the simplest case the negative subset) and unmarked terms either to a proper subset (for example, the opposite, positive subset) or the improper subset of the total extensionality itself. Thus in what is its acceleration? acceleration may either be positive and the opposite of deceleration or it may mean acceleration catena predicate whether the predicate is positive, neutral or negative. Sometimes there is a marked term in addition to the unmarked one to refer to positive predicates. For example, longness and strongness can only refer to the opposites of shortness and weakness. But length and strength are unmarked and even things which are short and weak have a length and a strength, just as things which are light have a weight. To have a length, then, means to have one of the predicates of the length catena. Length in this sense does not denote a catenated predicate, but stands for the total spectrum ranging from extreme shortness to extreme longness. The occurrence of ambiguous, unmarked terms is one of the deficiencies of the ordinary variant of the present and many other languages. Usually one has to put up with a term which may denote either the positivities or other predicates of a catena as opposed to its negativities or other concatenated predicate(s), or the extensional predicates of the catena in contradistinction to those of all other catenas. 2.2.3 SUBDIVISIONS OF THE CATENA'S EXTENSIONALITY In the theory of catenas attributes and relations are characterized on the basis of their position in, or with respect to, a catena or system of catenas. We shall say that this theory and any other body of thought which rests on its conceptual framework is of a 'catenical' nature. It is not just the reference to catenated predicates and other predicates related to the concept of the catena which is typical of catenical thought --thought is practically unthinkable without reference to such predicates-- but also the recognition of those predicates as belonging or related to one or more predicate catenas. We shall draw a distinction between a predicate's being 'catenated' and its being 'catenary'. A catenated predicate is a predicate of a catena as extensional element, that is, a component proper part of a catena. A catenary predicate, on the other hand, is a predicate of a catena as intensional element or a predicate which the catena, or one of its parts, solely has as a catena, or as a part of a catena. The meaning of this catenary is being or pertaining to a catena. So the catena itself is a catenary thing (and not a catenated thing). And if two predicates are opposed or otherwise catenated to each other, there is a catenary relation of oppositeness or catenatedness between them. The neutralness (or 'neutrality') of neutral, catenated predicates is a catenary attribute because they can only be neutral (in the catenical sense) as part of a catena. Catenated predicates are first-order, and catenary predicates such as oppositeness and neutralness second-order predicates. Like all predicates they may be proper or improper. Given a certain collection of attributes or relations which is the extensionality of a catena, there are theoretically countless ways of subdividing such a collection. (There are already four possibilities if there is merely one negative and merely one positive predicate besides the neutral one.) In practise however --that is, in ordinary language-- only a limited number of types of subdivisions are found and do make sense. The first subset to be distinguished, then, is the singleton which solely contains the extensional catena element with the catenical value 0 as degree of actualization between negative values on the one hand and positive ones on the other. This neutral predicate on the line we have termed "a neutrality" (but not "a neutralness"). In the first instance tho, neutrality is a catenary, secondary attribute (and with this meaning of neutralness an expression like the neutrality of the catena has no reference). Yet, by also calling a neutral thing "a neutrality" we make use of a feature of the present language in which things which have a certain predicate often acquire the name of this predicate itself, preceded by the definite or indefinite article. For example, 'a special(i)ty' is something special, 'a beauty' is something or somebody beautiful, 'an abrasion' is something which has been abraded. (Compare also fellowship, community, externality or other multiplicities of meaning.) In a loose, metonymical sense the singleton of the neutral catena predicate may be said to be 'neutral' too, and to be 'a neutrality' (altho the set itself does not even exist). All the other predicates, and catena subsets of predicates which are not neutral, we shall term "unneutral" or "polar", and "unneutralities" or "polarities". Noncatenated predicates are neither neutral nor unneutral, but nonneutral and non-unneutral. Even a catenary predicate such as neutrality itself is, strictly speaking, both nonneutral and non-unneutral. (Un- negates the meaning of the base word within the next higher framework which is that of the catena in the case of neutrality; non- negates in general, subject to no restriction.) A catena element or subset corresponding to positive catena values only, or to negative catena values only, will be termed "monopolar", or "a monopolarity". In the former case it is a positivity, in the latter case a negativity. Catenically, positivity has nothing to do with certainty, actuality, affirmation or agreeableness, and negativity nothing with negatoriness or disagreeableness (at least not on the basis of its being positive rather than negative, or its being negative rather than positive). It is of paramount importance here to guard against traditional misassociations: the catenical definitions of positive and negative are based on mathematical and similar usage, and a positive number is not certain or uncertain at all, nor affirmative, while a negative number is not negatory at all. Negative is as much nonpositive as positive is nonnegative and we can be as sure that something is negative as we can be that something else is positive, or neutral for that matter. The neutrality of a catena is the limit element closed in by the catena's positivity on one side and by the catena's negativity on the other. In general however, any predicate or predicative subset 'limits' another catenated subset, if it corresponds to only one value, and if this value is one of the two values (theoretically among them possibly +INFIN and -INFIN) between which the values of the subset limited by it lie (assuming that all interjacent catena values belong to the value set of the predicative subset). Thus, altho the neutrality (subset) is a limiting unit, for it limits the positivity (subset) and the negativity (subset), this does not mean that, conversely, a limit predicate or subset must be neutral too. On the contrary: extremities (which are extremely unneutral) also limit positivities and negativities but then at the other end of the scale. A predicative subset is 'limited by' another one, if the latter limits the former. The positivity and the negativity of a catena are both limited by the catenated neutrality, that is, the neutral predicate of the same catena. The duad of positive, complete monopolarity and negative, complete monopolarity may be said to be limited by the neutrality as well, if we only look at the corresponding absolute values. This duad we shall call "the complete bipolarity" of the catena. Both monopolarities and bipolarities, whether complete or not, are unneutralities for they do not have the value 0 in the corresponding set of catena values. Complete bipolarity is unneutrality, and also bipolarity, in the broadest sense. (Complete is used here in the sense of comprising all extensional catena elements with the same, proper or improper, catenary predicate.) A neutrality and a complete bipolarity which is catenated to it (and thus limited by it) are the catena supplement of each other. Two catena (extensionality) subsets are the catena (extensionality) supplement of each other, if the union of both subsets is a catena extensionality. Two catena subsets which are opposites of each other cannot be catena supplements of each other (as they do not include the neutrality), and two catena subsets which are supplements of each other cannot be opposites of each other (as the neutrality which is one of them is not opposed to the predicates of the other.) Electropositivity and electronegativity, acid and basic, intelligence and unintelligence are opposites and not catena supplements of each other. On the other hand, rest and motion, equality and difference, normality and abnormality (in a statistical or similar sense) are supplements and not opposites of each other. The traditional confusion of the distinction between opposition and supplementation --and several other types of relations between primary predicates and things-- is closely related to the disregard for the neutrality and for the total catenary structure it belongs to. All proper, catenated predicates are 'atomic' in that they correspond to only one value or degree of actualization, and in that they are thus an atom in the primary world. To 'have a certain proper, catenated predicate' is to have it in the most literal sense. When we speak about "the positivity" and "the negativity" of a catena, however, we refer to subsets of usually several positive and several negative predicates and their corresponding, positive and negative values. This is why the positivity and negativity are improper predicates of the catena (unless there happens to be only one positive and only one negative degree of actualization). To have the/a positivity or negativity of a catena is an abbreviation for saying that the primary thing in question has one of the proper, catenated predicates which belong to the positive or negative subset of this catena. (Note that to be happy, for instance, means to have the/a positivity of the happiness catena and is an abbreviation or 'generalization' of the same kind.) Neutralities are always atomic and proper but unneutralities may be either proper or improper predicates. Improper unneutralities can be subdivided into bipolarities and improper monopolarities (either complete or noncomplete), dependent on whether they are both positive and negative, or only positive or negative. The sole catenated, proper nonpolarity is the neutrality; the most important kind of catenated, improper nonpolarity is the so-called 'perineutrality'. This is a predicate of which the catenical value collection contains only low positive values, the catena value 0 and high negative values (close to 0). To express perineutrality, that is, 'moderateness' or 'moderation', people often employ the terms medium or middling, sometimes without even mentioning the positivity of the catena (as in large, medium or small and it's middling). Medium large, of middling height and moderately expensive are all perineutral, improper nonpolarities. (In agreement with the use of positive, neutral and so on, we shall use the term perineutral for the predicate itself and not for the persons or other primary things which have this predicate.) The reference to perineutralness rather than to neutralness is typical of catenas of so-called 'vague' predicates, that is, catenas for which it is not immediately clear which predicate is the neutral one (while the collection of physical or other noncatenical values one deals with in the first place also contains only nonnegative values, with or without 0 as an extreme noncatenical value). In everyday language many more kinds of catenical concepts are found besides the perineutral moderate(ness) and the more simple ones. Every gradation in the language with respect to an (improper) catenated, primary predicate concerns a subdivision of a catena extensionality. So the concept very intelligent, for instance, is the concept of a special kind of noncomplete, improper monopolarity (corresponding to high positive catena values). The attribute (or derelativized relation) being-the-most-intelligent is a special kind of atomic polarity, namely an 'extremity'. Predicates like moving fast and a little asymmetrical are noncomplete bipolarities. The connected series of predicates or predicative subsets which are extremely positive, quite positive, positively perineutral, neutral, negatively perineutral, quite negative, very negative and extremely negative could be presented as a prototype of the predicate catena as much as the trinity of (complete) positivity, neutrality and (complete) negativity. Some typical subdivisions of the catenary extensionality are shown in figure I.2.2.3.1. 2.3 OTHER PREDICATES FROM A CATENICAL PERSPECTIVE 2.3.1 NONDETERMINATIVE PREDICATES When our knowledge about a particular thing is extended by a new attribute or relation of which we are sure that the thing concerned has it, this normally is a further determination of its nature for us. The class of predicates for which this does not hold is that of 'nondeterminative predicates'. Take, for example, being a thing (or being-a-thing). This is an 'attribute' every thing in the domain of discourse has. Being part of the universe cannot even be an attribute and is also conceptually nondeterminative. Being classifiable and collectable (in a set-theoretical sense) are of the same type. Being itself (regardless of domain) or being a thing (in a particular domain) is the common denominator for all nondeterminative 'attributes' of this kind. Strictly speaking, there is only one 'attribute' of being or existence: existentiality. This is what all (existing) beings (which are things in some domain) have in common. (As existence is something all beings have in common --predicative or nonpredicative, primary, secondary or whatever-- it is nonsensical to suggest that existence or existentiality would be a first-order predicate or that it would be of any other, definite order. Typical of existence is precisely that it is of no particular, predicative order.) A thing must always have 'the attribute of existence' if such a universal pseudo-attribute is conceptually recognized. It is something else, however, whether the idea or concept of a thing denotes something in reality and whether a conceptual combination of predicates, or predicates and parts, is a real thing (rather than a mere set collected by its creator). The thing one has in mind may, then, be an object or other nonbasic thing, it may also be a predicate. Imaginary things (such as gods, demons and other supernatural 'beings') are but too often saddled not only with impossible combinations of predicates but also with impossible predicates. Attributes and relations which are predicated of a thing while thinking about it, and which the thing would not have if it were not conceived of, or had not been conceived of, are a mere result of a person's own reflections on the thing in question. The name we shall use for this type of nondeterminative predicate is reflectional predicate. Reflectional predicates are not determining for the things considered but for the considerations, thoughts or reflections themselves. Being thought of is a reflectional predicate, and so is being denoted by an atomic expression in the language. (Other examples have already been mentioned in 1.7.2.) Whereas, theoretically, universal attributes such as the attribute of existence belong to all (real) beings, members of the subclass of reflectional predicates belong only to a certain category of things. Thus being-collectable may be a universal attribute, being-collected (in a general, set-theoretical sense) is a reflectional predicate. And when collecting is used in a concrete, everyday sense being-collected is even a determinative primary predicate (or rather pseudo-predicate, as we will see). To decide whether or not 'two' things are identical, one cannot look at their universal attributes, because those attributes are precisely what they are supposed to have in common as beings or as things in the domain in question. And, altho one could, one must not take their reflectional predicates into account either when discussing the possible identity of 'two' things. Even to be able to pose the very question itself one must have given the 'two' things different names or descriptions to start with. But 'having-the-name-a' or 'having-the-name-b' is a reflectional attribute which is not determinative for the thing, nor is 'being-written-' or 'having-one's-name-written-on-the-left-hand-side' and 'being-written-on-the-right-hand-side' with respect to, say, a sign of equality (a = b). It is but too easy to confuse distinctions in one's own reflections on reality with distinctions, or rather the lack thereof, in reality itself. Of course, distinctions in our thought are also distinctions in reality. But then, they are distinctions in a sort of propositional reality, not in the reality the thought is about. Like universal predicates, reflectional predicates do not belong to any predicative order either. They cannot be classified as first-order (being only the predicate of something that is not a predicate itself), second-order (being only the predicate of a first-order predicate) or higher-order, because they simply are not real predicates of the thing conceived of. In reality they stand for a predicate of the thinker 'imself, or of 'er thought, and as such they are of the first predicative order but not as a reflectional attribute or relation of the thing thought about. Whereas universal and reflectional predicates belong to the category of nondeterminative predicates, it is the category of determinative predicates in which we find the primary, secondary and higher-order predicates we have already been acquainted with. 2.3.2 CATENALITY AND NONCATENALITY Each catena is a totality of all atomic positivities, one atomic neutrality and all atomic negativities which are inseparably linked together. Having a positive predicate of catena C is the complete positivity of catena C, having a negative predicate of catena C the complete negativity of that catena. Loosely, we call having a positive or negative predicate "predicates" too. They are, then, improper predicates. Altho improper, we classify them as catenated predicates with the atomic, proper predicates to which they refer. Typical, improper, catenated predicates we have thus distinguished are, besides monopolarity (positivity or negativity), moderateness and bipolarity. Now, there is also a limiting case we have not yet discussed. It is the predicate having a predicate of catena C, not just a monopolar, perineutral or bipolar one. The catena 'subset' corresponding to this predicate is the improper 'subset' of the extensionality of the catena concerned, that is, the entire extensionality itself. A primary thing which has a predicate of a catena is a 'catenal', and the predicate of having-a-predicate-of-a-catena is 'catenality'. (These semi-neologisms are introduced here because of the importance of the distinction between catenality and noncatenality, and --as we will see-- also between noncatenality and neutrality.) If not further qualified, catenality is a derelativized relation since a primary thing may be catenal with respect to one catena or system of catenas and not catenal with respect to another catena or system of catenas. When catenality is interpreted in its most general sense, that is, with respect to any catena, it is questionable whether there is any primary thing that is not catenal. At least all objects are catenal. Catenality is not what all positively catenal (for example, happy), neutrally catenal and negatively catenal (unhappy) persons, objects or things have in common (and what they do not have in common with other things). So far as this aspect is concerned, positively, neutrally and negatively catenal things have nothing factual in common. They may have the possibility of being positively, neutrally or negatively catenal in common but that is a mode, not a fact. Catenality is not what all positivities, the neutrality and all negativities have in common either, because what they may have in common are secondary predicates, and as a predicate of primary things catenality is a primary predicate (albeit improper and, strictly speaking, not existing on our construction). The differences between catenality, noncatenality and neutrality or neutral catenality can easily be demonstrated by means of the motion- and happiness-catenals. 'Motion catenality' is having a predicate of the motion catena, that is, having the predicate of being-in-motion or of being-at-rest. It is concrete things which have such predicates. Since abstract things are neither in motion nor at rest (certainly not the predicates of the motion catena themselves), they are noncatenal with respect to the motion catena. 'Happiness catenality' is having a predicate of the happiness catena. It is sentient beings which have such a predicate. Noncatenal with respect to the happiness catena are insentient, concrete beings like stones, plants and artifacts, and all abstract entities. They are not happy, not neutrally neither happy nor unhappy, and not unhappy; they are noncatenally neither happy nor unhappy. (The question of which beings are exactly happiness-catenal, and when, is a scientific one, and the answer to this question need not concern us here.) Neutrality with respect to the motion catena, or motion-catenated neutrality, is being-at-rest. This is something entirely different from being-abstract, that is, being noncatenal with respect to the motion catena. A thing which is at rest is not less 'concrete' (in the sense of motion-catenal) than a thing which moves. Happiness-catenated neutrality is the predicate a sentient being has when it is responsive to (real or imaginary, oneiric or nononeiric) impressions, and when it is neither (made) happy nor (made) unhappy. This state of being is wholly different, again, from that of a being (even if an object) which is not responsive to impressions at all and which cannot even be brought into a certain happiness-catenary state (at least not at the moment concerned). So when people say "neither happy nor unhappy", they may refer to two basically different states of being. Not happy could even refer to one of three different conditions: (1) unhappy, the opposite of being-happy; (2) unhappy or neutrally neither happy nor unhappy, the catena supplement of being-happy; or (3) insentient, that is, noncatenality with respect to the happiness catena. While catenality is a limiting case of an improper, catenated predicate, it does not seem appropriate to classify it as a catenated predicate itself, simply because there is no extensional catena element left to which it is catenated. Conceptually it may be inseparably connected to noncatenality but that is not a catena element either. (Noncatenality would even be a privative pseudo-predicate, if catenality had been a proper predicate.) Moreover, every predicate is 'linked' to its negation denoted by non-, of whatever order or type. We have now distinguished three catenical, main categories of predicates: (1) catenated (primary) predicates; (2) catenary (secondary) predicates; and (3) two (sorts of) noncatenated, primary predicates, namely catenality and noncatenality. As primary things can only have primary determinative attributes, and secondary things only secondary determinative attributes, the different catenical concepts and the corresponding terms should not be mixed up. Thus primary predicates (concepts, numbers or secondary things) may be positive as secondary things, but objects and other primary things can only be positively catenal. (If they are called "positive", "neutral" or "negative" nevertheless, these words may be used in a different sense, often in a sense specifically related to one or a few catenas only.) Objects may be good, bad or something else, but goodness itself is absolutely not good (or bad) -- it might be goodness-predicative and goodness-catenary (or badness-catenary), that is, part of a goodness- (or badness-)catena. Only objects or other nonbasic, primary things are catenal (for example, happiness-catenal) -- other things can only be catenary (for example, happiness-catenary). And everything that is catenary is always noncatenal. 2.3.3 CATENICAL ASPECTS Negation itself is not a typically catenical concept, but the concepts of catenality and noncatenality and the negatory relationship between them certainly are. Negation is a secondary relation but unlike limitation, opposition and supplementation (in the catenical sense) it is not catenary. In a way, however, all these catenical, secondary relations are more or less negations. Limitation is, then, negation on the borderline or fringe of the framework of the predicate negated itself; opposition is negation within the framework of the complete bipolarity (of which the predicate negated is only a monopolar part); catena supplementation is negation within the framework of the catena extensionality or the catenality; and, finally, what we shall call "aspect negation" is negation within the framework of the aspect concerned, in particular of a form of catenality or of a form of noncatenality. Aspect is the name we shall use for the imaginary collection of all extensional elements and subset-predicates of one catena and the corresponding noncatenality. Also combinations of such conceptual sets may be termed "aspects". Attributes which form part of the aspect of heaviness, or the aspect weight, for instance, are: heaviness (that is, all proper and improper heaviness attributes), the neutrality which limits heaviness and lightness (in practise the perineutrality medium heavy), lightness (all lightness attributes) and non-heaviness-catenality (the attribute not having any weight, not even 0). It looks as tho two aspects could be distinguished for every two-place relation: one from the standpoint of the fundament, and one from that of the terminus. This is misleading altho it depends on the kind of relation how easily the error can be shown. For comparative notions it is immediately obvious that there is actually merely one aspect involved. Consider, for example, the relation heavier than: if A is heavier than B, B is lighter than A, and if A is lighter than B, B is heavier than A. Hence, the aspect comprises in both cases the same predicates, namely being-heavier, being-lighter and the corresponding neutrality and noncatenality. But what if A loves B and B is loved by A, while not being-loved but hating is the opposite of loving? In this case loving and being-loved are 'isorelative', that is, they concern one and the same relation. (As the relation is binary it may also be said that being loved is the 'reverse' of loving. In combinatory logic the term inversion is used when the order of variables in a two-place predicate expression is changed.) The intensity of A's love and of B's being-loved is necessarily the same. There is only one catena value for this relation regardless of the position from which it is considered. Yet, this still makes it theoretically possible to discern two 'related' aspects: that of love, hate and nonpolarities, and that of being-loved, being-hated and nonpolarities. There are many noncomparative predicates which are each other's isorelative, and which each have an opposite of which they are no isorelative. An example is honor(ing) with the opposite dishonor(ing) and the isorelative being-honored. One should bear in mind, however, that predicates which are each other's isorelative need not be catenated. For example, planting and being-planted, being-a-parent and being-a-child are isorelatives; yet they have no opposites because they are not part of any catena to start with. In a way predicates like hate and being-hated, honor and being-honored, parenthood and childhood are as inextricably linked as love and hate, and as honor and dishonor, but there is a significant difference. To love or to have the predicate of love, is as real as to hate or to have the predicate of hate, and living beings cannot have both predicates at precisely the same moment with regard to the same thing. (To understand this one must not forget that a whole and one of its parts, or two different parts of the same whole, are not the same thing.) On the other hand, to be loved is not 'as real as' to love: ontologically someone or something that is loved does not have any proper predicate whatever on the basis of its being loved. It may certainly change or be changed or influenced because of its being loved, but all the proper predicates it may have for that reason are ontologically contingent -- at the most the relation of loving-and-being-loved and those predicates are related as cause and effect. Thus it is quite feasible, and common, to like or dislike someone and to be liked or disliked by that person at exactly the same moment. Yet, the state of being liked or loved, or disliked or hated, by the other does not correspond to any logically necessary, proper predicate in the person liked or disliked. One person may take someone else's hate or love to heart, whereas another person may just make little or nothing of it. All passive isorelatives such as being-liked, being-disliked, being-planted, being-a-child (in contradistinction to being-a-parent) are linguistically contrived pseudo-predicates. And as the argument is analogous with respect to three- or more-place relations, this implies that a multiplicity of relational positions (fundament, terminus, and so on) has no bearing on aspectual diversity. 2.3.4 ANTONYMICS AND ANTONYMICAL METAPHYSICS In antonymics (a branch of linguistics) 'antonyms' are words of so-called 'opposite' meaning. For example, antipathy is the antonym of sympathy. As words, antonyms form part of a series to which also belong synonyms (with the same meaning), homonyms (alike but with a different meaning) and paronyms (with the same stem). Apart from the fact that antonymics treats of words, it differs considerably from the catenical approach in that it lacks any methodical conception of oppositeness. The great discrepancy between catenical and antonymical theory can be illustrated by means of a few examples of pairs of antonyms: larger/smaller but also equal/different, and starting/finishing but also continuing/finishing (catenically only the former ones may be opposites); motion/rest (they are not opposites: rest limits motion); concrete/abstract (the first term refers to a kind of space-time catenality, the second one to noncatenality); yes/no and masculine/feminine and mental or spiritual/corporeal (there is no catenary relationship between these entities); artistic painter/house-painter (either both are 'painters' in the same sense, and then the words are not antonyms, or the word painter is used in two different senses, but then they are homonyms and not antonyms either). If antonymics is to be a scientific study at all, then only of what the speakers of a certain linguistic community believe to be opposites, or of the different ways in which they employ the term opposite itself, however inconsistently or superficially. But such (social) science is not more than a descriptive or statistical enterprise which will not lead to conceptual insight by itself. It may just turn out to be a mere survey of the common lack of insight in traditional language and thought. (The semantic differential used in psychological research is an antonymical device of the same nature.) The most famous (if not notorious) pair of antonyms is masculine/feminine, male/female or man/woman. In other words: yang and yin, or lingam and yoni. In yang-yin cosmology 'yang' is an active principle in nature which happens to be masculine, and 'yin' a passive principle in nature which happens to be feminine. When they combine, they produce all that comes to be: 'the phallic and the yonic united for both procreation and production' -- and solely for procreation and production. For some reason the masculine pillar, represented by the sunny side of a mountain, supports the heavenly realm of lightness, heat, dryness, consciousness and many other commodities (the sunny side of life), whereas the feminine pillar, represented by the shady side of a mountain, supports the 'opposite', earthly realm of darkness, cold, wetness, unconsciousness and suchlike incommodities (the seamy side of life). In other antonymical cosmologies there may be a right side which is associated with the masculine, the civilized world, culture and heaven, whereas the left side is associated with the feminine, the uncivilized world, nature and the earth. The yang, lingam or right side is 'positive'; the yin, yoni or left side is 'negative' in all these beliefs which were, or still are, espoused by peoples and people of very different racial or ethnic backgrounds. All of them may believe in some union of the positive and the negative but there is no neutrality as a limit element between catenated positivities and catenated negativities. (It should not go unnoticed that we can be quite sure that what emerges from the juxtaposition of the 'positive lingam' on the right and the 'negative yoni' on the left in yang-yin and similar, metaphysical or ideological, systems has been actively assembled and consciously propagated by masculine figures, albeit on Earth and not in heaven.) Of course, it is repugnant androcentrism to exclusively associate being-a-woman or the feminine with what is evil, uncivilized, passive or emotional and with matter, earth and death, while associating being-a-man or the masculine with what is good, civilized, active or rational and with mind, heaven and life. This is a moral evil of yang-yin-based and similar doctrines -- an evil which seems to be more of a man's evil than a woman's evil. What is objectionable in these doctrines from an ontological and scientific point of view in particular is, firstly, that conceptually entirely different relationships between predicates and between nonpredicative things or propositions are all lumped together; secondly, that predicates are created which serve only an exclusivist purpose, while other predicates or classes are ignored altogether; and thirdly, that the juxtaposition of the entities collected is arbitrary, both with respect to the choice of pairs put on the list and with respect to the side on which the members of these pairs are put. The predicates hypostatized are attributes like 'masculinity' and 'femininity' which are linked to 'being-a-man' and 'being-a-woman'; in general all predicates of belonging to a certain class of things. The things themselves, however, should be distinguished on the basis of certain component parts or qualities they necessarily have, and which nonmembers do not have. Instead of sticking to the (improper) attribute of having these parts, or to the typical qualities or combination of parts and qualities every member of the class in question must have in order to belong to it, an attribute is produced which not only comprises all aspects with respect to which members of this class are catenal, but which also determines which predicate of this aspect these members are supposed to have. For example, a man may be active or passive, good or bad, 'conscious' or 'unconscious', and a woman may be active or passive, good or bad, 'conscious' or 'unconscious'. There are only a few parts (organs, chromosomes and/or hormones), and perhaps some proper attributes, a human being must have to be a man or to be a woman. In spite of this men are harnassed with an overall property of masculinity in yang-yin and other antonymical ideologies and must be, or are supposed to be, active, good, 'conscious', strong, rational and so on, whereas women are dressed up with an overall property of femininity and 'are' passive, bad, 'unconscious', weak, emotional and so forth. (The choice of attributes may vary.) To deny that any such special connection is assumed or suggested in these metaphysics and ideologies is tantamount to removing the very pillars which support the whole sex-based establishment. The predicate which is ignored or neglected in this tragicomic cosmos of deep superficiality is usually the neutrality or perineutrality of the catena. Where a metaphysical system wholly revolves about 'starting' or 'increase' and 'finishing' or 'decrease' it denies the existence of continuation; where it wholly revolves about active, light or hot and passive, dark or cold it denies the existence of the concatenate perineutralities; and most obviously, where it is exclusively expressive of 'positive' and 'negative symbolism' it forgoes catenated neutrality altogether. Closely related to yang-yin and lingam-yoni systems is dialectic, the so-called 'critical' investigation of the process of change in which an entity passes over into its 'opposite', or of the development thru stages of thesis, antithesis and synthesis. Underlying this theory is the same antonymical metaphysic. Only the spirit of the dialectical mechanism is quite different: the physical and the mental, for instance, may not be looked upon as moments to be united, but rather as moments to be sublated. This need not concern us here. It is the problem of the yang-yin metaphysician to solve the 'conflict' between war and peace, or between diarrhea and constipation; it is the problem of the dialectician that he or she has to await a 'synthesis' between these opposites. All these antonymical, metaphysical doctrines suffer from the same lack of catenical discernment and from the same lack of scientific prudence, especially with regard to empirical statements. While the yang-yin cosmology is dialectical, the essence of dialectic rests on yang-yin dualism. The pairs of opposites emphasized may only be different. What is the opposition between man and beast in the one, for instance, may have been superseded by that between man and machine in the other. Let us, finally, list the most important, catenical and other relations which are all lumped together under the common denominator of 'oppositeness' in antonymical metaphysics and ideologies. They are: catenical relations: (1) opposition or contrariness; for example, between lightness and darkness (this always requires a third predicate, namely a neutral or perineutral one); (2) limitation and supplementation; for example, between rest and motion (in these cases one member of the pair comprises another pair itself); (3) aspect negation; for example, between concreteness and abstractness, and between life and death (dependent on the definitions); noncatenical relations: (4) inversion or isorelativity; for example, between honor and being-honored, and between parent and child (there are only two 'classes' if the relation is binary but there are three or more if it is three- or more-place); (5) difference in class membership in a system of (supposedly) two classes; for example, between man or masculinity and woman or femininity, and between man and beast or machine; (6) contradistinction; for example, between painting and sculpture (this is a distinction on the basis of 'opposite' qualities of the entities selected, not on the basis of their own inherent oppositeness); (7) contradiction between propositions in terms of logical incongruity; for example, between (A is) human and (A is) not human. 2.3.5 THE SENSE IN WHICH PREDICATES ARE NONCATENICAL Primary predicates like childhood and parenthood, masculinity and femininity, painting, and being-human are not catenated predicates. Yet, it may be that they can ultimately only be defined by means of component parts and predicates which are catenated. In that case they would all be improper predicates after all (or pseudo-predicates), but we shall not attempt to prove this, nor is it necessary here to assume that they are. What is truly important is that we make clear whether or not a proper or improper predicate or pseudo-predicate is catenated or forms part of a catenical aspect. We can do this by proving or demonstrating that it is, or by postulating that it is. There is hardly any other context in which the meaning-variance thesis (as already mentioned in 1.2.1) is of comparable significance. The axiomatic system in which catenated predicates occur (and indirectly also catenalities and noncatenalities) is that of the catena, and it is this system which determines here the meaning of the term for such predicates, at least partially. For example, if someone argued that 'love' is not the opposite of hate, then love is still the opposite of hate, but the thing 'e would be talking about and which 'e would call "love" would be another thing than the thing we are talking about when saying "love". Thus 'er love and our love would plainly have a different meaning. That is not to say that people could not disagree on the meaning of love even if they do agree that it is the opposite of hate. After all, its meaning is only partially fixed by this opposition (unless there is already a consensus on what hate means.) But if someone calls something "love" that is not opposed to hatred, the predicate referred to (if any) might be of no catenical aspect. (Usually tho, the ideologues of 'love' mix up all senses possible and impossible.) If positive is used in the sense of prescribed (as in positive law) or in the sense of complete or absolute (as in positive disgrace), it is certainly of no catenical aspect, even not as a secondary predicate. Similarly, neutral in the sense of not taking sides in a quarrel or war or not aligned with an ideological grouping does not refer to catenated neutrality either. In such cases neutrality happens to designate a privative primary predicate of no catenical aspect. The situation is not dissimilar for negative when it is used to denote mere denial, refusal, prohibition or nonactivity (as in the case of negative right). If positive, neutral and negative are not employed in the context of the catenary trinity, they simply do not refer to catenated predicates at all. It can be quite arrogant to claim only one 'true' meaning for what is merely a word, yet it is of paramount importance not to confuse divergent meanings of what turn out to be homonyms. While we can clearly not do without the concept of the catena where it concerns catenated predicates, catenalities and noncatenalities, we can also hardly do without it where it concerns all other primary predicates. Noncatenical predicates like thinking, walking and painting all admit indirectly somehow of degrees. Thought is more or less intelligent, more or less interesting, more or less literary, and so on. Somebody may walk fast, neither fast nor slow or slow, and somebody may walk more more or less gracefully. Art may be as naturalistic as possible, it may be entirely abstract or something in between. It is also beautiful, indifferent or ugly; and yet painting and art themselves are not catenical concepts. All these examples show the significant part catenated predicates act in the whole primary world of objects and abstract things. We have until now classified catenated predicates and some noncatenated predicates only on the basis of the general concept of the predicate catena. It is obvious that by classifying catenas themselves we will even learn more about the position, nature and role of catenated and other catenical predicates. 2.4 WAYS OF CLASSIFYING CATENAS 2.4.1 THE FOUR MAIN CRITERIONS OF CLASSIFICATION When we say that a predicate like larger (than) is comparative, it is, properly speaking, not correct to suggest that the predicate by itself has a comparative character. It is rather the catena to which larger belongs which is comparative. Smaller and as large as, the predicates catenated to larger, are just as comparative. It is impossible that a comparative predicate would be catenated to one which is not, simply because it is first of all the catena to which it belongs which is comparative. This illustrates, too, how the nature of a catena determines the nature of its extensional elements. So the classification of catenas is indirectly also a classification of catenated predicates and catenical aspects. Catenated, primary predicates do not only have secondary attributes or relations on account of their position in a catena, they also have such attributes and relations, albeit improperly, on account of the position the catena they belong to, or refer to, has itself. Catenas can be categorized in at least four different ways. The following criterions of classification are partially dependent, partially independent of one another: (1) according to the range of catena values; this yields 'finite', 'semi-finite' and 'infinite catenas'; (2) according to ordinary language; on the basis of this criterion one can distinguish 'explicit triads', 'quasi-duads', 'quasi-hexaduads' and 'quasi-monads'; (3) according to the position in a derivation system; this categorization starts with a distinction between 'basic' and 'derivative catenas'; and (4) according to the scope of catenization; this criterion differentiates 'catenas of universal' and 'of special scope'. We shall treat of the second classification in the following sections of this division. The third and fourth classifications are important enough to devote a separate division to. The first classification that relates to the range of catena values is mainly of empirical interest. Until now we have taken it for granted that a complete positivity would comprise all positive values, and a complete negativity all negative values. This is, strictly speaking, not correct. What we should say is that they comprise all the positive or all the negative catena values, for we may not be justified in assuming that there is a predicate corresponding to every value or number which is mathematically (that is, theoretically) conceivable. It may be implausible in particular to assume that the total set of catena values is a continuum of which each mathematical value between two different values corresponding to a catenated predicate corresponds to a catenated predicate itself as well. Nevertheless, such a hypothesis would not amount to more than the acceptance of an infinite number of abstract entities, something that may not be as questionable as the belief in infinite collections of concrete objects. A 'finite catena' is now a catena of which the value collection has both a lower limit (inf C) and an upper limit (sup C). The degree of catenality with respect to such a catena is confined to a minimum extreme value and a maximum one. A catena is symmetrically finite if, in terms of catena values, the modulus of the lower limit equals the (modulus of the) upper limit. (Since there is at least one negative catena value, the minimum must always be negative, and since there is at least one positive value, the maximum must always be positive.) If they are not equal, the catena is asymmetrically finite: |inf C| ¹ |sup C|. A catena such as the motion catena is a symmetrically finite catena as the velocity of light is the maximum velocity possible, both in a negative and in a positive direction of the same dimension. This implies that the slowness catena is finite too, but whether it is symmetrically finite depends on the position of the neutral value and the way catena values relate, or are made to relate, to the different velocities; on the 'catenization' so to say. When applying the same classificatory criterion to the catena's range of values, we can also distinguish 'semifinite' and 'infinite catenas'. A semifinite catena is, then, limited at one side and unlimited at the other, whereas an infinite catena has neither a lower nor an upper limit. If temperature, for instance, is conceived of as a physical phenomenon, and not as something felt by living or sentient beings, the physical heat catena corresponding to this quantity is semifinite because there is a lowest temperature and (presumably) no highest temperature. 2.4.2 EXPLICIT TRIADS A whole of primary predicates may solely be called "a (predicate) catena" if it has been demonstrated or postulated that it comprises a predicate which is neutral between a predicate or set of predicates which are positive and a predicate or set of predicates which are negative. It depends on the language spoken, among others, how easily or plausibly this can be done. If the ordinary variant of that language has already an expression for the positivity and for the negativity, and ideally also one for the neutrality, the tripartite structure of the complex system of secondary predicates can often be immediately ascertained. Such is particularly obvious for triads like the one of electropositivity, electroneutrality and electronegativity. But also happiness, cheapness, quickness, honor(-ing), more and acid with their concatenate, limiting and opposite, predicates may be considered examples of more or less explicit triads. In the case of all these and similar catenas the two monopolarities have their own names in ordinary language, and are recognized, too, as opposites in this language (even when the neutrality is taken notice of, and the opposites are not alone). The expression for the one monopolarity is thus often formed by adding a prefix like un- or dis- to the term for the other; unhappiness and dishonor are but two examples. In the event that the neutrality of the catena in question does not have its own name (like equal or neutral in the sense of not electrically charged or neither acid nor basic) it is either disregarded or described in a rather circumlocutory and/or inadequate way (usually in terms of (neutrally) neither .. nor ..). The phenomenon that there is a compact atomic expression for a predicate in ordinary or colloquial language one time, and that one needs to have recourse to circumlocutions another time, is of course a subjective, reflectional criterion of subdivision for predicates or predicate catenas. Whatever the reasons may have been, or still are, it is the positivity and the negativity which are or have been judged of enough weight to deserve a simple name in the case of explicit triads, and not the neutrality and bipolarity, for instance. The reason to speak of "triad" even if no neutrality is recognized in addition to the two monopolarities is that this recognition of neutrality is a prerequisite for speaking of a catena at all; the duad of two 'inseparably connected' predicates just is not a catena per se. Insofar as the language which is our present means of communication does not have a general expression for explicit triads or their predicates, we will call these catenas after their positivity. Conversely, the positivity of an explicit triad is the predicate after which it is called. Thus electropositivity is the positivity of the electropositivity catena; happiness the positivity of the happiness catena; more or moreness the positivity of the moreness catena; and so on. Unless there are nonlinguistic, systematic reasons not to do so, we shall conceive of predicates denoted by terms prefixed with un-, dis- or similar prefixes as negativities. Hence, unhappiness, dishonor, inelasticity, and so on, 'are' negativities. Love is the positivity of the love catena of which hate is the negativity. Should one believe that hate is the positivity, then love is the negativity of the hate catena. Since explicit triads are called after their positivities, they may also be referred to as "positivity catenas". 2.4.3 QUASI-DUADS: BIPOLARITY AND EXTREMITY CATENAS A catena of which the extensionality is implicitly subdivided into two subsets in ordinary language, assuming that no subset is disregarded, is a 'quasi-duad'. (Quasi-, because every catena is to be interpreted as a triad in the end.) If the predicative units distinguished are the complete or non-perineutral bipolarity and the neutrality or perineutrality (disregarded or not), this quasi-duad is called after its bipolarity: "a bipolarity catena". If one unit is an extremity and the other the catena supplement limited by it, we shall speak of "extremity catena". Every extremity catena is called after the extremity explicitly recognized in the language concerned. There are no separate expressions for the monopolarities of a bipolarity catena. They have to be described by means of circumlocutions; for example, motion in positive direction and motion in negative direction, positive abnormality and negative abnormality, positively charged and negatively charged. If we assume that a predicate like normality is solely catenated to abnormality (and that there is no neutral predicate neither normal nor abnormal), then the catena of both predicates is a quasi-duad. (It is something else of course to assume that there is no such catena at all.) This quasi-duad of normality and abnormality can only be conceived of as a bipolarity catena of which normality is the neutrality or perineutrality; abnormality is, then, not neutral, or at least not perineutral. To look upon normality as a neutrality between positive abnormality (what is too much) and negative abnormality (too little) would imply that no variation is possible within the range of the normal. This would probably be incompatible with ordinary usage where within the limits of the 'normal' some variation seems still to be possible, altho the extent to which deviation is tolerated may diverge considerably (not in the least when abnormal is predominantly a doxastic, normative notion). The fact that normality is probably to be interpreted as moderateness in ordinary usage has much to do with the fact that the catena of which abnormality is the bipolarity is a catena of special scope without a point which is clearly neutral. (What special scope means in this context will be discussed in the division on the scope of catenization.) As terms for the predicates of an abnormality catena normal and abnormal are understood in a purely statistical sense, as designations from the perspective of the mean or most frequent value in a frequency distribution. They are, then, not used in some normative or evaluative sense like according to a rule or standard. If abnormality is taken to be the opposite (in the catenical sense) of normality, limited by a neutral attribute neither normal nor abnormal or the corresponding perineutral predicate, the catena of these attributes is an explicit triad: the normality catena. The direct reason to regard normality here as the positivity of a positivity catena is not that it tends to be evaluated positive in ordinary language, because this is probably due to the series of misassociations from affirmation to affirmity to positivity to goodness, and vice versa. The direct reason is merely that normal is the base-word from which abnormal has been derived. But indirectly the above associations appear to be the very reason for the direction the derivation has taken in ordinary language. If there is a link between the abnormality and the normality catenas, then the perineutrality of the former catena is the positivity of the latter one. In this case it can also be defended from a (nonlinguistic) systematic point of view that the abnormality predicate of the explicit triad must be designated a negativity, because the values of this predicate deviate more from the mean value or the 'mode' than the value of the concatenate predicate neither normal nor abnormal. 'More abnormal' is, then, less like what is related to the statistical mean or mode. The relationship between the motion and the slowness catenas is of a similar nature: slowness is the perineutrality of the quasi-duad of motion and rest, and at the same time the positivity of the explicit triad of slowness, fastness and the neutral predicate neither slow nor fast. The neutrality of the motion catena, rest, is in a way an extreme form of slowness and the positivity of the slowness catena comprises in terms of the motion catena slow motion in a positive direction, rest and slow motion in a negative direction. It will turn out that the slowness catena is the same sort of derivative catena as the normality catena, and that the motion and abnormality catenas are both original quasi-duads, that is, 'original' with respect to the derivative explicit triads; they are not necessarily basic with respect to a whole derivation system. (Theoretically it is not only possible to derive positivity catenas from bipolarity catenas but also the other way around -- something we will not attempt to do here.) A catenary quasi-duad which undergoes transmutation to become an explicit triad has to be strictly distinguished from a quasi-duad which is simultaneously an explicit triad. Being both a quasi-duad and an explicit triad has nothing to do with derivations, but is a question of wealth of words. A catena which is both a quasi-duad and an explicit triad has atomic expressions for both the bipolarity and the two monopolarities. For example, change (in the sense of change of value or change of degree), increase and decrease all belong to the same catena: the quasi-duad of the change catena, which is identical to the explicit triad of the increase catena. 2.4.4 QUASI-HEXADUADS AND QUASI-MONADS The set of the physical predicates deep, neither deep nor shallow and shallow seems to be the extensionality of an explicit triad, and similarly, the set of high, neither high nor low and low in a purely physical sense too. Yet, in point of fact, solely the values of and below the zero level of the value collection of the original catena --let us call it "the altitude catena"-- occur in the value collection of the former and solely those of and above that zero level in the value collection of the latter. Therefore, the values corresponding to the physical predicates from deep to shallow represent only one half of a catenary system and those of the physical predicates from low to high the other half. It is the combination of all six predicates of the two triads together which is a catenary collection, and it is the whole of which such a combination is the extensionality which we shall call "a quasi-hexaduad". Granting that normality is the positivity of a derivative normality catena and slowness of a derivative slowness catena, consistence requires that the positivity of a quasi-hexaduad be that combination of predicates which also corresponds to the perineutrality of the original catena. For the above-mentioned predicates related to the altitude catena this is the set of all shallowness and lowness predicates, which we shall refer to as "shallow-or-lowness". Hence, the quasi-hexaduad concerned is the shallow-or-lowness catena. Proximity may also be a common denominator for shallow-or-lowness but this term does not only apply to altitude; it equally applies to what would be 'latitude' and 'longitude' in a three- or more-dimensional, spatial system. As quasi-hexaduads and explicit triads are both named after the positivity of the catena, the term positivity catena itself can be used for both of them. Catenas with respect to which there is an atomic expression in ordinary language for the improper subset of its extensionality, that is, for the catenality, are 'quasi-monads'. The predicate itself which serves as common denominator of all the catenated predicates in question is a 'quasi-monadic predicate'. All quasi-monadic predicates are catenalities but, conversely, catenalities need not be quasi-monadic. There may be important catenalities no-one has ever thought of, let alone assigned a name to in the language spoken. The concreteness catena is a quasi-monad identical to the quasi-duad of the motion catena as long as we define concrete directly or indirectly as motion-catenal. Concreteness itself is in this case a quasi-monadic attribute. Length, width, height, speed, and so on, are all quasi-monadic attributes or relations, at least if we do not read "length" as "longness", "width" as "wideness", and so forth. As noted before, terms like long and wide are unmarked, and when someone wants to know the width of a road, 'e does not necessarily assume that it is wide. What is its width? means what is its (degree of) wideness catenality? (or narrowness catenality if narrowness is positive). Thus, the quasi-monad of the width catena is at the same time an explicit triad, namely of narrowness, the neutral or perineutral neither narrow nor wide and wideness. The quasi-monad of the speed catena is nothing else than the motion catena in one sense and the slowness catena in another. By calling a predicative whole "a quasi-monad" we force ourselves to ultimately distinguish three types of extensional elements of that whole; by calling a predicative whole "a quasi-duad" we force ourselves to recognize the bipartite structure of one of its two extensional subsets (in the case of bipolarity catenas), or we force ourselves to look upon the first subset as part of the second, and the second subset itself as of a tripartite nature (in the case of extremity catenas); by calling a predicative whole "an explicit triad", we force ourselves not to forget the third predicate or predicative subset in addition to the two monopolar ones. This classification of catenas on the basis of the existing vocabulary of the ordinary, nontechnical variant of the language employed does, strictly speaking, not tell us anything about catenas themselves; it merely tells us something about linguistic usage. Yet, this grouping together on the basis of language spoken is very useful as it will make it easier to switch from the ordinary or traditional way of thinking in that language to catenical thought. It will be practically impossible now to ignore that there are really three primordial kinds of catenated predicates involved where formerly only one or two, or more than three, were believed to exist or to be primordial. 2.5 THE CATENA'S POSITION IN A DERIVATION SYSTEM 2.5.1 BASIC OR ORIGINAL CATENAS AND DIFFERENCE CATENAS Logically necessary relationships between catenary variables are of great import. Consider, for example, the case in which one can only have a predicate corresponding to the catena value 0 with respect to the one catena, while having a predicate corresponding to a negative or positive value with respect to another catena. It is then logically impossible to be neutrally catenal with respect to both catenas at the same time. We shall not deal here with those functional relationships which are logically contingent, such as causality, but only with those which exist on the basis of the definitions of the catenas concerned. To make these relationships explicit we shall express them as mathematical functions with each variable assuming one of the values of one catena's value collection. By means of these functions new catenas are derived, as it were, from other ones. If the derivation does not change the dimension, we shall call the catenas between which the relationship exists "equidimensional to each other". Catenas which are not derived from others are in our terminology 'basic catenas'; and the catenas derived from them 'derivative catenas'. While all basic catenas are 'original catenas', any derivative catena may itself be an original catena in a further derivation. Together all the catenas that are derived from one and the same collection of equidimensional catenas not derived from one another (the base) form with that base a catenary derivation system. Thus the basic catenas of the spatiotemporal derivation system are those catenas which correspond to one spatial dimension: let us say, the 'longitude', 'latitude' and 'altitude catenas'. (There may be more.) Every primary thing that is catenal with respect to any of these basic catenas is catenal with respect to all of them, and with respect to the whole catenary derivation system. Of two primary things which are catenal with respect to the longitude catena, the longitude of the one is either more (positive), the same or less (more negative) than the longitude of the other. The catena corresponding to this positivity-difference in longitude is a so-called 'bicatenal positivity-difference catena'. If neither primary thing is fixed or a particular object, the catena concerned is bivariant; if one of them is fixed, then monovariant. (They cannot be fixed both, because then there would only be one value and potential value, whereas a catena requires at least three potential values.) Now, the longitude of the one primary thing is also more neutral, the same or less neutral than the longitude of the other, whatever the neutral longitude may be. Hence, we can also derive bicatenal, monovariant and bivariant, neutrality-difference catenas from basic or other original catenas. When primary things are considered as wholes in themselves, and when they are then compared, the positivity- or neutrality-difference catena is bicatenal. But the primary things in question may also be component parts of one and the same whole. If the catena value is then a value of this whole, and not of one of its component parts, the difference catena in question will be termed "monocatenal". Given that the two component parts have their own characteristics (like head and tail), monocatenal bivariant difference catenas of the longitude catena indicate the direction of the primary whole concerned: in the event of a positivity-difference catena its extremity-directedness, and in the event of a neutrality-difference catena its neutrality-directedness. Two longitude catenals may be said to be close to each other, far from each other or something in between. It does, then, not matter whether the one catenal has a more positive, or a more neutral, longitude than the other. So there is also a proximity catena of proximity, farness and a concatenate neutrality or perineutrality. Proximity means that the modulus of the positivity-difference (the distance) between two longitude catenals is small, that is, smaller than a certain other positivity-difference (the neutral or perineutral distance). From the proximity-catenary angle it is irrelevant whether this difference is positive or negative. (It is also then that every 'distance' is nonnegative by definition.) That is why a catena like the proximity catena will be called "a modulus-catena". Such a modulus-catena is a bicatenal monovariant neutrality-difference catena. The proximity catena is therefore the modulus-catena of the bicatenal bivariant positivity-difference catena of the longitude and similar, basic catenas. For the proximity catena the two longitude catenals in question are considered as separate wholes, but if they are conceived of as those component parts of one and the same whole which differ most in longitude, proximity is nothing else than shortness and farness nothing else than longness (insofar as this one dimension is concerned). Like the proximity catena, the shortness catena is a modulus-catena. Distance is now called "length". However, the shortness catena is not the modulus-catena of the bicatenal, but of the monocatenal bivariant positivity-difference catena of the longitude and similar catenas. Monocatenal monovariant catenas would relate to the value of a whole with at least two component parts, of which one were to have a fixed predicate. Such catenas do not seem to exist, or if existing, do not seem to play a role, for having a certain part-predicate would, then, only imply having a certain whole-predicate. We shall therefore say that difference catenas are: (a) bicatenal and monovariant (like all modulus catenas); or (b) bicatenal and bivariant (like the original catena of the proximity catena); or (c) monocatenal and bivariant (like the original catena of the shortness catena). By means of mathematical symbols we can clearly define the several kinds of derivative catenas mentioned here. Let, then, x be the value of the original catena predicate, and X the set of all these values. We use the symbol d (of direction) to indicate the value x in respect of which a greater, equal or lesser deviation of two things is compared. Thus d = 0 when considering what is more neutral, and d > 0 when considering what is more positive. If a thing has a value x1 with respect to an original catena, d determines the kind of catena with regard to which this thing is catenal too. We shall therefore call the catena value d "the aspectual value". A comparative value x2 now determines the kind of catena element the thing in question has with respect to the catena determined by d. This value of comparison may also be a constant c. If P is the set of derivative catena values corresponding to the positivity, N the singleton of the value corresponding to the neutrality and M the set of values corresponding to the negativity, then a difference catena is in general a catena for which P = { x3; | d-x2 | > | d-x1 | }, N = { x3; | d-x2 | = | d-x1 | }, M = { x3; | d-x2 | < | d-x1 | }, on the condition that |d-x| = d-x for d=+INFIN, and |d-x| = x-d for d=-INFIN The definitions for the specific difference catenas are now: (a) positivity-difference catena: d.c. for which d=supX (possibly d=+INFIN); (b) neutrality-difference catena: d.c. for which d=0 ; (c) monovariant difference catena: d.c. for which x2 is constant (x2=c) (while x1 is variable); (d) bivariant difference catena: d.c. for which both x1 and x2 are variable; (e) monocatenal difference catena: d.c. for which it is possible that x3 ¹ x1 and x3 ¹ x2 (catenal 1 and catenal 2 are component parts of catenal 3); (f) bicatenal difference catena: d.c. for which necessarily x3=x1 ; (g) modulus-catena: bicatenal monovariant neutrality-difference catena. (This derivation amounts to taking the modulus of the original catena's value: P = {x1 ; |c| > |x1| } or P = {x1 ; |x1|< |c|} , and so forth.) It is worth noting, firstly, that in the general definition of the difference catena positive difference is positivity-moreness and evaluated positive by entering > instead of < for the comparative positivity in |d-x2| > |d-x1|; and secondly, that the value of d is found back in the name of the kind of comparative catena -- only modulus-catena is a special case. Thus we speak of "a positivity-" and of "a neutrality-difference catena". It does not even make sense to distinguish a 'polarity-difference catena', as there is no unique aspectual value which pertains to it. On the other hand, 0 is the aspectual value of the neutrality-difference catena which comprises exactly the same predicates. (Note that comparative catenas with a nonextreme, nonneutral aspectual value are not recognized in ordinary, nontechnical language.) The perineutrality of an original catena has to be evaluated positive as the neutrality-moreness of the derivative catena. In many instances traditional thought has been geared to polarity-moreness catenization with the accompanying negative evaluation of neutrality-moreness. So slowness may be conceived of as the negative opposite of fastness which is positive and affirmative on the polarity-moreness approach. Yet, in the theory of catenas we shall stick to the positivity of moreness and the crucial role of the aspectual value in the naming of comparative catenas and their predicates. 2.5.2 OTHER DERIVATIVE CATENAS From a catena like the strongness or strength catena we can directly derive the strongness-moreness or 'strongerness' catena. But besides the derivations stronger or more strong, weaker or less strong and equally strong or equally weak we also know derivations like strengthening and weakening. There thus exists a strengthening catena as well. In other systems we will find an honoring catena, betterment catena, heating catena, and so on. All these comparative catenas are increase catenas as explicit triads or differentiation catenas as quasi-duads. Differentiation stands to difference or otherness and different or other as strengthening stands to strongness and stronger, and as increase stands to moreness and more. Also differentiation- or increase-catenas can be subdivided into positivity-differentiation and neutrality-differentiation catenas (or any other type dependent on the aspectual value taken). And, analogously to the case of difference catenas, the increase catena of an explicit triad is a positivity-increase catena, and the increase catena of a bipolarity catena a neutrality-increase catena. These similarities are obvious. They hold for every increase or differentiation catena and the corresponding moreness- or difference-catena. Roughly speaking, the difference-catenary approach is primarily nontemporal, whereas the differentiation-catenary approach is primarily temporal, at least on the assumption that every comparatively catenal thing exists over a period of time. Differentiation, increase or decrease can be active or passive. For example, active positivity-differentiation means making less or more positive(ly catenal) and passive positivity-differentiation becoming or growing less or more positive(ly catenal). Active neutrality-increase is making-more-neutral(ly catenal), and passive neutrality-increase, becoming- or growing-more-neutral(ly catenal). (Literally speaking, one cannot make something positive or neutral, or become positive or neutral. A primary predicate just is or is not positive or neutral, while it is a nonpredicative primary thing which can or cannot be made or become positively or neutrally catenal.) Each differentiation catena is, as it were, the common denominator of two catenas: an active (transitive) and a passive (intransitive) one. Both catenas are each other's isorelative but --as already explained in 2.3.3-- the passive variant consists of pseudo-attributes only. The fact that a catena is a difference or differentiation catena, whether active or passive, says almost nothing about its position in the total derivation system, except that it is not a basic catena. Only if the original catena is basic, is the comparative catena a catena of the first level of derivation. In general, it is of the (n+1)-st level, if the original catena is of the n-th level. (Basic catenas are of the 0-level of derivation.) Catenas of the same basis are interchangeable. For example, the longitude, latitude and altitude catenas are interchangeable in that the spatial co-ordinate which is regarded as longitude, could also be latitude or altitude instead, and vice versa. Catenas derived from two interchangeable catenas in the same way are interchangeable themselves. Interchangeable catenas are always equidimensional, but equidimensional catenas need not be interchangeable. The difference and differentiation catenas of the longitude catena, for instance, are equidimensional to it but not interchangeable with it (with the exception of the monovariant positivity-difference catena for which c=0, which is identical to it). Monocatenal and bicatenal difference catenas are also equidimensional, but not interchangeable either: the length of an object, for instance, or its shortness catenality, is something else than the distance between this object and another object, or its closeness catenality. Unlike difference and differentiation catenas, which are equidimensional to the original catena from which they are derived, differential catenas have their own dimension. Consider, for example, velocity. If v represents an object's velocity, then v=ðs/ðt (with ðs as the distance traveled and ðt as the time spent); v is therefore s-differentiated-to-time, and its dimension is m/sec. On the basis of a terminological analogy between value collections and catena extensionalities, we may say that one can derive the motion catena by differentiating the longitude catena, or a catena interchangeable with it, to time. Thus we shall call the motion catena, the quasi-duad corresponding to velocity, "a time-differential catena". The term velocity is also used in the more general sense of rate of occurrence or action. In that case it corresponds to any time-differential catena, not just that in the derivation system of the longitude catena. The differential catenas to time of the longitude, latitude and altitude catenas are mutually interchangeable. It may be said that each of the three time-differential catenas is a motion catena; it may also be said that the motion catena is the common denominator of these and similar catenas. This is no fundamental issue. Starting from a differential catena which is derived from a basic catena, we can in turn derive a difference or other comparative catena from it. For example, in the physical system of the longitude catena, the slowness catena is a modulus-catena of such a differential catena. The dimension of this modulus-catena is the same as that of the differential catena, namely m/sec. But also when we now comparatively derive a new catena from the slowness catena, for example, the bivariant differentiation catena with extreme aspectual value, the dimension remains the same. Thus the dimension of this retardation catena is also m/sec. On the other hand, deceleration (and also acceleration) has the dimension m/sec2 in physics. The catena to which this deceleration belongs, however, is not the differentiation catena of the slowness- or speed-catena, but the time-differential catena of the speed catena. Just as a derivative and a first derivative are the same in mathematics, so a differential catena is the same as a first differential catena. (In the theory of catenas a derivative need not be a differential catena tho.) A second differential catena is, then, the differential catena of a differential catena with respect to the same form of catenality or quantity. The deceleration catena is no such second differential catena; it is the first differential catena of the modulus-catena of the first differential catena of the longitude catena or a catena with which it is interchangeable. In traditional mathematics the differentials ðv or DELTAv and ðt or DELTAt are evaluated positive, if the new v- or t-value is closer to the positive extreme than the old one. The aspectual value is on this account supX or +INFIN. Now this view is typically that from the perspective of positivity-moreness, based on the positivity-increases of v and t. What underlies this conception is positivity-differentiation. The differential catena thus derived is a positivity-differential catena. It is not possible to make a mathematical differentiation universally comparative, because the aspectual value will always determine the value of the derivative function. On the other hand, we are just as justified of looking at DELTAv and DELTAt from the perspective of neutrality-moreness, and to evaluate DELTAv and DELTAt positive if the new v or t is closer to zero than the old one, and negative if it is farther away from it. The catena thus derived is a neutrality-differential catena. If û1 is the catena value of the original catena, and f+(û1) the value of the positivity-differential catena, the value of the neutrality-differential catena is û2 = f0(û1) = ( | f(û1) | × û1 × f+(û1)) ÷ ( | û1| × f(û1)) for û1¹0 and f(û1)¹0 . If û1 ¹ 0 and f(û1) = 0, then f0(û1) = 0 regardless of the value of f+(û1). (This is because we choose a point on the curve which is a point on the tangent midway between the lower and the higher triangular points.) If û1 = 0 and either f(û1)¹0 or f+(û1)¹0, then f is indefinite; and if û1 = 0 and both f(û1)¹0 and f+(û1)¹0, f0 is infinite (even if f+ is finite). If A is the difference catena of B, then B may be called "a sum catena of A". Similarly, if C is the differential catena of D, D may be called "an integral catena of C". For example, the quasi-monad of energy can be conceived of as an integral catena of the physical force catena with respect to the length catena. Differential and integral catenas have to be distinguished from the related quotient and product catenas. The product catena of the physical force catena and the length catena would be the physical moment catena, while the integral catena is an energy catena. Nevertheless, differential and quotient catenas, and also integral and product catenas, have the same dimension, granted that the original catenas are the same. As the kinds of catenical derivations are closely related to the kinds of mathematical operation it is worth our while to briefly consider the position of the most simple mathematical operations. The first pair of operations is, then, that of addition (a + b = c) and substraction (a - b = c). There is no repetition involved in these operations. In the theory of catenas it is the derivation of a comparative and equidimensional catena which is the analog of the mathematical sort of operation on this zero-level of reiteration. (All mathematical operations or functions may also be employed, however, to express logically contingent relationships between catena values, something which is not our concern here.) The prototypical mathematical operation on the first level of reiteration is multiplication (a × b = c). This is in the first instance nothing else than a form of reiterative adding-up: b × a = a + a + ... + a , or b × a = SUM(i=1, b) ai (ai=a for every i). Its correlative is division (a ÷ b=c). The derivations of nonequidimensional differential and integral catenas, and of quotient and product catenas, are the catenical analogs of mathematical operations on this level. The prototypical mathematical operation on the second level of reiteration is involution or the raising of a quantity to power (ab = c or a××b = c). This is in the first instance nothing else than a form of reiterative multiplication: a ×× b = a × a × ... × a , or a × b = PRODUCT(i=1,b) ai (ai=a for every i). The correlative of this second-level operation is evolution, the extraction of a mathematical root ( b ROOT a=c ). In their original shape the numbers were what mathematicians traditionally call "natural". It would be naive to take it for granted now that the number of sorts of mathematical operation is thus exhausted. For we can continue ad infinitum by repeating the operation on the previous level of reiteration. On the third level this would involve reiterative involution with its related forms of operation. But on this and higher levels ordinary, and also mathematical, language just lack the terminology to express ourselves, even if we would like to. Nevertheless, it is possible to develop a universal notational system for reiterative operations of all levels by means of novel mathematical symbols. Suffice it here to recognize that there are not only other catenas on the first level of reiteration besides differential catenas but also catenas on higher operational levels of reiteration. They are catenas of primary predicates for which there is even no name in scientific or technical noncatenical parlance. 2.5.3 FACTITIOUS AND NONFACTITIOUS DERIVATIONS A catenical value belonging to a certain catena may be, but need not be, equal to some empirical value relating to this catena. It may be that the choice of empirical quantity is arbitrary, both with respect to the 0-point selected and with respect to the unit used. Thus the empirical value may be always positive or nonnegative, in which case it is impossible that it would be equal to the catenical value. In general there is a relationship between the catenical and empirical value which can be expressed as û=k(v). In this formula û [v with a caret over it] is the catena value, v the empirical value and k what we shall call "the catenization function". Whereas derivation is a transformation from the one catena or form of catenality to the other catena or form of catenality, catenization is a transformation from what is possibly not clearly catenary to what is explicitly catenary. Now, if û1 is the catena value of the original, first catena, and û2 that of the derivative, second catena, then it is the derivation function which describes the relation between these two catena values: û2= d (û1). Instead of "û2= d(û1)" we may write "û2 = e(û1) + E". We now define a factitious derivation as a derivation for which (necessarily) û1¹0 and/or E¹0 if û2=0. For a basic catena E=0 and û2 = û1, and therefore û1=0 if û2 = 0. Hence, basic catenas are not factitiously derived, still regardless of the fact that they are, properly speaking, not derived at all. The codification of catenas according to the factitiousness of their derivation is thus really another subdivision of derivative catenas. It is a codification in addition to that according to the operational level of reiteration. For differential catenas û2= A × ðû1÷ðw + B = A×f ' (û1) + B (for positivity-differential catenas A×f+(û1) + B, for neutrality-differential catenas A×f0(û1) + B; A¹0). Here û2 = 0 does not in any way determine û1, nor B. Hence, û1 is not necessarily positive or negative if û2=0, and therefore differential catenas are nonfactitious catenas if B=0. The derivation is only factitious if B is taken to be positive or negative. On the zero-level of reiteration there is a clear difference between necessarily and not necessarily factitiously derived comparative catenas. Thus bicatenal monovariant positivity-moreness- or -increase-catenas are nonfactitiously derived if B=0 in û2=Aû1 + B with A¹0. (If A=1, then the nonfactitiously derived positivity-moreness catena is identical to the original catena.) If B¹0, then we must consider them factitiously derived. The formula of the derivation of a bicatenal monovariant neutrality-moreness- or -increase-catena is û2 = A | û1 | + B (A¹0 and B÷A<0). Thus B¹0 and also û1¹0 if û2=0. Hence, all modulus-catenas are derived in a factitious fashion. Bivariant comparative catenas, on the other hand, are nonfactitious if one takes E=0, because û2=0 determines neither E in û2 = e (û1,1,û1,2) + E nor û1,1 or û1,2. The reason to distinguish factitious from nonfactitious derivations is that this creates additional clarity with respect to the relationship between physical 'reality' (or theory) and catenical theory. The recognition that a predicate's or catena's transformation is artificial is of importance where the exact assessment of the neutral, empirical value is concerned. The terminology underlines that the choice of a special, polar value of the value collection of the original catena as the new 'neutral' catena value, and the assignment of some positive or negative value to the constant E, is farfetched if such derivative 'neutralness' is meant to be of universal significance. The choice of any value other than 0 for û1 if û2=0, or for the constant, is then purely arbitrary. (Where such a choice is not arbitrary we are dealing with special sets of catenals in closed systems, something we shall discuss in the next division of this chapter.) The variety of possible, factitious and nonfactitious, transformations could lead to a situation in which different empirical conditions would correspond to the same sort of catenated 'neutrality'. But because of the central role of neutrality in the catenary structure it is especially ambiguity with regard to this predicate which should be avoided as much as possible. Interaction between different catenas derived from one and the same original catena can give rise to incompatible conceptions in which the neutrality of the original catena, or the one derivative catena, is the polarity of the derivative, or another derivative, catena. Such confusion does not exist where the original catena's neutrality remains a neutrality in the derivation, and it need not exist where the derivation itself generates a new empirical perspective (as in the case of differential catenas) or where the catenals of the original catena are not the catenal of the derivative catena (as in the case of monocatenally derived difference catenas). Just as there is a rule in mathematics that evolution goes before multiplication -- 2×3××2=18, and not 36-- and just as one can make known one's deviation from this rule by means of additional symbols --(2×3)××2=36--, so we shall for the sake of clarity adopt the rule that nonfactitious goes before factitious with regard to catenary derivations. This rule of nonfactitious priority reads in full: "unless it is mentioned explicitly, or is implicit in its definition, that a predicate or a catena to which it belongs has been transformed factitiously, this predicate or catena is taken to be derived in a nonfactitious way". This rule does not affect the sign of the monopolarities; and rightly so. Whether a monopolarity is evaluated positive or negative, and its opposite the other way around, is of no import so far as the catenary structure is concerned. According to the rule of nonfactitious priority predicates such as normality and abnormality are each other's catena supplement and not opposite. By assuming their relationship to be one of catena supplementation they constitute a nonfactitious catena, namely the abnormality catena of which normality is the neutrality. This means that something that or someone who deviates in only the slightest (recognizable) degree from the mean or 'mode' is, strictly speaking, already 'abnormal'. If we considered the relationship between normality and abnormality to be one of opposition, these opposites would constitute the normality catena, but this catena is a necessarily factitious, comparative catena (with the abnormality catena as an original catena and one degree of original abnormality as the arbitrary, new limit of derivative 'normality'). Should one speak explicitly of a normality catena, or the neutrality-moreness catena of the abnormality catena, normality (as a positivity) and abnormality (as a negativity) will be opposites. For predicates like slowness and fastness the factitiousness of their derivation follows already from the meaning of slow and fast (since the type of comparative catena to which they belong is always factitious). Thus whatever speed we take as high (fast) or low (slow) is arbitrary from a universal point of view. But let us assume that in a certain context 10 km/h is 'slow'. Is then an object which moves in a negative direction at a rate of 10 km/h negatively or positively catenal? Without further qualification the answer is that it is negatively catenal. Only with respect to the slowness catena --if mentioned explicitly-- is it positively catenal. And without further qualification it is neutrally catenal if it is at rest, however 'extreme' its slowness may be in this case. Such is of course not to play down the fact that motion and rest are necessarily relative concepts themselves, given the absence of any absolute and universal, spatial frame of reference. 2.6 THE SCOPE OF CATENIZATION 2.6.1 THE OBSCURITIES OF A CLASSICAL PARADOX Imagine that a theorist approaches you and asks you whether somebody whose height is 150 cm is short or tall. Suppose you answer that such a person or --to be precise-- such a body is short. Suppose, too, that you further admit that somebody who is only 1 mm taller than somebody who is short, is also short. Your interrogator may then keep going and eventually force you to conclude that somebody whose height is 200 cm or more is still short. 'E will be ready to point out that this is a paradox, because you would agree with 'im that somebody who is 2 meters tall is tall, and not short. Your paradoxical partner of discourse may also employ other examples. 'E may tell you that somebody who runs from one city to another will remain far from that city forever, because 'e started out far away, and being merely 1 dm closer will keep the runner always 'equally' far away. Or, 'e may have you agree that one grain of sand is no heap of sand, and that one grain more will still not make a heap of what is no heap. Nevertheless, you will be stuck at the end with a gigantic amount of grains of sand which you have not been allowed at any moment to start calling "a heap". It is such a 'heap' this kind of paradox derives its classical name from: sorites. Crucial in these paradoxes is the inductive statement that P(n) implies P(n+1) for all n. P(n) is, then, a propositional function reading something like "the thing T has the predicate P if it consists of not more than n grains of sand" or "... has a height of not more than n mm", and so on. To defuse the sorites paradox several solutions have been offered. Some logicians have maintained that the statements are false or that the general premise is somehow illegitimate and is neither true nor false in that it does not have a truth value. Others have given up bivalent logic altogether and have introduced a many-valued logic to 'solve' the antinomy. Especially when applying a 'logic of accuracy' it would seem that ordinary logic could remain applicable to so-called 'vague' concepts like short and far. In such logic propositions are not simply true or false, but it is assumed that there are also intermediate degrees of truth, and truth-values themselves are identified with accuracy values. On this view the accuracy of somebody's being short would be greater to the same degree as 'e would be shorter. The whole idea hinges very much on the assumption that there would be only one shortness predicate and that a body has this one predicate to a greater or lesser degree. Apart from this assumption, it appears also to defy the fact that one can be equally sure that two things which are not equally short are both short. The statements in which one expresses these opinions may be equally accurate. Is it necessary for us to take part in all kinds of artificial resolutions of the sorites paradox? And is it really an antinomy we all have to suffer from? Or are we just made to believe that there is something wrong, because we cannot prove that everything is all right? To find this out we should not immediately plunge away into logical or mathematical formulas, but start at the beginning, that is, the phase which precedes these formulas. One of the first questions is then what it means that someone says that somebody is short, or that a city is far away. Theoretically, these meanings must either be related to those of opposites such as tall and close, or be entirely dissociated from the meanings of such related expressions. If terms like short and far are related to their opposites, they are treated as catenary notions; if not, then as some sort of absolute notions. As catenated predicates shortness and farness, however, presuppose the existence of a particular catenary entity, and the meaningful use of the corresponding predicate expressions presupposes the psychological availability of such a catena as a frame of reference. So there are two options open to the theorist. Firstly, the predicate mentioned in the original premise is catenated, but then there is somehow a catenary frame of reference. Or, secondly, there is no catena involved whatsoever, but then the predicate is in some sense absolute and not (necessarily) opposed to what is ordinarily taken to be its opposite. Someone could indeed say without making use of any particular frame of reference that a body of 150 cm is 'short', but then it would in no way be contradictory to conclude later that somebody of 200 cm were 'short' as well, or even both 'short' and 'tall'. It is only contradictory if we do make use of one and the same frame of reference in the two cases, and if the predicate corresponding to 150 cm is a shortness predicate on this view, whereas the one corresponding to 200 cm is not (because it is tallness or a predicate medium tall). The schizoid lover of paradox wants us to meaningfully say that a body of 150 cm is short (something we can solely do by means of a catenary frame of reference psychologically available to us) and having done so 'e forbids us to use this internalized information for a while until we must use it again to conclude that a body of 200 cm would not be short. The logic of the sorites lover may be sound but 'e draws on a pre- or extra-logical inconsistence. 'E should either assume that catenary comparison is possible all the time or that it is not possible at any time. In the latter instance, the short and far of the premise just do not mean what they mean in ordinary language. And if a general, catenary comparison is possible all the time, we do not entirely depend on a comparison with a smaller degree of shortness or farness of the particular body or distance concerned. We can then compare every degree of shortness or farness with what we would ordinarily call "short" or "far" (just as the theorist asks us to do at the beginning and at the end). Of course, this still leaves us with a wide, fuzzy area between short and tall, and between far and close, but that is not what the paradox is about. The paradox is about things which would be 'short' and 'tall', or 'far' and 'close', at the same time, while short and tall, or far and close, are opposite catenated predicates which cannot be possessed by one and the same thing at one and the same moment. The supposition that the inductive premise on which the paradox depends is false, is equivalent to the supposition that there is some n for which P(n) is true and P(n+1) false. It has been argued that this supposition is untenable, because something that is far at time t and not far, say, one second later, would have to have moved a considerable distance. But negation and opposition, and logics and pragmatics, are mixed up here. Firstly, to say that something is 'not far' does not yet mean that it is 'close'. And secondly, if something has moved over an incremental distance which can even not be recognized as a case of coming closer, it does only not make sense in practise to speak about the object's being far first and its not being far one second later. It does not follow tho that the object would not have moved at all, and that it could not have crossed a more or less theoretical borderline in the meanwhile. And this borderline between far and not far is in practise one between far and a perineutral neither far nor close, rather than between far and close, or between far and a neutral neither far nor close. Moreover, if we took a larger unit of measurement (something that is not a logical issue), there would be nothing remarkable about P(n) being true and P(n+1) being false. For example, if n is the number of half meters, S(3) is true (somebody who is 150 cm tall is short) and S(4) false (somebody who is 200 cm tall is short). It has also been argued that there could be no sharp boundary between shortness and tallness, farness and closeness, and so on, because empirical reality would exhibit no discontinuity. This, however, is an odd statement if we realize that it is precisely the function of the introduction of the shortness- and closeness-catenas to reduce the number of length predicates (which is practically unlimited) to two or three. Saving empirical continuity could then only mean that we would not be allowed to speak of "short" and "far" at all, but only of the exact distances involved. Given that this is ultimately not possible either, one always sacrifices that 'continuity' however small one would take one's unit of measurement, unless there is a smallest unit corresponding to separate length predicates which can be individually recognized or measured. But even in that case one could not have been permitted to speak of short or long in the first place. We have now had enough of the dire confusion of patients suffering from 'soritis'. What remains very interesting nevertheless is the question of the psychological availability of catenary frames of reference, not only where it concerns extremities or non-perineutral polarities, but where it concerns all catenated predicates, perineutral or not. What particularly deserves our attention here is the question of what could determine the boundaries between concatenate predicates, and the question of how sharp they are in practise. 2.6.2 SPECIAL AND UNIVERSAL CATENIZATIONS It depends on the context what one calls "small", "medium large" or "large" and, furthermore, on the size of the things one is familiar with in such contexts. This familiar is, then, a psychological notion: to be able to call some things "small" and other things "large" it is not necessary to see all these things together at one and the same moment. It certainly is the easiest and most accurate way of comparison, but it is not a prerequisite for the meaningful use of terms like small and large, for we do have a memory which does not only make us remember physical sounds or sound combinations like small, medium and large, but also objects of a small, of a medium and of a large size. In both cases the things remembered are of the same physical or perceptional nature, especially when taking loud, medium loud and soft as examples of catenated predicate expressions. The confrontation with new things in the same context may change someone's idea of what is 'small' or 'large', 'short' or 'tall', and so on. Thus, if someone has always lived among adult people whose average height used to be 160 cm, and then moves to an area where the average height of adult people is 200 cm, 'e will eventually start calling people "short", whom 'e used to call "tall" or "medium (tall)" before. On the other hand, if someone had never been confronted with anybody else, and only knew 'er own (body's) height in terms of centimeters, 'e would have no idea whether 'e were 'short', 'tall' or something in between; at least, 'e would have no reason to consider 'imself unneutrally catenal, that is, short or tall. The fact that the use of predicate expressions like small, short and close is context-dependent implies that we do not compare a catenal with all other things in the universe that are catenal with respect to the same catena, but only with catenals in a particular proper subset of this universal set. And the fact that we may describe two things with the same physical dimension in different catenical terms means that the context or special subset also determines where we draw the line or fuzzy border between smallness and largeness, between shortness and tallness, between closeness and farness, and so forth. Hence, the transformation from empirical to catenical value is related to a special collection of catenals, not to the universal collection of all catenals. That is why we will say that the scope of catenization is 'special', rather than 'universal' in these instances. To compare a catenal with a number of other catenals from a catenary angle is in the first place to compare it with their mean value. Unlike their minimum and maximum value, and unlike their statistical mode, this is a truly general value of such a collection of catenals. If it is the mean of all the things that are catenal with respect to the same catena, it is a universal value. A catenization in which this universal, mean, empirical value is taken as a neutral catenical value is therefore a catenization of universal scope. Whether this mean is an average or an arithmetic mean, however, depends on the type of catenization function. In general: a mean value is the value m for which n k(m) = SIGMA k(vi) / n. i=1 If ûi [vi with a caret over the v, the symbol for the catena value] or k(vi ) = A*vi + B, then m is indeed the arithmetic mean; but, for example, if k(vi ) = A*log vi + B, m is a geometric mean; and if k(vi ) = A*1/vi + B, m is a harmonic mean. The mean value can also be taken as a neutral value if the catenization is special. It is, then, simply not the mean over the class of all the catenals but over a proper subclass thereof. It depends on the relevancy of the distinction drawn between the class of catenals taken into consideration and all the other catenals whether this can be justified. But in a closed system the mean can be based (or 'must' be based) on the mean of this particular system itself. This can have no repercussions on communication, because where there is communication the persons communicating cannot belong to different closed systems themselves, even if vehemently disagreeing. If someone belongs to a tribe, for instance, which never had any contact with other tribes, it does not matter that 'e bases 'er closeness- and smallness-catenization entirely and solely upon the distances and sizes of catenals in 'er own environment. It is not until 'e comes into contact with persons belonging to other tribes with different catenizations, that 'e cannot treat 'er own special collection of catenals as a closed system anymore (and neither can those other people). The referential collection of catenals compared with has now to be extended, but in practise it cannot be extended so far that it would comprise all the things in the universe that are catenal with respect to the same catena. 2.6.3 WHERE NEUTRALITY DETERMINES THE MEAN To take the mean value m of a special or universal collection of catenals as the neutral value is tantamount to assuming that k(m) = 0, that ______ ___ k(v) = 0 and that v^ = 0 [v with a caret over it is the symbol for the catena value]. It cannot be proved that the mean value is always the neutral value, and vice versa. And to be able to disprove it, one would first have to make clear whether such a claim is a linguistic, psychological, physical, normative or other kind of claim (or all at once). Moreover, one would have to agree on the type of catenization function and the exact form of catenality to be chosen in each case. Here we shall treat the equality of neutral and average or mean value merely as a postulate, albeit a challenging one indeed. The simplest mathematical form of this hypothesis of mean-neutrality is: ___ v^ = 0 (the mean catena value is 0). It applies to every independent form of catenality, and both to universal and to certain special catenizations. For special catenizations the distinction between catenals taken into consideration (and included in the mean) and all other catenals (not included in the mean) must be relevant. As already suggested, one may suppose that such a distinction is relevant if the catenals belong to a closed system. The hypothesis of mean-neutrality can be read in two directions: (1) given the neutral value (that is, its empirical equivalent), the mean is equal to it in a closed system or in the world at large; and (2), given the mean, the neutral value is equal to it. We also assume that the derivations are nonfactitious, if possible; this in accordance with the rule of nonfactitious priority. It should be interesting to first have a look at one or two cases in which the neutral value is given, before turning our attention to cases in which the mean is given or calculable. With regard to the energy increase catena increase of energy (or gaining energy) is positive, decrease of energy (or losing energy) negative, and neither gaining nor losing energy, but having a certain amount of energy nevertheless, neutral. According to the hypothesis of mean-neutrality no energy will 'melt' into nothingness in a closed system and no energy will 'spring' from nothingness, since the mean energy increase in such a system has to be 0. The independent form of catenality concerned is, then, not energy as distinct from mass but energy inclusive of mass. If there is energy (including mass) which does seem to disappear into or to arise from nothingness, the physical system in question is simply not closed. This impossibility of a closed system's increase-catenary mean not being 0, and thus of energy melting into or springing from nothingness, is precisely what the physical definition of closed system rests upon. The hypothesis of mean-neutrality (or a more specific derivative postulate) thus underlies the very principle of the conservation of mass and energy, and similar, physical principles of conservation. It might be objected that altho the hypothesis of mean-neutrality may hold in certain cases it does not hold in other cases. Yet, if someone believes to know a counterexample, it is imperative that all the basic assumptions are checked again. Take, for example, the suggestion that it would be false or absurd to assume that in a closed system all the objects are on the average (if the catenization is linear) at rest. Why could there not be more movement in one coordinate direction than in the opposite coordinate direction (granted that a closed system need not be spatially closed in all directions)? The flaw in this reasoning is that the movement of objects in the closed system is related to an external system, that is, a system in which we live ourselves, or a system of which the first, closed system would form part. But motion catenization with respect to that different or larger system (even if 'universal') is not relevant if the first system is a closed system at all. If it is, then rest in this system is the mean displacement per second; and the mean displacement per second in the two directions of a coordinate is then 0 in this particular system with respect to the coordinates of this system. That the average change of place may not be 0 with respect to a system in which we ourselves call things "at rest" or "in motion" is just not relevant if we are really talking about a closed system. 2.6.4 WHERE THE MEAN DETERMINES NEUTRALITY AND MODERATENESS As regards the original catena of the energy increase catena no neutrality is given, since energy in this sense is always nonnegative. Taking the mean energy of all objects in the closed system mentioned above, this mean would, then, only determine the amount of energy under which an object does have little, and above which an object has much energy, at least if no perineutrality were to be distinguished. Unlike the increase-catenary mean, which is always 0, this mean is variable in physical terms. It changes as the number of objects changes (because of fusion and fission, for instance). If someone did not have the slightest idea of what a short or tall, adult person would be, and 'e were confronted with (the body of) an adult person of a height of 150 cm, 'e might call that person "short" if 'e is shorter than 'imself and "tall" if 'e is taller than 'imself (that is, so much shorter or taller that it is noticeable). The average height in this imaginary, closed system would be a height between that of 'er own and that of the other person's body. If a third person turned up of exactly this average height, 'e would be called "neither short nor tall" or "of middling height" (assuming that the catenization would be linear). Yet, this picture is not a realistic one, because in practise everyone who knows how to use the words short and tall has already compared heights many times, and will also have an idea already whether 'e is short, medium or tall 'imself. Moreover, 'e will always use the expressions in such a manner that short, medium short or medium tall and tall cannot denote one and the same person or thing at a time. Such a person who knows how to use the expressions has already formed some mental frame of reference before facing a person 150 cm tall 'e is able to call "short". Even if 'e merely compares the other person's height with 'er own height, 'e has still to know whether 'e is short or tall or of middling height 'imself. Knowing this, 'e knows roughly what height is that of adult people who are neither short nor tall. Thus when the other person thereupon starts growing many mm consecutively (as in the imaginary sorites example), 'e only has to compare that other person's height with 'er own height and with what is the normal (neutral) or moderate (perineutral) height in 'er frame of reference. This means nothing else than that 'e sticks to the procedure 'e started out with, when 'e called the other person "short" the first time. The hypothesis of mean-neutrality implies that an adult person who has the mean height of all the adult persons belonging to a real or imaginary group on which the shortness catenization is based is neither short nor tall. Like in the case of the amount of energy objects have, this mean is variable in a physical sense. It is particularly variable because the limits of the special collection of catenals are very vague themselves -- there usually is no completely closed system in this respect. That is why it is not sensible from a pragmatic point of view to emphasize the mean value of one special collection of catenals at one particular moment. And we are usually not able to measure this mean either; we would just have to estimate it. Thus even granted that the mean, theoretically speaking, exactly determines the neutral value of the catena for the special collection concerned, it still does not make the boundary between positivity and negativity sharp in practise. Moreover, it should not go unnoticed that by the very addition to the collection of catenals of one object to be judged, the mean and neutral value itself moves in the direction of the value of the object to be judged. As there is no sharp boundary between positivity and negativity in practise when the neutral value is not clearly given, neither nor does usually not refer to neutrality here, but to perineutrality, together with medium, middling and moderately. Since the position of the neutral value is hard to establish, the perineutralities of such catenas remain recognized as such in common parlance. Where the boundary between positivity and negativity is sharp, and where the neutral value can easily be assessed, perineutralities tend to disappear and to reemerge as the positivity of a neutrality-moreness catena (as in the case of slowness). It is because of the practical impossibility to calculate the universal mean value that the scope of catenization must always be special when the derivation is factitious and the position of the neutrality not sufficiently clear. 3 ABOUT WHAT IS, CAN AND SHOULD BE 3.1 THREE TIMES, THREE SPHERES 3.1.1 TO BE IN TIME OR NOT TO BE IN TIME 3.1.1.1 ---------------------------------------------------------------------------- TEMPORAL AND NONTEMPORAL TRUTH To say that something did have what it did have, or that it did not have what it did not have, and to say that something does have what it does have, or that it does not have what it does not have, and to say that something will have what it will have, or that it will not have what it will not have, and to say that something has what it has, or that it has not what it has not, is true. [This is a variant and extension of a classical, philosophical dictum.] ---------------------------------------------------------------------------- We have been talking about things having component parts, attributes and relations, about wholes having whole-, part- and pseudo-attributes, and about catenas having one or more positive predicates, one neutral predicate and one or more negative predicates. But what does it mean to say that a certain thing 'has' or 'does not have' a certain part or predicate, or what do we suppose when saying this? A thing can have a part or predicate now without having it in the past or in the future, if its having is temporal. The relation of having is nontemporal, if its having this part or predicate in no way depends and can depend on the moment we look at it or talk about it. This might be the case with all relations of having in the second domain of discourse. Things in that domain did not have, do not have and will not have something in a temporal sense -- so it seems. At least the predicates catenas have they do not have just now. Catenas definitely have their component parts in a nontemporal sense of having. To have an element in a nontemporal sense is something else than to have it forever or eternally. Eternity presupposes temporality, and --it seems-- solely primary things could have something eternally, that is, at every moment in the past, now and at every moment in the future. (Hence, they are certainly not 'timeless' in a strict sense.) When we talk about things having parts and predicates in an ontological context we consider their situation from a nontemporal standpoint, but as regards primary things this does not imply that their having a part or predicate is itself nontemporal. Everywhere where we say that a primary thing 'has' a particular part or predicate (without making explicit that it has that element now), has and have must be understood to mean did have and/or do(es) have and/or will have. Did have, do have and will have correspond to did exist, do exist and will exist or to existing in the past, existing now or at present and existing in the future. One might wonder whether the fact that every real thing existed, exists and/or will exist does not mean that it would be 'time-catenal'. The 'time' or 'future catena' concerned would, then, be the whole of (existing-in-the-)past, (existing-at-)present and (existing-in-the-)future. Time itself would on such an account be a quasi-monad identical to the explicit triad of past (or earlier), present (or now) and future (or later). However, the reason that we shall not speak of "a time" or "future catena" is that it does not make sense to assume that there are such primary predicates like existing-in-the-past, -present or -future. It is rather the domain or universe of discourse itself which is temporal or considered at different moments in time. Another way of putting it is that it is the relation of having a certain part or predicate which is temporal. On the former view a sentient being that is happy, for instance, has the predicate of happiness in the present domain; on the latter view it is presently having the predicate of happiness. On neither view is being happy now a question of having some primary predicate of 'presentness' in addition to having the primary predicate of happiness. Yet, this is precisely what one would suggest by speaking of "a time" or "future catena". Even tho the notions past, present and future are not catenical, they do form part of a connected series. The name we shall use for such a series, which functions in a subsidiary capacity in our ontology, is auxiliary (series). Auxiliary series like those of past, present and future and of earlier, at the same time and later are, then, temporal auxiliaries. Altho such connected series can be divided into three subsets of which two appear or seem to be opposed to each other, they are not connected series of primary predicates, and therefore not catenas. 3.1.2 THE TRIADIC SPHERICITY OF REALITY 3.1.1.1 ---------------------------------------------------------------------------- THE THREE SPHERES OF INCLUSIVE TRUTH To say that something does have what it does have, or that it does not have what it does not have, and to say that something can have what it can have, or that it can not have what it can not have, and to say that something should have what it should have, or that it should not have what it should not have, and to say that it is not the case that something should have or should not have something when it is not the case that it should have or should not have it, is true. ---------------------------------------------------------------------------- When asserting that a thing has a certain part or predicate, this does imply that the thing in question can have this part or predicate but not that it is probable, neither probable nor improbable or improbable that it has it. And it does not imply that it should have it. When asserting that it can have such a part or predicate, this does not imply that it has it or that it should have it. And when asserting that it should have the predicate concerned, this does not imply that it has it either, nor that it can have it. (Ought implies can may be a useful ethical axiom, it is not an ontological proposition.) Thus in our discussion on the question of the parts and predicates which things have, we have until now restricted ourselves to one of three spheres only: the sphere of what is, of having, as distinct from what is possible or probable, or can be had, and as distinct from what should be or ought to be had. The sphere of having (and hence of being and doing) we shall call "the factual sphere". This sphere encompasses facts, events, situations or the world as it is, but not the mere existence of things independent of time and of their having other things or being had by other things. The three spheres only distinguish themselves with respect to relations, such as the relation of having-as-an-element, and such relations, or the absence thereof, presuppose the existence of the things related or not related. The existence of things per se is therefore not a fact as distinct from what is possible or should be. It is the existence of nonbasic things with particular parts or predicates which is a fact --or not a fact-- because such existence depends on the having of a certain kind of element. In the strict, basic sense one may speak of "a fact" when there is a relation between two things or types of thing. In a less strict, less basic sense a 'fact' may also be privative, when there is no relation between two particular things or types of thing. It may also be a complex of basic and privative facts, not unlike a 'situation'. In an even looser sense, a 'fact' may also be a true proposition in which the relation in question is mentioned. In any case it should be clear why we cannot see or feel facts in a literal sense: even if they were identical to the relations themselves, these relations would only be things in the second domain, not in the first domain to which we belong ourselves. They are not identical to those relations, because they exist 'always' in a nontemporal sense, whereas facts are temporal and only 'exist' when there is a particular relationship or type of relationship between particular things or types of thing. The sphere of the possibility of having (being, doing) something we shall call "the modal sphere". Regardless of the question whether a state of affairs does occur or does not occur, one can ask whether it is possible or impossible, necessary or contingent, probable, neither probable nor improbable or improbable. Only when it is impossible may one conclude that it cannot and does not occur, and only when it is necessary may one conclude that it must and does occur. When it is possible that a thing has a certain part or predicate, it is improbable (but not impossible), neither improbable nor probable or probable (perhaps necessary) that it has it. When it is contingent, it is not necessary, that is, again, improbable (perhaps impossible), neither improbable nor probable or probable (but not necessary). Expressions like possible and probable are not second-order predicate expressions, because they do not denote the predicate of a first-order predicate. Their different ontological status, which is similar to that of facts, lies in the way they relate things to other things (parts, predicates or external things). Like future and later, expressions such as possible and probable do not refer to primary predicates, while forming part of a connected series nevertheless. The first such series is, then, the series of necessary, possible (but not necessary) and impossible; the second one that of probable, neither probable nor improbable and improbable. When these two series are combined into one, the result looks very much like a catena, and one would be tempted to give such a series the name of an explicit triad: probability catena. So long as this full name is used, confusion is hardly possible, but there are two reasons why the series in question is not a catena. Firstly, its component parts are not primary predicates; and secondly, the number of component parts is not necessarily three or more. For example, if a relation or situation is either necessary or impossible, without intermediate degrees of probability, then the quantity concerned is binary and could not be catenary. (A factual quantity which is 1 when a relationship exists between two particular things, and 0 when it does not exist, is not catenary either.) The auxiliary series of necessity, impossibility and all the elements in between is a modal auxiliary. The terms must, may, might and can used in these contexts are also called "modal auxiliaries" by grammarians. The values of these modal auxiliaries (that is, auxiliary elements) vary between -œ (or 0: impossibility) and +œ (or 1: necessity). Adjectives typical of the modal sphere are able and capable when employed in the same or a similar sense referring to an ability or fitting quality. Such an 'ability' or 'fitting quality' is not an attribute on our ontology but is something a thing may be said to have if it can have a certain relationship with another thing, for example, if it can repair that other thing. The ability does not imply that it is probable or likely that the relationship will actually exist between the things in question. All it implies is that it is not extremely improbable in the strictest sense, that is, impossible. The concept of modality as expressed by terms such as can, (cap)able and probable needs much more analyzing but suffice it here to stress the difference between what is purely factual and what is modal, at least in some way. Just as we can distinguish an ontological auxiliary pertaining to modal conditions in a modal sphere, so we can distinguish an ontological auxiliary pertaining to normative conditions in a normative sphere. Also these conditions are in the first instance as little factual as their modal counterparts, and also these conditions admit of degree: something can agree with a normative standard to a greater or lesser extent. Instead of speaking of "probable" and "improbable" we speak of "superior" and "inferior" in the case of such a normative auxiliary (or in similar terms like good, better, (more) proper and bad, worse, less proper or improper). Also the values of this auxiliary series vary between -œ or -1 (most inferior) and +œ or +1 (most superior or supreme). Inferior and superior are used, then, in a normative and absolute sense. They should not be confused with the same terms used in a nonnormative and/or comparative sense. A term like ought, and terms like should and must, when used to describe normative conditions, are called "modal auxiliaries" too in traditional grammar. This universal employment of modal merely contributes to the confusion of the different ontological spheres in everyday language. On our terminology they should be termed "normative auxiliaries" (and words like will when used to form tenses, "temporal auxiliaries"). The correspondence, or lack thereof, between auxiliary terms like should and must in ordinary language on the one hand, and modal and normative conditions on the other, is illustrated in the following scheme (in which A is a primary thing, and p a primary predicate): * A can/may have p = it is possible that A has p = (the having of) p is possible with respect to A * A probably has/should have p = it is probable that A has p = (the having of) p is probable with respect to A * A must have p = it is necessary that A has p = (the having of) p is necessary with respect to A * A ought to/should/must have p = it is (normatively) superior/good that A has p = (the having of) p is (normatively) superior/good with respect to A 3.1.3 THE REALNESS OF FACTS, MODES AND NORMS What is factual relates to factual conditions or facts; what is modal (impossible, improbable, and so on) relates to modal conditions or 'modes' --as we shall call them-- and what is inferior, neither inferior nor superior or superior relates to normative conditions or norms. Each one of these three types of entity has its own ontological status, and none of them is more real or concrete than the other. Skeptics might object that norms, unlike facts, do not exist, except maybe as factual, propositional attitudes or expressions thereof -- as cultural or subcultural norms that is. They may add that we cannot perceive them thru our senses, and that we cannot arrive at them in a rational and/or objective way. But that we cannot perceive them is no reason at all to reject their existence. It is also impossible to perceive predicates and the thoughts of other people. More importantly, it is also impossible to perceive facts. The skeptic may now rejoin that we may not be able to see facts, but that we are able to decide from what we see what is a fact or not. Yet, if 'e is a skeptic at all, 'e must admit that 'e merely sees patches of different colors and tones, and that 'e cannot immediately derive from a white patch in 'er own visual field the 'fact' that 'e sees, say, a white piece of paper, let alone that this piece of paper is white in some objective sense. It is not that plain either what would be a fact in a field like, for example, nuclear physics, where the connection between what is observed and what is called "a fact" is far remoter. Factual statements always or usually require an additional cognitive processing, that is, a lot of extra reasoning, and one should not allow this in the factual sphere while disallowing it in the normative sphere. It is precisely the question of how to arrive at norms in a way which does not basically differ in plausibility from the assessment of facts which is a major challenge of this whole Model. Skeptics might also query the definition of the word norm . This is a very difficult question indeed, yet not different from the problem of how to define a 'fact'. We are able to define norms without being able to exactly and satisfactorily define what a 'norm' is, just as we are able to define facts without being able to exactly and satisfactorily define what a 'fact' is. If we assert that a norm is what one or a thing ought to have, to be or to do, then this leaves us with the question of what ought means, just as the assertion that a fact 'exists' if, and when, there is a relationship between two things leaves us with the question of what is means. (Compare the assertion that a norm 'exists' if, and when, there ought to be a relationship between two things.) And if we assert that a norm is what makes a normative proposition true or correct, then this leaves us with the question of what true or correct (and normative) mean, just as facts also leave us with the question of what true means (that is, correct with respect to descriptive or factual propositions). Or, if we assert that a norm is what makes a state of affairs proper or superior, then this leaves us with the question of what proper or superior mean (independently of the content of a particular norm), just as the statement that a fact is what makes a state of affairs occurring leaves us with the question of what occurring means. All these considerations show that the 'realness' of factual, modal and normative conditions is in principle the same. There may be gradual differences but either all three spheres are real or none of them is, and either all three of them are impenetrable or none of them is. The notions fact, mode and norm are not only distinct notions (or factual, modal and normative conditions not only distinct entities) in the world of things like positrons, plants and people, they are also distinct notions (or entities) in propositional reality, that is, the world of thoughts and propositional attitudes. Also then norms are not facts (nor are modes or probabilities). Yet they have been, or still are, not seldom looked upon in this context as mere psychological and/or sociological data. This is understandable because in the realm of individual and social behavior there is a more or less complex pattern of standards indicating what is expected or considered normal, and referred to when judging the behavior of oneself and of others. It is this pattern, or these standards, which are (also) called "the norm" or "norms". Most of these cultural or subcultural norms, however, do themselves not pertain to propositional reality (to what one should think or how one should reason) but to nonpropositional reality (to what one should be or do). Having an opinion on what should be, or thinking about norms, affects the position of the normative as little as thinking about facts or modes affects the position of the factual or the modal. From an ontological angle normative conditions do not belong less or more to the realm of propositional attitudes than factual and modal conditions do. Some might believe tho that there is a difference in scope, that the range of facts and modes is the whole of reality, whereas the range of norms would merely be the behavior of people or human beings. Even if this were always the case, it would not render the behavioral norm ontologically dependent. What one ought to have (to be or to do) according to such a norm might still be entirely different from what would be normal or expected according to a factual, psychological or sociological pattern or standard (however large a majority would support such a cultural norm). The question whether a norm in the ontological sense does always exclusively govern the behavior of human beings or persons is a subject of normative philosophy and ideology because it concerns the actual content of norms, at least as far as nonpropositional reality is concerned. Since it is always persons who have thoughts (corresponding to propositional attitudes), ontological norms which relate to propositional reality, that is, propositional norms, do indeed concern (the propositional attitudes of) persons -- another content is not possible. But, conceptually speaking, norms may for any thing specify what relation it should have with whatever kind of other thing, whether it is human or nonhuman, living or nonliving, a thought, or something else. The function of those things for people or human, or other, living beings does not matter either from a general ontological point of view. 3.1.4 THE SPHERE A THING REALLY IS IN There is another reason why norms may have been looked upon by some people as facts, rather than as separate ontological entities. It is simply because ordinary language is fraught with ambiguities. This is especially evident where modal and normative thought are formulated in a pseudofactual fashion and modal thought also in a pseudonormative fashion (if not the other way around). For example, when asserting that the chance that something will happen is small or big, this chance's being small or big is presented as a fact, and the proposition this chance is small as true or false. As suggested before, confusion between the modal and the normative may result too from mixing up may for what is possible (a modal auxiliary) with may for what is allowed, because it is not bad or wrong (a normative auxiliary). Or, it may result from mixing up must for what is necessary (a modal auxiliary) with must for what is obligatory because it is good or right (a normative auxiliary). One must eat to live is not a normative statement but expresses the modal condition that one can only stay alive if one eats. In you must do it must is a factual-modal auxiliary, if it refers to the consequence that probably will follow, if one does not do something. It is, then, an obligation in a social or subcultural context but not as such in a normative context (altho it may happen to be normative at the same time). In a normative context something is a duty or obligation regardless of the consequences (such as punishment) which might follow, if one does not fulfil one's duty. Similarly, also the notion of right can be either a factual-modal or a normative concept, whereas commandment and prohibition are basically factual-modal notions. Whether must and may are normative or not depends therefore on the context, even when there is talk of duties or rights. It is possible to define right and duty in terms of it is (not) the case that one should (not), that is, of should (as we shall see in chapter 8), and for that reason it is not necessary to adopt a separate sphere of rights and duties besides that of norms and values. When continuing our attempt to disentangle the factual, modal and normative threads of thought, we will find that even the word norm itself may be used for a modal standard rather than for an ontologically separate normative standard. When formulating something in a pseudodescriptive way in the normative sphere, one may say that the norm is this or that. This formulation seems particularly self-evident since it is feasible and correct to speak of psychological and sociological standards of (assumed or purported) normalcy in an empirical, 'descriptive' way. It may also be asserted that it is superior or good or proper to be or to do this or that. Also this is presented as tho it were a fact. The proposition the norm is to have .. or it is good/right to have .. is, then, said to be true or false. An interesting case of the pseudofactual representation of modal concepts is the mathematical talk about certain kinds of numbers and about infinity. Many mathematicians and logicians have believed that their imaginative constructions would be as real as their paper and ink, as long as they were free from contradictions. These mathematicians or logicians did not realize that they were merely talking about the possibility of existence, that is, merely about modal existence, and not about factual existence. For example, if infinity exists at all, then its modal nature is incorporated into the definition or concept itself. This is clearly so in the following definition of an infinite set: a set capable of being put into one-to-one-correspondence with a proper part of itself; and in that of infinity: the limit of a function which can be made to become and remain numerically larger than any preassigned value. To say that infinity in this sense exists is, then, not a factual but a modal statement. Other definitions, however, are pseudofactual, like infinite which is extending or lying beyond any preassigned value however large, or infinity which is unlimited extent of time, space or quantity or indefinitely great number or amount. It is especially these latter types of definition which do implicitly presuppose some kind of modality, but which only mention 'facts', which have caused people to believe that (the existence of) infinity would be of the same nature as that of this paper and ink. They have thus come to believe in numbers like in angels, and in sets like in gods. Even if there actually were no set in the whole universe with that particular dimension, they would still pretend that they would be talking about a fact rather than about a mode or modal condition. The modal nature of a thing may be apparent from the use of can or (cap)able in its definition, it may also lie in the reference to its function. This is the action for which a thing is specially fitted, that is, can be used. One and the same word may even have different meanings dependent on whether the accent is on the thing's function or on its form. Form is a purely factual concept denoting a thing's shape and structure. A 'stoma', for instance, may be described as a 'small opening like a mouth in form or function'. The meaning of stoma thus follows either a descriptive, factual definition of mouth (when taking the form of a mouth) or a functional, that is, modal, definition of mouth (when taking the function of a mouth). Many definitions, particularly of artifacts, are of a mixed factual-modal nature tho. For example, in seat with four legs and a back, as one of the definitions of chair, the having of four legs and a back is a factual form of having-as-an-element. The modal part of the definition is implicit in the term seat when this is defined as a thing (an artifact) which is made so that one can sit (comfortably) on or in it. A seat remains a seat also when no-one actually sits in or on it, and even when no-one should sit in or on it. A 'pen' is an instrument for writing or drawing with some fluid like ink. An instrument, in turn, has been defined as a 'means whereby something is achieved, performed or furthered' or 'is done or made to happen'. This is must be nonspheric, for if it were spheric, that is, factual, the definition would be erroneous. An instrument is not something whereby we necessarily do or make something in the factual sense (whether in the past, the present or the future); an instrument is something whereby we can do or make something, and this is a modal condition, not a factual one. When an instrument is defined as a 'tool used for delicate theoretical or practical work' (as in mathematical or medical instruments) used is nonspheric too, and must be read as (which) can be used. Just like a seat, a pen remains a pen even if no-one has used it, uses it or will use it, and even if no-one should use it. A pen is not only an instrument itself, it is also a handy tool for the construction of new instruments; that is to say, of new theoretical instruments. It is in this way that having a pen can contribute to the extension of our knowledge of what is, of what can be and of what should be. 3.2 NONPROPOSITIONAL AND PROPOSITIONAL REALITY 3.2.1 A HIERARCHY OF PROPOSITIONAL LEVELS In our ontological discussion of reality we have distinguished the first domain of reality from the second and higher-order domains. We ourselves and all animals, plants and nonliving, concrete things belong to the first domain, whereas attributes and relations, and catenas of attributes and relations, belong to the second. We have now also distinguished three spheres of reality which do not concern existence per se but the nature of the relationship between existing things. This encompasses the relationship between a thing and an attribute which it has or does not have, which it can have or cannot have, and which it should have or should not have. In practise this triadic sphericity of reality does only seem to make sense for the first domain of discourse for this is the domain in which we as persons can exert our influence, and can be influenced ourselves by what should be. The ontological system we have developed is a body of thought about existence, about reality. Until now it has been confined to those things (real or hypothetical) which were not thoughts or systems of thought themselves, and we have assumed that this reality is independent of the thoughts about it. Hence, when a person is (said to be) thinking about something, this thinking itself does not make it exist, nor does it cause it to have a certain part or determinative predicate -- at the most the thing may get a reflectional predicate as a result of this thinking (see 2.3.1). We vehemently reject the idea that all existence, and all facts, modes and norms, would be dependent of, that is, immediately occasioned by, thoughts or feelings about them (including sense perception). We even more vehemently reject the solipsist idea that all existence and the factual, modal or normative forms of reality would solely depend on 'my' mental processes, or the anthropocentrist idea that they would all depend on the mental processes of human beings only. Thinking may affect the existence and shape of certain things very much, but only indirectly after subsequent action has been taken. It is, then, the action which affects it, not the thinking itself in a strict, direct sense. From the perspective of the process of thinking reality consists of: * one or more persons thinking about reality (having thoughts about what is, can or should be); * thoughts (about reality as it is, can or should be); * the reality thought about (the rest being the reality not thought about). As we have, until now, only included into our ontological framework entities which are not thoughts themselves, we have not yet left the lowest level of a new ontological hierarchy: that of zero-, first- and higher-order levels of propositional reality. The zero-level is, then, the level of nonpropositional reality to which we belong ourselves as persons and as bodies. But also predicates and catenas belong to this level, and facts, modes and norms insofar as they pertain to relationships between nonpropositional entities. The term proposition will be employed here as a synonym of (primary) truth-bearer, as something that is true or false. This accords quite well with the etymology of the word and (one of) its lexical meaning(s). It depends on which theory of truth or truth-bearers one adheres to, whether a proposition (in this sense) is the same as the meaning of a sentence, a sentence, a sentence token, an utterance, a statement, or something else of that ilk. The availability of the concept of proposition is far more important here than the question of its final formal analysis, tho its use might give the appearance of wholly committing ourselves ontologically. However, all the claims in which we make use of the concept of a proposition, or in which we differentiate the propositional and the nonpropositional, are indifferent between the options mentioned. Whether a proposition is something abstract, such as a thought or the meaning of a sentence, or something more concrete, such as a sentence token or an utterance, we can (and must) tell a nonpropositional reality apart from a propositional reality. And, furthermore, it is essential that such a proposition is always about something. Propositional reality is the world of propositions or propositional attitudes. Attitudes are hypothetical constructs in which a person's diverse thoughts, feelings and tendencies to act are arranged into a more or less coherent pattern. The cognitive aspect of someone's attitude concerns 'er thoughts and beliefs; the affective aspect the feelings 'e has about something; and the conative, aspect the person's behavioral tendencies. The expression propositional attitudes, refers, first of all, to the thoughts and beliefs people have about reality as it is thought or believed to be. We shall not exclude the possibility that it also refers to people's feelings and behavioral tendencies if, and insofar as, they are expressed in or translatable into propositions or statements. Thus verbs of propositional attitude are not only verbs like to know but also verbs like to hope and to intend. Propositional reality is then also the world of feelings, intentions, conscious desires and tendencies about and with respect to reality as it is felt to be, intended to be, and so on. Thinking, however, is the phenomenon most typical of propositional reality, and we shall often only mention thoughts for the sake of simplicity. In the first instance thoughts are thoughts about nonpropositional reality, but they may also become the object of thought themselves, and also these thoughts about thought may, again, become the object of thought, and so on and so forth. Hence, whereas there is merely one level of nonpropositional reality from the propositional point of view, namely the zero-level, there is in principle no definite number of levels of propositional reality. Thoughts about nonpropositional reality constitute first-order propositional reality, those about first-order propositional reality, second-order propositional reality, and so on. However, second-order propositional reality does not only encompass thoughts about (or propositional attitudes towards) thoughts about nonpropositional reality, it also encompasses thoughts about (and propositional attitudes towards) the special relationship between first-order thoughts and nonpropositional reality. And this relationship may be factual, modal or normative, like any relation within first-order propositional reality. The beginning of this hierarchy of propositional levels is shown in figure I.3.2.1.1. It is obvious that when speaking of "lower" and "higher levels" in this hierarchy, the words lower and higher must not be given the connotation of worse or inferior and better or superior. We could have labeled the zero-level "the highest level" and every next level "a lower level". As in any objective, theoretical hierarchy these words have no evaluative significance. 3.2.2 DESCRIPTIVE, SPECULATIVE AND NORMATIVE THOUGHT We can think about the world as it is (was/will be), as it can be, or as it should be. If, and insofar as, our factual thought is merely a matter of observation or empirical experience, it is descriptive. Such 'descriptive' thought, however, may also concern modal conditions rather than factual ones, especially when it is stated that something is possible. In the case of thought about modal conditions it would be better to use the term speculative, or some such term, to denote that the process of thinking is not grounded in mere observation or actual sense experience, and that it is inconclusive in the factual sphere. Of course, one can also 'speculate' about facts and norms but the meaning of to speculate is then simply that of to think. Finally, normative thought unequivocally designates thought about norms, or about the world as it should be. The belief about what is possible or probable is a form of speculative (modal) thought, and the belief about what is good or superior a form of normative thought. Now, modal conditions --we have assumed-- are entirely independent of normative conditions, and yet this does not mean that the belief in what can be is not determined by the belief in what should be. Especially the belief in what cannot be, or is highly improbable, is but too often a mere expression of the lack of belief in what should be (and, similarly, the belief in what can be a mere expression of faith in what should be). But these facts are not facts of the same level as the modal and normative conditions the belief is about; they are facts of speculative and of normative, propositional attitudes themselves. Obviously there are different levels on which facts, modes and norms are operative. Let us use the word ground to refer to the zero-level of the propositional hierarchy. Nonpropositional reality is then the ground-level on which we live ourselves, at least as biological beings. Factual, modal and normative conditions on this level are 'ground-facts', 'ground-modes' and 'ground-norms' or 'factual', 'modal' and 'normative ground-conditions'. Thus, it is descriptive thought about the nonpropositional world in which we live which yields the ground-facts (if the propositions are true). In such thought the ground-world is described as it actually is. Speculative (and statistical) theories about the ground-world which show that states of affairs are impossible, improbable, neither improbable nor probable, probable or necessary yield the ground-modes (if true). And normative theories about the ground-world, if true or correct, supply us with the ground-norm or -norms of this world. On the first propositional level, descriptive (factual), speculative (modal) and normative theories are themselves objects of descriptive, speculative and normative thought on the second propositional level. A descriptive theory is, then, thus or so, can be thus and so, or should be thus and so. This applies equally to speculative and normative theories. That a descriptive theory about the ground-world is thus and so is, then, a first-order fact, whereas the proposition that it is thus and so is a second-order proposition. Similarly, it is a first-order fact that a normative theory has a certain characteristic, whereas the proposition that it has this characteristic is of the second order. The first-order facts of descriptive, speculative (or statistical) and normative theories about the ground-world are first-order facts of thought or 'first-order propositional facts'. Their first-order modes are, similarly, first-order modes of thought, and their first-order norms, first-order norms of thought. But the object of second-order theories is not only first-order theories. It is also the relationship between the ground-world and those first-order theories. If, and when, such a relationship exists, we call it "correspondence" (between the ground-world and a theory about the ground-world). The fact pertaining to this relationship is neither a ground-fact nor a first-order fact of thought as defined above. We shall call it "a first-order fact of correspondence". In the same way there are one or more first-order modes and norms of correspondence. The combination of propositional hierarchy and the division of reality into a factual, modal and normative sphere leads to a quite complicated, but systematic, conceptual structure. It leaves us with interesting questions we cannot treat here. One is whether all norms of descriptive, speculative and normative thought are the same, and another whether the first-order norms of thought and of correspondence are the same as the second- and higher-order norms of thought and of correspondence. If so, we need only speak of "the norms of thought and of correspondence". (One may also speak of "principles".) Yet, these questions do not concern our ultimate conceptual framework but rather the content of norms or principles. At this stage we shall not yet argue for any particular substantive norm or principle, let alone for the universal scope of such a norm or principle. Nevertheless, we cannot refrain from taking a look at the normative principles which remain implicit in thought which is purportedly purely factual, empirical or descriptive. 3.2.3 THE NORMATIVENESS OF 'PURELY DESCRIPTIVE' THEORIZING Both descriptive and normative theories (and also speculative or statistical, modal ones) need be coherent in order to be valid, and both depend on a number of axioms which must be accepted without proof. But --it has been contended-- which descriptive theory is 'true' can be empirically ascertained: it is verified if it corresponds with reality (the facts); falsified if it does not correspond with reality. Normative, ethical or moral theories --it is then contended-- cannot be empirically verified or falsified. But this in itself is a banality simply following from what empirical means: capable of being verified or falsified by observation or experiment. The underlying suggestion is tho, that there would be only one true descriptive or factual discipline, whereas all coherent, normative theories would or could be equally 'valid' however contradictory among themselves. In four steps it can be demonstrated that this kind of factualism is in complete error, and that every so-called 'purely descriptive' form of theorizing depends as much on norms or normative choices as an adequate normative discipline. Firstly, let us agree that there would indeed be solely one true, factual theory corresponding with reality as a 'unified whole', and that all other coherent, factual or descriptive, theories, and all incoherent ones, are false. This, then, would be a fact and ... not more than that! (Strictly speaking, only the true theory's correspondence with reality is a fact, whereas in the case of false theories there is no fact, or the 'fact' is a privative one.) It is not a fact tho, that an utterance or a complex of utterances ought to be true or ought not to be false: that is a norm -- a norm of correspondence to be precise. Thus, as soon as someone assigns a higher value to a theory which has been verified because it has been verified, or which has never been falsified because it has never been falsified, 'e is involved in a normative act or an act expressive of (the belief in) a norm (if it is not to be a mere question of personal preference). The suggestion, however implicit, that a true theory or truth is superior to a false theory or falsehood requires or presupposes a normative principle of truth. Hence, those who stress the need of empirical verification or falsification, and who reject untrue, factual or descriptive theories must also reject any and every normative theory that does not recognize a principle of truth(fulness) even tho that normative theory might be coherent. Secondly, no descriptive discipline could describe the whole of reality in all its details, and certainly covering law models do not do that. (Isolated factual conditions as such do not explain anything.) Every descriptive theory must confine attention to those aspects of reality it deems relevant. In itself it is simply a fact that some aspects or details are relevant, while others are not. But as soon as someone assigns a higher value to a theory or description which describes a relevant state of affairs than to an irrelevant theory or description, altho both theories or descriptions are true, 'e is involved in a normative act or an act expressive of (the belief in) a norm (if it is not to be a mere question of personal preference). The inherent suggestion is that a relevant description or relevance is superior to an irrelevant description or irrelevance, and this requires or presupposes a normative principle of relevance. Hence, those who demand a true theory or description to be relevant, and who reject irrelevant, factual theories or descriptions must also reject any and every normative theory that does not recognize a principle of relevance even tho that normative theory might be coherent and recognize a principle of truth. Thirdly, something is only relevant with respect to a certain entity looked upon as a goal, objective or value to be aimed at (as we will see in the chapter on relevancy). To treat an entity (a certain point of a scale, or a certain predicate of a catena, say) as a goal or objective is a normative act or an act expressive of (the belief in) a norm (if it is not to be a mere question of personal preference again). This requires or presupposes a normative principle which determines what the one or more goals are (or should be) with respect to which something is relevant or not. Hence, those demanding a true theory to be relevant with respect to one or more particular goals, and who reject factual theories irrelevant to this goal, or these goals, must also reject any and every normative theory that does not recognize a principle furnishing at least this particular goal, or these particular goals, even tho that normative theory might be coherent and recognize a principle of truth and one of relevance. (An example of such a goal may be the happiness of all happiness-catenal beings.) Of course, it may be that the developer of a 'purely descriptive' discipline will object that choosing goals is not 'er task at all, and that 'e 'has to' leave that task to others. (Note that having to itself is normative.) Yet, without this choice 'e cannot describe anything in a relevant way, and leaving the choice to a particular other person or group of persons is itself a choice which is heavily value-laden. If the factualist actually leaves the choice to the state, 'e chooses the goals of the state; if 'e leaves the choice to private enterprise, 'e chooses the goals of private enterprise; and if 'e leaves the choice to a community of egalitarians, 'e chooses the goals of egalitarianism. Moreover, the factualist's work is not only of normative significance with regard to 'er explicit choice of objectives, or clients, or people under whose orders 'e decides to act, it is also of normative significance in 'er way of classifying, in 'er terminology, in the assessment of results, and so on and so forth. Fourthly, of two true theories or descriptions which are both relevant with respect to the same goal(s), the simpler theory or description is superior to an unnecessarily complicated theory or description. It may not always be clear which theory or description is simpler in practise but simpler is to be understood as requiring a smaller number of primitive notions and axioms or principles. Applying this same principle of parsimony to normative theorizing means that a coherent normative theory which recognizes a principle of truth, a principle of relevance, and two or more principles furnishing its goals must be rejected too if another coherent normative theory which recognizes a principle of truth and a principle of relevance has only one principle furnishing the same or the same and even more acceptable goals. It does in no way follow from this what that goal should be, or that there is one ultimate goal. It does follow, however, that the original factualist claim that all coherent normative theories would or could be equally 'valid', independently of the existence and adoption of descriptive theories, cannot be sustained. We have started with drawing a sharp dividing-line between the factual and the normative spheres, between fact and value. Subsequently we have discovered tho, how this distinction becomes blurred more and more when not considering facts and norms as objective givens in themselves, but when considering thought about facts and norms, that is, factual and normative beliefs or disciplines. Facts and norms themselves may be entirely independent of each other, in our theorizing on facts and norms, the normative principles of factual thought may not differ from those of normative thought at all. The question whether the normative principles of factual thought actually recognized or presupposed are really the same as those of normative thought is itself a factual issue we cannot deal with here. Even if ultimately the norms of a 'purely descriptive' discipline and of a normative discipline are necessarily the same, the facts need not be. 3.3 PROPOSITIONAL REALITY AND LANGUAGE 3.3.1 THE INTERPLAY OF THOUGHT AND LANGUAGE A very attractive feature of propositions, if defined as the meanings of sentences, or in some such way, is that they are language-independent. Thus the sentence water is transparent and the sentences in all other languages with exactly the same meaning correspond to, or 'are', one and the same proposition: the proposition water is transparent. Altho every language may have a sentence with a meaning identical to this proposition water is transparent, it is not hard to conceive of some sentence in this language for which there is no exact equivalent in a particular other language (not belonging to the same cluster of 'languages'), and vice versa. In that case there is a proposition which can be uttered in this language but not in some other language, and a proposition which can be uttered in some other language but not in the language which is our present means of communication. The next step is then to conceive of a proposition which cannot be uttered without change of meaning in any language. Thinking (not speaking or writing) along the lines of such propositions (if possible) would be as language-independent as propositions are themselves: words may be the instruments of thought, that does not imply that thought could not do without words. The question whether thoughts can be entirely language-independent is closely related to the question whether the communication of thoughts, and of other elements of propositional attitudes, such as feelings, can be entirely independent of language. As the transmission or exchange of thoughts and feelings can take place outside the verbal medium of a spoken or written language, it seems evident that propositional communication is at least not wholly language-dependent. Yet, our present means of communication, and also the most important or easy means of communication (in the present context), is verbal communication in a particular language. It is therefore of great import to have some idea if, and to what extent, the expression of thoughts and feelings depends on the kind of linguistic medium used, given that such a medium is used. After all, we may prefer to plane away the rough and defective parts of the language employed, rather than to alter our thoughts themselves because we could not express them properly and easily by means of a tool still largely controlled by the invisible, dead hand of tradition. That there is a relationship between language on the one hand and people's thought and behavior on the other, is generally acknowledged. Thus it has been stated that 'we think the way we speak', and it has been added to that that 'we speak the way we think'. A special aspect of this 'speaking likeness' is the connection between language and 'ideology' in the broadest sense of the word, including both political and nonpolitical, religious and nonreligious ideologies. If the interplay between language and thought is not entirely illusory, a dissimilar ideology must in some respect correspond to a dissimilar linguistic usage (maybe just a different connotation for some words), especially in a field it is primarily concerned with. For example, it has been argued that one and the same labor situation may be described in completely different ways dependent on one's political or economic point of view. The active person giving or doing something in such a situation may be the 'worker' for the one and the 'employer', or the person said to give work, for the other, whereas the passive person receiving something is the 'capitalist' for the one and the 'employee', or the person said to take work, for the other. (The difference in usage is even more clear in languages in which the employee is labeled "work-taker" and the employer is termed "work-giver".) Now, the truth may be that in a particular labor situation the same person gives one thing (for example, work) and takes another thing (for example, labor power) but the exclusive emphasis on one party's giving and the other party's taking is ideological. The difference in terminology, that is, language, therefore bespeaks a difference in perception, and with it a difference in thought, even tho the conditions are the same. It is sometimes said that language is not only a means of communication to tell other people something about reality, but also a means to create reality, or rather one's perception of reality. Words can make and break such perception. Tho language is itself a product of society, it has been pointed out that it can alter the relations between people themselves as long as the right linguistic tools are used. As the prime instrument of communication language is also the vehicle for the spread of ideologies (and as a general means this applies to both good and bad ideologies). But as a product of society language is itself already infused with the spirit of past and present thought which may be compatible or incompatible with a new or future doctrine. And altho language may not create ideology since ideology only manifests itself in language --as has been argued-- this does not refute the argument that language perpetuates a particular ideology or way of thinking. When a present-day language still draws traditional distinctions which are the remnants of exploded ideas, or when it draws no relevant distinction because it never did so before, it goes on creating an impression of normality and abnormality which is counternormative. The sanctioning of such an impression is, then, political, religious or otherwise ideological. Language is just too often lagging behind new developments: the social relations (as between the sexes) may have changed while linguistic usage has not yet been adapted. That is why some characteristics of a particular language may be relics which do not so much reflect a present, but a former world-view of the community of speakers of that language. Research has shown that words determine to a certain extent the organization of what is perceived, that they 'stabilize and confirm such an organization'. And conversely, when certain differentiations have become or are deemed important, these differentiations make their way into the verbal categories of the language. The most obvious reason for a difference in such categories is, of course, a difference in the conditions different linguistic communities are living under. Yet, some people do not have 'sibs' (only sisters and or or brothers), and other people do not have 'parents' (only a mother and a father); nevertheless one would say that (at least in this respect) the conditions are the same in the linguistic communities concerned. It has been said, however, that it is not inherent in a particular language to provide us with a simple and short verbalization. Having to say "one or more sisters and or or brothers" would, then, only be a question of having to describe one's conditions in a more or less cumbersome way, and the (needed) length of verbalization would depend in principle on the context. For example, we may describe a figure just as "a rectangle" (without mentioning its position, size, and so on), and we may describe a color just as "green" (and not as "a little bit yellowish green"). But these two examples differ essentially from each other, and context-dependency is therefore too vague a concept to explain or justify the length of verbalization with. Being-a-parallelogram, having-a-certain-position and being-a-certain-color all represent a factor which --let us say-- admits of degrees. (For the sake of convenience we assume that the factors are one-dimensional.) Now, one can determine an angle of a parallelogram as accurately as one wishes, and one can locate a color in a spectrum more or less accurately (altho the meaning of color terms always remains arbitrary to some extent) but in each case one has supposed that the factor being a parallelogram and the factor color are relevant. The accuracy of the description of this one quality is then further dependent on the same contextual features which make the factor itself relevant. The question whether the introduction of position, size, and other factors (not just degrees of accuracy) into the description is required, may depend on entirely different contextual features tho. If they are, one adds an affix, an adjective or adverb, or an adjectival or adverbial, subordinate clause (in the present language and in languages with a similar structure). Changing a description from sib to sister or brother, or from parent to mother or father, introduces the factor gender. Granted that everyday language is not obliged to produce short verbalizations everywhere, and that it can only have a limited vocabulary, a systematic procedure would be to denote a sister with female sib and a brother with male sib in those contexts in which gender matters. But there are but too many languages where it is the other way around: they have words for brothers and sisters but not for sibs. Or, there is a word for sibs, but it is rarely employed in comparison to the words brother and sister. While it is a truism that language is cumbersome at one place and efficient at another, it may be quite interesting to find out where it is cumbersome and where it is short and clear. If it is not short and clear until a new factor has been introduced, then it carries the inherent presupposition that that factor is relevant in every context. This implies that language can have the tendency to make appear relevant, and to make people believe that something is relevant that is actually irrelevant (except under specific circumstances). And this is much more serious than the converse, because it underlies stereotypical thinking and the disbelief in equality (as we will see later). (Altho in this regard the sister/brother dichotomy may be innocent compared with the asymmetrical girl/boy, spinster/bachelor, queen/king and similar traditional juxtapositions.) People's acting and thinking is responsible for the emergence of language, but once it is there, it is this very language which, in turn, can have a great impact upon people's thinking and acting. Obviously it depends on what language what that impact is, and how strong or far-reaching it is. Like (almost?) all instruments also language can be used for praiseworthy and for blameworthy causes. The point is to nail its implicit ideological prejudices and presuppositions, and to counterbalance it where it is askew. It has already been said before that change of language, or rather an improvement of language, is certainly not unimportant for anyone who has to transmit new knowledge in the field of training, education, cultivation, and the like. The right use of language will promote that people actually discern what is there, and that they will act accordingly. This may either involve a difference where no distinction was drawn before, or no difference where an irrelevant or false distinction was drawn before. As has been argued correctly, people are not always and not solely objects of their language. Those who create language themselves may not change the ground-facts, yet they do somehow 'participate in the formation of the world', even if only in the creation of new facts of thought and correspondence. And creation often involves destruction: fettered by traditional thought, these language users must employ the weapons of thought to destroy the fetters of tradition. 3.3.2 CONCEPTUAL AND EVALUATIVE MEANING A phrase can be used to express or evoke a state of mind which is cognitive, and it can be used to express or evoke a state of mind which is affective or conative. In the former case it is the conceptual meaning of the phrase which counts, in the latter the evaluative meaning. These different 'pragmatic aspects of language' are related to the different purposes for which such a system of symbols is applied. Words are used on the one hand 'to record, clarify and communicate' (cognitive) thoughts, whereas they are used on the other hand to show or create feelings, or to incite people to act in a certain way. The first kind of use has been termed "descriptive", the second "dynamic". The evaluative meaning of a word or phrase may be emotive or normative. It is 'emotive' on our terminology if, and insofar as, it is used to express a personal feeling, say, the feeling that something is beautiful or ugly, pleasant or unpleasant. It is 'normative' if, and insofar as, it is used to express the conviction that something is right or wrong, or good or bad in a normative sense. Emotive meaning is a kind of factual meaning. Beauty and ugliness, and all forms of pleasantness and unpleasantness, are facts, albeit relational facts with respect to one particular being that experiences something as pleasant, unpleasant, and so on. To say that something is nice or unpleasant does not describe the thing in itself, however, and therefore the use of words for this purpose is not descriptive (of the thing in question). Similarly, to say that something is right or bad (in a normative sense) does not describe the thing or action itself either, and therefore also the use of words for this purpose is not descriptive. The concepts of denotation and connotation refer practically to the same distinction as that between conceptual or descriptive and evaluative or emotive meaning. The connotation is, then, what is implied apart from what is explicitly named or described. It is the subsidiary meaning of a word of which the conceptual or descriptive meaning is of primary significance. It may also be the case tho, that only the emotive or evaluative meaning of a word or phrase is important, and that it has no, or only a vague, conceptual meaning. In that case the term connotation does not properly express the essentially evaluative nature of the word or phrase concerned. The distinction between conceptual and evaluative meaning is also present where it is said that linguistic symbols are not only related to concepts in a narrow sense but also to so-called 'stereotypes'. These 'stereotypes' then underly the emotive meanings of terms. The evaluative meaning of a word (or phrase) may be negative, indifferent or positive. If it is positive, the word is meliorative (or 'laudatory'); if negative, pejorative (or 'derogatory'). A word may have the same unneutral evaluative meaning in the whole linguistic community, it may also have a meliorative meaning for some people and a pejorative one for others, while having the same conceptual meaning. Altogether there are the following possibilities with respect to differences in usage between two groups or communities that in general speak the same language: (1) the phrase itself is only used by one group, not by the other (for example, the name of a religious institution or practise); (2) the phrase is used by both groups but the conceptual meanings are not the same, nor are the evaluative meanings (for example, the word religionist and perhaps ideological); (3) the conceptual meaning is the same but the evaluative meanings are different (for example, revolution and perhaps God and the Party); (4) the conceptual meanings are not the same but the evaluative meaning is (for example, freedom and democratic). The evaluative meanings of a word can diverge widely, even when the word has no or hardly any established conceptual meaning. Thus the word god has a strong meliorative meaning for theists and a strong pejorative meaning for antitheists (and a nonmeliorative evaluative meaning for nontheists in general). There is no universal evaluative meaning of this word in the present language so long as there are enough speakers of this language who worship one or more gods besides speakers who do not. It is only because the word god did arouse in their time an extremely deep, positive feeling in most, or the most powerful, speakers that certain thinkers in the past decided to dignify the principal being of their world-view by the then-laudatory title god (or God), even tho that being did not look like the or a 'god' of their contemporaries in any way. This is a question of 'persuasive definition': use a familiar term without changing its evaluative meaning; give it an entirely new conceptual meaning, and thus alter the direction of people's interests -- hopefully that is. When the word god has acquired a strong negative evaluative meaning in later times, unsuitable for any meliorative persuasive definition, it is in the first place because of its association with the content and historical record of what have been the dominant forms of theism. It may technically be possible to give the term god any descriptive or conceptual meaning one likes, but those who reject all irrational supernaturalism that violates the principle of truth and all discriminatory exclusivism that violates the principle of relevance are not capable anymore of using the term melioratively in an ideological context. And therefore we shall not apply the name god (with or without capital) to anything we value, even not --or rather, certainly not-- to a principal being, and least of all to (the) supreme being. (In a religionist society this may require some courage, because there one risks the wrath, not of any omnipotent god, but of the barons of the worshipbuilding industry.) Words such as good, right, nice and pleasant, which are used to express a positive evaluation or emotion itself, are typically meliorative, whereas words such as bad, wrong, awful and unpleasant are typically pejorative. Such words may have an evaluative meaning, they have no fixed descriptive meaning at all. A term such as just or justice belongs to the first category as well. While it can conceptually be defined in many different ways (like the word god), it has been pointed out that it is not trivial which definition is chosen, since 'to choose a meaning is to take sides in a social struggle', because of the universal meliorative nature of just and justice in the present language (unlike the word god). 'Everyone' is in favor of justice, and this is why the term justice has a 'universal' meliorative meaning. And 'everyone' is against injustice, and this is why the word injustice has a pejorative meaning, even if there is no unanimity whatsoever with regard to its conceptual content. Justice has a built-in rightness or goodness, and injustice a built-in wrongness or badness. When words have a built-in negative evaluation (like injustice) they do not merely describe, if they describe at all. To say that acts or situations denoted by these words are bad or wrong is an analytical statement which does not convey any substantive, normative or other evaluative information independent of the time that and the place where the proposition is uttered. Thus in the present language taking something is only called "stealing" when it is wrong, or judged to be wrong, and therefore stealing is wrong (and also you should not steal) is an analytical truth. Similarly, killing someone is only called "murder", and telling something that is not true "lying", when it is wrong, or judged to be wrong, and therefore murder is wrong (or you should not murder) and lying is wrong (or you should not lie) are analytical truths as well. To say, for example, that you are against stealing, or that one ought not to steal, is empty rhetoric. If it serves any sensible purpose at all, such a statement can only serve another purpose than the direct transmission of substantive information. What it may tell us at the most is that there are ways of taking something which are wrong and ways which are not wrong. But this is a truism. What would be interesting to know is what criterions to apply to distinguish the wrong ways of taking and having from the right ways of taking and having. A speech community is not a monolithic herd of people who use all words in the same way and with the same feelings. (At most a community of linguists could be such a herd.) For example, the word suicide may have a definite negative connotation for some and not for others. This may be a question of a different moral outlook, but also a question of a different linguistic usage. Those who do not condemn self-killing (in general) as a form of killing or self-killing, just cannot use the word suicide, if it has a negative connotation for themselves or for the group they relate to. Similarly, those who do not condemn erotic contact between (close) (adult) relatives as a form of erotic contact, just cannot use the word incest, if it has a negative connotation for themselves or for the group they deal with. (As the original meaning of incest is impure it is not surprising that the word incest does have a negative connotation.) If a term such as suicide does indeed carry a pejorative load in the language used, people will start calling certain acts of (intentional) self-killing "sacrificial" instead of "suicidal". Self-killing is , then, 'sacrificial' (or heroic), if it is (believed to be) good, right, justifiable or excusable, and 'suicidal' if it is (believed to be) bad, wrong, not justifiable or not excusable. However, these differences in terminology have no bearing on substantive normative issues, for the question remains whether self-killing, or for that matter, erotic contact between relatives, is ever wrong, and if so, why. And the same applies to all other forms of killing and intimate physical contact. Those who do not morally condemn certain acts of taking would not call them "stealing"; and they would not call certain acts of telling a falsehood "lying"; and not certain acts of killing "murder"; and not certain sexual acts "perversion". All these words have a negative, emotive and normative meaning. It only makes sense to say that a particular act described by means of a phrase with a clear conceptual and no definite normative meaning is right or wrong, or neither right nor wrong. The revelation that 'everyone' or 'all reasonable people' (or 'everyone who has no perverted mind') agree that murder, theft, lying, incest, perversion, injustice, and suchlike, are wrong is an intuitionist platitude. Those who start from such statements lack any insight into the functioning of language and the pragmatic aspects of the diverse meanings of its constituents. Those who finish with such statements express a type of moral thought which is too shallow to allow for any worthwhile perspective on normative affairs. 3.4 LANGUAGE AS MEANS AND AS PRODUCT 3.4.1 THE CULTURAL NORMS OF LINGUISTIC SYSTEMS On the propositional level we use language in the first place to solve a coordination problem, a problem of interdependent decision-taking. It is in interaction situations that cultural norms emerge which serve as a guideline for people's behavior or actions. In general, the members of a community adhere to such a guideline, and are expected to adhere to it. There are several types of these cultural norms --as has been demonstrated-- such as 'partiality norms' (or 'norms of partiality') which stabilize a status quo in which one of two parties has a notably better position than the other one. (Cultural and subcultural norms are often called "social norms", but as the content of such norms is not seldom quite a- or antisocial, we shall not use that expression, unless they are really 'social' in every respect.) Insofar as language is indeed a means of communication the cultural norms playing a role in interaction situations in which language is employed are so-called 'coordination norms'. It is these norms which prescribe an action, or type of action, and which produce an equilibrium, if the people involved do act, and keep on acting, in the way prescribed. If the problems are recurring problems, and if the solutions are generally accepted and established, one speaks of "conventions". But the answer to a new problem which will keep recurring in the future may also be a kind of artificial ruling which has been called "a decree". Whether the solution is such a decree or a convention, the interests of the parties concerned coincide, and the success of the one participant (for example, the writer) is also the success of the other (for example, the reader) -- insofar as the employment of language is purely a question of communication, that is. In a study on conventions in particular it has been pointed out that in a situation of interdependent decision not only first-order expectations are important but also higher-order ones. A second-order expectation is, then, an expectation about a first-order expectation. In the same study a convention of language is conceived of as a regularity in behavior 'restricting one's production of, and response to, verbal utterances and inscriptions'. The agents are said to have 'a common interest in all doing the same one of several alternative actions' and the convention is sustained by this common interest and by the expectation that others will do their part. The crucial thing is that no explicit agreement (or decree) is necessary, if the content and strength of mutual expectations suffice. Experiments have shown that in an interaction situation people will try for a coordination equilibrium which is somehow salient, which --so it has been said-- 'stands out from the rest by its uniqueness in some conspicuous respect'. (The equilibrium does not have to be the best one judging from another point of view than that of coordination alone.) A special convention which is claimed to play a role in every possible language is what has been called "the convention of truthfulness". If such a convention prevails in a certain community, sustained by the general will to communicate, the possible language is said to be an actual language of that community. But --as the argument goes-- in practise there is a 'tight cluster of very similar possible languages' and on this view a convention of truthfulness in a single possible language is a limiting case never reached. If the 'languages' of the cluster are very similar, communication is not or hardly impaired, however. In the case of written language this cluster may encompass, for example, a complex of closely related spelling systems (or 'one' spelling system which is not necessarily uniform). It has also been pointed out that taking some risk with regard to communication has benefits too. Firstly, the different languages of the complex can meet different individual demands and be suited to different tastes and purposes. Intolerance itself, and a lack of insight with respect to the several variants of the spoken and written language, may do already much harm to regular discourse. Secondly, a child that still has to learn the language needs more information to identify a language (or spelling) in a cluster than the cluster itself. This is important, given that complete analyticity does not exist, and that the idea of a convention of truthfulness in a single possible language is an illusion. (Compare the reservations we had to agree to in the preceding division.) Whether these arguments are entirely persuasive or not, they do illustrate very well that the belief in a (necessarily) uniform, spoken or written, language is a chimera. The idea of one language without variants, and separate from the actual 'languages' belonging to the same complex, is therefore expressive of a prejudiced attitude in which one variant (or 'language') among others is given an exclusive status. Coordination norms are related to so-called 'technical norms' in that they are a means for the attainment of a certain goal: coordination. But this goal itself is usually a means for the attainment of a cooperative goal of a higher level. The direct objective may be linguistic, the ultimate goal is, even if only communication is mentioned, of a social, moral, esthetical or other nature. This should already refute the claim that questions of language are purely practical, rational or technical issues, because people do not communicate simply to communicate (save in exceptional cases). Even if language is conceived of as a mere system of coordination norms, necessary and good to solve problems of communication, much still depends on how the questions are posed. Certain presuppositions remain always implicit in the formulation of a scientific or technical problem which affect the scope of possible solutions, if only because of the conceptual framework used. This is quite obvious with regard to established language, such as 'received' pronunciation and 'official' spelling. But it is also evident where it concerns the technical demands made upon the rendering of any language, dialect or sociolect: that it is learnable, readable and writable (when represented by means of visual symbols). For example, does one start from the present situation and check how easy a proposed new word, meaning or spelling can be learned by people who live now and who have grown up in another pattern of lingual expectations? Or, does one direct one's attention to a future generation in the experiment represented by nonspeakers of the language concerned to whom the proposed novel variant is taught? And then, we must not forget that a certain easily learnable, readable and writable alternative may be an excellent solution to a certain coordination problem, but is perhaps incompatible with another, older solution upheld in the same linguistic community at the same time. So we had a good reason not to select her as gender-neutral and -transcending adjective (with the pronoun he) so long as her is simultaneously used by others of the same speech community to refer exclusively to female beings (among which ships, countries and a few other peculiar things), even tho we ourselves could have accepted the loss of the exclusively feminine her and masculine he. What is labeled "standard usage" in connection with a certain language is not just a system of coordination norms, it is at least partially also a system of partiality norms. These are cultural norms which play an important part in standardized languages and which just cannot be explained or justified in terms of the need of an easy communication alone. This should be clear enough with respect to the institution of an official or national spelling: as soon as it strikes the eye that someone makes a mistake according to official or national usage, the transmission of the meaning of the word has already taken place perfectly. (Of course, one orthography may be easier to recognize than another, but this is not inherently the case if the so-called 'incorrect' usage consistently follows an existing orthographic rule, or a different existing orthographic rule.) It has been pointed out that once partiality norms stabilize an existing situation, the nature of the considerations whether to deviate from them, or not, changes fundamentally. Deviation from the then-normal pattern is not only going to cost an extra effort, nay, it plainly becomes something 'morally wrong or subversive'. This is why deviation from the status quo becomes harder when it is fortified by partiality norms. Moreover --it is said-- the sanctions backing these norms are imposed impersonally, altho they favor one party against the other. Such is necessary, because otherwise they will lose their effectiveness as a disguise for the exercise of power on which they are really based. Also educated people, also parents of children, and also people whose dialect or sociolect have become the official or national language, are supposed to fully observe the rules of 'cultivated' usage, regardless of their personal tastes and preferences, and also if a nonofficial variant could be equally well read and understood. Whereas in other cases the influence of cultural norms may be harmonizing, and their nature social, we see how they assume quite a coercive character in this case. Evidently both aspects go together in institutionalized linguistic systems (whether officially decreed or not) which do not solely serve good communication. Partiality norms have been associated especially with the institution of private property. As the argument goes, (sub-)cultural norms of private property (such as those governing trespassing and inheritance) do in the first place protect the haves and their descendants in a socioeconomic state of inequality. (We will return to this view in 9.2.2.) It is indeed remarkable how close the connection is, historically, between these norms which serve to protect private property and the (socio-)linguistic partiality norms of the official or institutionalized language which had to approximate as much as possible the dialect of the wealthiest region(s) and/or the sociolect of the propertied class. While it is the former which are responsible for an unconditional sanctity of private property, it is the latter which are responsible for an unconditional sanctity of traditional linguistic usage. 3.4.2 THE VALUES OF LINGUISTIC SYSTEMS When we speak about cultural norms as we have done until now, we are primarily interested in what people using a particular language ought to do in the light of these norms (altho this does not tell us anything about what they ought to do in the light of an independent ontological norm). We have, then, already presupposed a system of one or more values, or a theory of value. Communication itself is of course such a value but --as noted before-- almost never an ultimate value. Also conservatism is a de facto value in linguistic affairs, whether one likes to accept it personally or not. Conservatism is often recognized as an orthographic principle, if it rests on a word's etymology. Such a principle is relative, however, since it not seldom depends on how far back in history one is willing to go and to disregard the neglect of etymology people in former times displayed themselves. For example, the words kategori(e), kritikal and kub(e) thus spelled would be 'more etymological' than the variants with a c (and y), and so are all words with -iz- instead of -is- (as in neutralize and neutralization). Also beauty is a de facto value in matters of language, but esthetical reasons to pronounce or spell a word in one way rather than another can never be advanced to justify a particular official or standard linguistic variant. On the contrary, love of beauty is an argument against any and every form of artificially institutionalizing language, unless something like a national taste is seriously believed in. If a whole language community really had the same taste and convictions, uniformity would come naturally, that is, automatically, and would not have to be enforced by dint of institutionalized systems. Yet, keeping together the different parts of a linguistic or national community has been mentioned as the key value of institutionalized language. This view is generally connected with the belief that a unitary language (especially a unitary pronunciation and spelling) is a practical necessity to enable the smoothest possible communication between the speaker or writer and 'er contemporary listeners or readers. Even if this were true tho, it would not determine which variant should be the standard one, and the proponents of unitary language have never, or rarely, based their choice of a particular variant as the unitary language on the criterions for the easiest way to learn and understand that language (for example, the easiest way to pronounce and/or spell it). The values of the proponents of an artificially imposed unitary language are not really the values of language as a technically adequate communication system but usually (or always?) the values of the unitary state, or the values of elitism and conservatism. Insofar as language is a purely communicative device, conventions suffice --as we have seen-- to solve coordination problems, and it is by no means necessary to formulate these conventions and to promulgate them. (This is not to say, of course, that it may not be convenient to come to explicit agreements with respect to actually recurring communication problems, for example, when in a speech community with a great internal variation the groups farthest removed from each other cannot understand one another any longer.) The belief that an entirely uniform linguistic system would have to be decreed rests on the misconception that every deviant sort of usage would have to be excluded in general. And it also rests on the exploded idea that communication problems could solely be solved by means of verbal, explicit agreements. If language were really that rigid, the 'normal' change of linguistic norms (semantic change, for instance) would never be possible. The norm of good communication --it has been argued-- does require of the speaker and writer that 'e violate lower-level linguistic norms in a creative way when necessary, and it does require of the listener and reader that 'e show the necessary tolerance and cooperation when interpreting the information received. Remarkable in this view is that --again-- tolerance is stressed as a value not from an ethical but from a linguistic vantage point. Even if there were no officially decreed or institutionalized language, this would not mean that everything would be possible with mere chaos as a result. For everyone who wants to successfully forward or exchange information will have to recognize (at least implicitly) a definite core of conventions common with the group 'er information is aimed at; otherwise 'e will simply not be understood, or otherwise people will not take the trouble to try. Now, conventions only exist because of the consistence of acting. Hence, it is the consistence of acting which is the central value of language and of thought. (Altho it may not be the de facto value of a particular linguistic variant.) 'Inconsistent' acting must, then, not result from a lack of principle but at most from a conflict between different principles or rules, when a choice must be made one way or the other. Since not one linguistic principle or rule is the only true one, the systematic application of several principles or rules will probably lead to the emergence of nonuniform, but closely related, linguistic systems, products of the spontaneous growth of one language (called "cluster of languages" in another, technical sense). Thus, on the basis of the phonematic principle one spells -or (as in labor) and -er (as in center), altho the spelling -our (labour) and -re (centre) may be preferred on the basis of the etymological principle. (It should be superfluous to note that the writer's nationality or ethnicity is irrelevant in this respect.) Due to an emphasis on different principles one may accordingly conceive of the emergence of a more phonematic spelling system besides a more traditional, etymological one in the language which is our present means of communication (and in other languages also of the emergence of a more phonematic besides a more morphematic system). The conventionality of each orthographical or other linguistic system which is actually used on a smaller or larger scale (perhaps on a universal scale) does, and need, not depend on a decree in which an exclusive status is rendered to only one linguistic system or variant thereof. It should solely depend on the common interest which two or more, independent persons take in the exchange of their thoughts and feelings by means of the spoken and written word. If they do not leave the communicative core of the language in question, and if they systematically apply its intrinsic rules, then their spoken word is correctly pronounced, and then their written word is correctly spelled. In the books of this Model we will take cognizance of the fact that the language which is our present means of communication actually has many lexical, semantical, pronunciational and orthographical variants. Where there are two or more options open to us, but where it would be inconsistent to employ more than one variant, the most regular (or least irregular) and the most phonetic (or least unphonetic) variant is employed, regardless of its being perhaps traditionally more frequently used in one country than in another. For example, catenas, criterions and millenniums are chosen instead of catenae, criteria and millennia, and thru, tho, fulfil and practise instead of through, though, fulfill and practice. In no way does this imply that other variants would be incorrect. If they are in actual use by a sufficient number of speakers or writers, it can only be inconsistent usage which is incorrect. 3.4.3 THE SEX AND AGE OF TRADITIONAL LANGUAGE The issue of sexism and language has attracted much attention in feminist studies in particular, and it has been convincingly demonstrated in these studies that the series he, him, his, and words like man, cannot and do not function as genuinely gender-neutral expressions in traditional parlance. Moreover, it has been shown that sex discrimination is endemic to grammatical conventions in the traditional variant(s) of the present language (and considerably more so in similar variants of certain other languages). Little or no attention has been paid, however, to the crucial role played by the concept of relevancy in questions of sex discrimination, in the rejection of any other discriminatory usage and in the logic and principles of conversation itself. Traditional language does not only reveal that it is, or has been, backed up by a sexist (or sexually irrelevantist) world-view, it is not age-neutral either. The intimate relationship between the various attitudes, with regard to gender and age but also with regard to class and minorities, can easily be detected in ordinary traditional language. Such language is, then, not only a product of stereotypes, it promotes them too, or serves as an instrument for their promotion, notably by dint of the emotive meanings of words. If the old he and man could really be used in a genuinely gender-neutral way, they ought to be applicable to any person regardless of gender. But it has been correctly pointed out that one cannot say, for example, "he is the best" of a female, or "she is the best man for the job". Now, it has been argued that if it is clear that the speaker knows the gender of the referent, 'e is expected to specify this gender. In other words, the speaker would not convey less information than 'e could. But the rejoinder is then that it would be as inappropriate to say "that is the best person" of someone whose gender is known as it is to say "that is the best man" of a female. Hence, a man simply behaves differently from a person: the latter is undisputably gender-neutral, the former not. Many similar examples in feminist literature show that the so-called 'neutral' performance of he and man as 'advertised by traditional lexicographers easily breaks down even under normal speaking conditions'. Is it true, as has been suggested, that people do not convey less information than they can under normal speaking conditions? Of course not. Literally interpreted this suggestion cannot be taken seriously. In pragmatics (as a branch of linguistics) it is only stated that one should make one's contribution 'such as required by the accepted purpose and direction of the conversation'. This is called "the cooperative principle", and on this principle one should not convey less relevant information than one can, and not more than is relevant or than one believes to be relevant. Relevancy, therefore, plays a central part in any 'normal' conversation; even tho it may merely be informational relevancy. Whether a factor such as gender is relevant or not in a particular situation or context is not always clear, but a linguistic system which does not have any truly gender-neutral and -transcending word to replace the yin and yang specimens is deficient in this respect. This does not only concern pronouns and adjectives like his and her but also nouns, or pairs of nouns, like actor-actress, bachelor-spinster, launderer-laundress, king-queen, and so on. (In the traditional variants of certain other languages this even applies to almost all nouns denoting people engaged in these kinds of activity or function.) The denotations of king and queen and the connotations of bachelor and spinster are remarkably asymmetrical: the former are expressive of some more aristocratic, the latter of some more proletarian type of sexism. Yet, the imposition of gender differentiation in traditional language is not per se sexist in the sense of being sexually unneutral. If both the conceptual and evaluative meaning run parallel, it need not be. In practise tho --as has been argued-- sex-distinguishing terms do not seldom go with a differential appraisal. Even if the imposition of gender differentiation were not called "sexist" by itself, and even if, after having distinguished them, men and women were put on an equal footing, the factor gender itself would remain irrelevant (in many, if not in most instances). It is only one factor or set of factors among an innumerable number of other factors or sets of factors, each of which might or could be pertinent in the circumstances concerned. Why not have different nouns and pronouns for each activity or function to distinguish the big from the small, the good from the bad, the rich from the poor, without there being an inclusive noun and pronoun to denote both the big and the small, the good and the bad, and so on? Of course, the idea is absurd; probably as absurd as those people find it whose language has gender-transcending nouns and pronouns (in addition or not in addition to masculine and feminine forms) that there are languages in which the sexual distinction is foisted on the speakers, however irrelevant. And probably as absurd and awkward as the speakers of this language find it that there are traditional languages in which different grammatical forms have to be used dependent on whether one possesses a penis and testicles or a vagina and uteris oneself; and that there are traditional languages with (at least) two words for the pronoun you, whereby the choice of which one to use depends on factors such as age(-difference) and class(-difference). In the latter cultures or subcultures concerned older people tutoyer minors and younger people but expect them to use the polite form of you nevertheless. Fortunately, there is even no forced gender distinction between a male second person (u?) and a female second person (ewe?) in any variant of this language. People could, then, not spell "you" anymore when writing to you. They would first have to make sure whether you were a 'u' or a 'ewe'. There are dictionaries painstakingly compiled by lexicographical worthies which define man as human being, especially an adult male human but woman as adult female person, and male as plant or animal that is male but female as plant or animal that is female, especially woman or girl as distinguished from man or boy. The supposedly symmetrical harmony of yang and yin is definitely (and painfully) lost in such definitions. Even with respect to the distinction male/female it appears necessary to differentiate between men and boys and women and girls, because boys are certainly not men and girls are certainly not women (or if they are, then to their detriment, as we will see). Some might object that male and female are age-transcending terms which can be employed instead of the longer phrases man or boy and woman or girl. They are indeed age-transcending but at the same time so impersonal as to refer to any unisexual plant or animal. Is a 'boy' in traditional language just a male minor without any special connotation? This can hardly be maintained, since the word boy was at least in olden days also used for men of a class felt to be inferior (namely servants) or of a race felt to be inferior. The archaic meaning of knave (akin to words denoting 'boys' in other languages) is, similarly, also male servant or man of humble birth or position. (Not coincidentally it means dishonest fellow as well.) According to the traditionalists' lexicon a 'girl' or 'maid' is not just a female minor but, besides a female servant, it is also an unmarried woman who is (still) young or of any age. Again, the asymmetry in the meanings of boy and girl is symptomatic. The only human beings escaping from both boy- and girlhood are adult men who are not of humble birth or position and who do not belong to a class or race felt to be inferior (by adult men who are not of humble ...). Girls and boys are small humans, and so are women, judging by the traditional use of the diminutive -ette to denote, for example, 'bachelorettes', 'suffragettes' and 'brunettes'. By now, it will not come as a surprise to anyone that the counterpart of a 'man Friday' is not a 'woman Friday', but a 'girl Friday' in traditional language; nor will it that 'bachelor girls' existed long before 'bachelor boys' were born. And while boy(-)friend and girl(-)friend do seem to be analogs, their use is certainly not alike under all conditions. Where a woman could call any of her female friends "a girl-friend", a man would in the same sexually exclusivistic milieu provoke quite different reactions by calling one of his male friends "a boyfriend". The codes of behavio(u)r of some exclusivist dictionaries allow solely males to have girl- and solely females to have boyfriends. A dictionary belonging to that category may state that a man or boy likes his girl-friend but may not be in love with her, while leaving the poor user (m/f) in doubt as to whether females are always in love with their boyfriends or not. 3.4.4 SOME EXAMPLES OF LINGUISTIC DEFICIENCY To be correct a linguistic variant should be consistently based on a general rule or principle inherent in the language concerned. But even if a language has several variants which are correct in this sense, this does not mean that the linguistic system as a whole cannot be deficient in one or more respects. Some might argue that correct language is never deficient, because it would always be up to a 'normal' standard, as actual usage is presupposed when speaking of 'correctness'. But this would merely hold if there were only linguistic rules in a narrow sense which mattered, such as the rule inherent in the present language that the plural in writing is formed by the suffixation of the letter -s or the letters -es. In a wider sense, however, it is also a linguistic rule that one should be able to express fairly easily what one believes to be important, or what often returns in one's thought and conversation. What has been called "the norm of good communication" requires that the language user does not have to frequently take refuge to a clumsy circumlocution to express the same thing every time. It also requires that no distinction has to be made where this is believed to be irrelevant, and that such a distinction can be made where it is believed to be relevant. What is important or relevant, and certainly what is believed to be important or relevant, depends on one's world-view, or on extralinguistic principles. It is therefore the very combination of the principle of good communication and one or more of such extralinguistic principles which may render a particular linguistic system deficient. Nonetheless, as a product of society such a system may be very efficient from the standpoint of traditional world-views, and perhaps, even from the standpoint of an outmoded, former world-view. Thus, in a time and at a place that sex is deemed important under all circumstances it does not bother men or boys, and it does not bother women or girls, that they cannot speak of persons, of sibs or of launderers, regardless of their gender. A linguistic system which forces them to genderize is, then, not felt to be deficient, because they are not interested in a person as a person but as a man or boy or as a woman or girl only; not in a sib as a sib (or person) but as a brother (male) or as a sister (female) only; not in a laundry worker as a laundry worker (or person) but as a launderer (male) or laundress (female) only. (And incidentally this is also why the subcultural norms of such a time and place convulsively stress the difference between clothes and ornaments males ought to wear or not to wear, and those females ought to wear or not to wear, not only in periods of sexual preparation and excitement but all the year round, day and night.) Altho it is very useful to have feminine and masculine pronouns like she and he when sex is relevant, the distinction between persons and nonpersons is so important and so often used that we could not do without a special, personal pronoun (which is gender-neutral and -transcending because it is personal). This is the reason why we have introduced (in Speaking person-to-person) the series (')e, (')im and (')er, parallel to the nonpersonal (and general) singular it, it and its, and the plural they, them and their. (In connection with the spelling 'e or e the consistent spelling for the first person pronoun is i instead of I, unless the capitalization follows a general rule.) Altho 'e, 'im and 'er are very closely related to already existing pronouns and adjectives, the adoption of these terms is certainly more far-reaching than some older proposals which have confined themselves to the unneutral use, not the irrelevant use, of genderized terms. It is relatively easy to come up with truly gender-neutral, linguistic conventions or decrees. As a reaction to the so-called 'generic' use of masculine terminology, which has been exposed as a joke, it has been urged, for example, to always mention both the feminine and the masculine equivalent, or either the feminine or the masculine equivalent. On this view people will just have to say "he or she", "her or his", "man or woman", and so on, and equally frequently the reverse, when speaking of someone who may be either male or female. They must take care too, of course, not to use derogatory, traditional expressions such as spinster or (meter) maid, and they must not speak of "a woman driver" or "a male secretary" unless also speaking of "a man driver" and "a female secretary" respectively in the same circumstances. Moreover, those insisting on gender neutrality in the language have demanded that language users not only say "men and women" instead of "men" but also "actors and actresses" instead of "actors", "launderers and laundresses" instead of "launderers", and so on, unless the people spoken about would definitely all be male, or for that matter, all female. Unfortunately, by thus rejecting the unneutral use of traditionally masculine terms, the irrelevance of the gender distinction itself is not transcended. A joke is turned into a yoke, because everyone would now be forced to say everything double. (This is a disaster in languages in which all, or almost all, nouns and pronouns of the type in question are genderized. Even in the present, written language no-one has ever managed --it seems-- to consistently use he or she and her or his, and equally frequently the reverse, everywhere where required according to the proposed rule.) Quite often, a larger amount of relevant information does not entail that we have to say more, because there is one word which has the same meaning as, for example, a noun with an adjective or adjectival subordinate clause. (Take ice instead of frozen water other than snow.) But it is a rule that a smaller amount of relevant information is not to be conveyed by having to say more. Nevertheless, this is precisely the case in speech which is not gender-( and age-)transcending: authors and or or authoresses, for instance, gives less information than authoresses, aunts and or or uncles less than uncles in all cases that gender does not matter. If authoress does convey more relevant information than author, it should be because of the suffix -ess, and the use of author is then to be considered as to be free from gender, that is, gender-transcending. Since males do not have their own appendage then, feminine suffixes become sexually exclusive, and ought to be discontinued in gender-transcending usage. If sex is to the point, it is to be indicated by the adjective, like in female dancer and male dancer: m./f. bachelor, f./m. fisher, m./f. god, and so on. The worst thing is not to accept that nouns which are traditionally masculine and purportedly gender-neutral will in future refer to women and girls as well, altho they are merely characterized by the absence of any standard suffix to specify gender (as the absence of -ess in authoress). (Thus female king does not have to be substituted for queen, unless a 'female king' is a female monarch, and a 'male queen' the husband or widower of such a chieftain.) If there is no good alternative, the refusal to accept terms without a genderizing affix as gender-transcending terms is responsible for a linguistic system which may be gender-neutral, but which is even more deficient than the traditional system from the standpoint of easy communication and informational relevance. The deficiency of systems which force the speakers and writers of a language to make distinctions on the basis of gender or age regardless of context is a very important kind of deficiency, as it is closely connected with, if not a form of, sexism and agism or --if preferred-- sex- and age-linked irrelevantism. These isms are, in turn, expressive of exclusivist attitudinal complexes and ideologies. (This does not mean that linguistic deficiencies could not be of a purely linguistic character, and would necessarily be related to a particular kind of ideological attitude or practise. Yet, even if they are not, they may be a nuisance or a cause of confusion.) Another kind of deficiency which is not purely linguistic is due to the fact that unmarked terms such as big, old and relevant have both an affirmative ('positive') meaning, and a general dimensional meaning (designating the extension of both bigness and its negation, of both being-old and its negation, of both relevance and its negation). Marked terms such as small and low often designate the negativity of a catena, whereas unmarked terms can designate either the nonnegative predicates or all the predicates of such a catena, that is, the catenality in question. Since our catenical terminology can deal with these distinctions, we can live with the double meanings of unmarked terms. Where it comes in handy, however, we may distinguish the marked ('positive') from the unmarked (general) meaning, especially when there is no catena involved. Thus, we shall employ relevance and consistence to designate the negation of irrelevance and inconsistence respectively, while employing relevancy to designate the whole aspect of being relevant or irrelevant, and consistency the whole aspect of being consistent or inconsistent. Marked terms such as small, weak, low and irrelevant have in general a pejorative evaluative meaning, whereas the antithetical, unmarked terms have a meliorative meaning. This phenomenon has been the basis of one of the criticisms against the unmarked use of he, him and his (for both males and females, and for males only) as opposed to the marked use of she and her (for females only). In this light the connotation of she is, at least on balance, inferior to that of he, just like small would be of a lower value than big. (This also explains the traditional use of the diminutive for women and girls where it is not used for men and boys.) The evaluation inherent in the connotation of unmarked terms is typical of catenary 'maximalism' or 'extremism': the higher, the better; the bigger, the better; the faster, the better; the louder, the better; and so on and so forth. It is this lust for the most which definitely has ideological, if not serious ideological, implications. Closely related to the question of the ambiguity and positive connotation of unmarked terms is the absence of a word to denote the neutrality of a catena. From an extremist point of view this neutrality is not interesting; only the maximum is, or the maximum and minimum. Therefore the language users often have to take refuge to clumsy circumlocutions of the neither nor type in traditional parlance. Strictly speaking, these expressions do not even denote neutralities but nonpolarities encompassing noncatenalities. For example, speaking of the neutrality of the happiness catena, people could only say "neutrally neither happy nor unhappy"; and speaking of the neutrality of the honoring catena, they could only say "neutrally neither honoring nor dishonoring". Those given to extremist thought are merely interested in as much happiness, and as much honor, as possible (and as ends in themselves ). Therefore they do not realize that a linguistic system without a general device to directly denote the neutralities of such catenas is deficient in this respect. Not having such a device perpetuates catenary extremism or unneutralism, but the question is, of course, whether this matters or not. In the Book of Fundamentals it will become evident that it does, and we will then see how to go about it. 3.4.5 WRITING AND SPEAKING ON NEW TERMS The introduction of new words, or of new meanings, in order to put an end to a linguistic system`s deficiency, or simply, to extend its vocabular and semantical range, can take place in the medium of the spoken or in that of the written language. It is therefore important to know whether one of both mediums is perhaps the primary one. We should not forget that some linguists have insisted that the spoken language is of prime significance and other linguists that the written language is (particularly in questions of orthography). It seems, however, that the generalized question whether the spoken or the written language is of prime significance is itself already inaptly formulated. Yet what we can be sure about is that at least the impact of written language has become enormous since the invention of printing (about five-and-a-half centuries before the manuscript of this Model was word-processed in a computer). It is in the written language that important, 'normal' distinctions in present-day 'natural' languages were once artificially introduced or reintroduced. And when it is said that 'new usage can supplant the old with comparative ease' and that 'it is encouraging that there is one barrier which can be scaled with relative ease', this probably applies in the first place to the medium of the written language, if only because one can take more time when writing than when speaking. Later on the changes in, and additions to, the written language are bound to produce parallel new words and meanings in the spoken language, at least among those people between whom the exchange of thoughts and feelings takes place. Even if in 'the partnership of language and (nonlinguistic) cultural norms, language is by nature the autocratic factor' --as has been remarked-- it does not follow that it is not people (or male and female human beings) who maintain and create the kind of language we are dealing with here. Supplanting particular linguistic conventions with a new usage may be a question of the writer`s or speaker`s ideology, but rejecting or ignoring such usage is not less a question of ideology. Conventions, even 'traditional' ones, are prerequisite for language, but there are other conventions, or decrees, which are prerequisite for the viability and expressivity of a new attitude, of new normative convictions. Let no-one tremble with the thought of a limited number of his, of his or her, nay, of `er, linguistic conventions or decrees being discredited. It is not the right attitude when the linguistic rules concerned did serve, do serve or will continue to serve irrelevantist or other objectionable purposes. Besides, it does not help, for the old man whose tongue is traditional language must needs pass away eventually anyhow. This is as certain as the fate of needs . [Copyright ©MVVM, 41-69 a(fter)S(econd)W(orld)W(ar) M. Vincent van Mechelen] [TRINPsite, trinp.org; owner Stichting DNI Foundation, reception2@trinp.org]