Very briefly put, a categorical framework is a specific category system of a P-language that describes the structure of the world perceived through the language community by categorizing its entities. There is one kind of category system that deserves our special attention: scientific taxonomy. Many scientific category systems are taxonomies, such as animal taxonomy (the Linnaeun system), plant taxonomy, etc. Of course, not all category systems are taxonomies. A category system is a taxonomy if and only if it breaks up into disjointed categories with exclusive relationships between any two categories at the same level. For the purpose of explication, we may conceive of a taxonomy as having both a vertical and a horizontal dimension. The vertical dimension concerns the level of inclusiveness of the category—the dimension along which terms such as collie, dog, mammal, animal, and living thing vary. The horizontal dimension concerns the segmentation of categories at the same level of inclusiveness—the dimension along which terms like dog, car, bus, chair, and sofa vary.
Kuhn worked out a theory of lexical/taxonomic structure of scientific languages1 in his taxonomic interpretation of incommensurability, some aspects of which we have touched on in chapters 2 and 7. For clarity, let us recapture some essential points of the theory here.
(a) The basic members in a taxonomy are taxonomic categories or kind-terms. For Kuhn, a taxonomic category is nothing other than a kind denoted by a kind-term. Kind-terms refer to a widespread category that includes natural kind-terms (including mundane kinds such as ‘tigers’, ‘lemons’, ‘water’, ‘gold’, ‘metal’, ‘heat’, etc., and cosmic kinds such as ‘phosphorous’, ‘electricity’, ‘hydrogen’, ‘H2O’, etc.), scientific kind-terms (the terms used in some branch of sciences as well as some terms from common language when they have a role in the specialty in question, such as ‘plutonium’, ‘the Compton effect’, ‘apparatus’, ‘instruments’, etc.), and many others. Some kind-terms (such as ‘force’, ‘compound’, ‘phlogiston’, ‘planets’, ‘mass’, ‘element’, etc.) have a greater level of generality than other kind-terms (such as ‘alloy’, ‘metal’, ‘physical body’, ‘salts’, ‘gold’, ‘water’). Since these more general kind-terms figure importantly in fundamental laws about nature, we have referred to them as ‘high-level theoretical kind-terms’; accordingly, these less general terms have been referred as ‘low-level empirical kind-terms’. A kind is what is denoted by a kind-term. In the following discussion, we will not distinguish kinds from kind-terms. Since any tree of kinds can be presented as a tree of names of kinds or kind-terms, we can discuss these properties at the lexical level.2
(b) There are two principles associated with kind-terms: (i) The Projectibility Principle: Kind-terms are clothed with expectations about the extensions of the terms, since to know any kind-term at all is to know some generalizations satisfied by its tokens and to form expectations about the unexamined events (potential tokens). Some of the expectations about kind-terms (especially for the low-level empirical kind-terms) are normic (admit exceptions), and the others (especially for the high-level theoretical kind-terms) are nomic (exceptionless), which are usually laws of nature. More importantly, these expectations of kind-terms are projectible in the sense that these expectations enable members of a language community who use the kind-terms to project the use of the terms to other unexamined situations, (ii) The No-overlap Principle: No two kind-terms at the same level of a (stable) taxonomic tree may overlap in their extensions. As a result, there are only two possible types of class relationships between two kind-terms, that is, either inclusive when a kind (cats) is included in a higher-level kind (mammals) or exclusive when two kinds (cats and dogs) are at the same level.
(c) A lexicon is a structured conceptual vocabulary of a given language, which is the mental module in which individual members of a language community store the community’s shared kind-terms/kind-concepts (clothed with expectations about their extensions) to describe and analyze the natural and social worlds surrounding them. The lexicons of the various members of a language community may vary in the expectations about the referents of the same kind-term they induce. Indeed, it is the different expectations about the shared kind-terms possessed by each member that distinguish different individual lexicons in a community. However, although different members of a language community may have different lexicons due to difference in expectations (different criteria for determining referents) about the shared kind-terms, these different lexicons are mutually congruent, or have a common structure. It is the shared lexical structure, instead of individual lexicons possessed by each member, that binds the language community together and at the same time isolates it from other communities.
To illustrate the lexical structure of a P-language, imagine, for a moment, that all shared kind-terms in a language community are connected to form a lexical network in which each kind-term is a node from which radiates net lines to tie some terms together and distance them from others, thus building a multidimensional structure within a lexicon. For different individuals, different materials which represent different expectations or criteria of the extension of the nodal term are used as net lines to connect nodes. What such homologous structures preserve, instead of the common materials for the net lines, is both the shared taxonomic kind-terms (the shared nodes) and the similarity relationships between them (the way nodes are connected). This shared structure among different individual lexicons in a language community is what Kuhn calls the lexical structure (lexical taxonomy) of the language. Stating it formally, the lexical structure of a language is the conceptual/vocabulary structure shared by all members of the language community, which provides the community with both shared taxonomic categories (kind-terms) and shared (similarity/dissimilarity) relationships between them.
All scientific languages are P-languages with lexical taxonomies, such as the Copernican taxonomy (in which the extension of ‘planets’ includes ‘earth’ but not ‘moon’ and ‘the sun’), the Ptolemaic taxonomy (in which ‘moon’ and ‘the sun’ were in the extension of the kind ‘planets’ but ‘earth’ was not), the taxonomy of Aristotelian mechanics (in which the kind-term ‘motion’ not only includes the change of position of a physical body, but also the change of quality such as growth—the transformation of an acorn to an oak and transition from sickness to health), the taxonomy of Newtonian mechanics (in which ‘motion’ only refers to the change of position, not the change of quality), the taxonomy of the phlogiston theory (‘phlogiston’, being its primary kind-term), and the taxonomy of traditional Chinese medical theory, etc. The list can go on and on. For a concrete example of the taxonomy of a language, consider the ancient Greeks’ taxonomy of the heavens on which Ptolemaic astronomy was based:
For the Greeks, heavenly objects divided into three categories: stars, planets, and meteors. We have categories with those names, but what the Greeks put into theirs was very different from what we put into ours. The sun and moon went into the same category as Jupiter, Mars, Mercury, Saturn, and Venus. For them these bodies were like each other, and unlike members of the categories ‘star’ and ‘meteor’. On the other hand, they placed the Milky Way, which for us is populated by stars, in the same category as the rainbow, rings round the moon, shooting stars and other meteors. There are other similar classification differences. Things like each other in one system were unlike in the other. Since Greek antiquity, the taxonomy of the heavens, the patterns of celestial similarity and difference, have systematically changed. (Kuhn, 1992, p. 19)
Since Aristotle, there has been an old epistemological problem about the relation of the categories of mind and the categories of the world. Corresponding to the two extremes of this relation are two extreme positions on the formation of human category systems. At one extreme, environmental determinism claims that human categorization is fully determined by the structure of the world we live in. The categories that we isolate from the world of phenomena we do find there because they stare every observer in the face. The environment does, according to this position, all of the work of categorization. Since the world we perceive has a fixed structure and our categorization is fully determined by it, we would eventually cut the world at its joints.3 At the other extreme, many others look to the order in the organism, and especially to the form of its cognitive constructs as the basis for the coherence of categorization. According to this intellectually based position, human categorization exclusively depends upon contextual factors embodied in cultures or language communities. The mind does all of the work of categorization.4
A better way to take is a middle road that countenances both pure environmental and pure intellectual bases for human categorization. This approach attempts to address the effects on our categories both of the discontinuities in nature and of our cognitive constructs, but with emphasis on the central role of theories or cognitive constructs in human categorization. There has been a developmental trend in cognitive science and psychology on human categorization, a trend away from a perceptual account of categorization, and toward a more theoretical and interest-relative basis for categorization. The issue on categorization has to do with explaining the categories found in a culture or its counterpart, a scientific community, and coded by the language of that culture or community at a particular time. Many studies in cognitive psychology, cognitive science, anthropology, and the history of science in the past three decades have found that the major part of human categorization is neither biologically fixed nor environmentally determined, but is perceived through the lenses of cultures and languages: it is determined by different contextual factors and varies widely across contexts. More specifically, there are three distinguished contextual factors that affect human categorization: cultural factors, linguistic factors, and cognitive factors.
Category systems can shift with cultures and traditions. Many types of categories, although perhaps not all categories,5 are culturally relative. The research in ethnobiological classification has found that many folk classifications of plants and animals are culturally relative. For example, the following is a taxonomy of the animal kingdom attributed to an ancient Chinese encyclopedia entitled the Celestial Emporium of Benevolent Knowledge: All animals were divided into (a) those that belong to the Emperor, (b) embalmed ones, (c) those that are trained, (d) sucking pigs, (e) mermaids, (f) fabulous ones, (g) stray dogs, (h) those that are included in this classification, (i) those that tremble as if they were mad, (j) innumerable ones, (k) those drawn with a very fine camel’s hair brush, (1) others, (m) those that have just broken a flower vase, and (n) those that resemble flies from a distance (L. Borges, 1966, p. 108).
It is well known that O. Spengler has expanded the group of culture-relative categories to include cognitive categories, and developed his general thesis of the dependence of categories on cultural contexts, based on investigation of a few high cultures of history. According to Spengler, the so-called a priori contains, besides a small number of universally human and logically necessary forms of thinking, forms of thinking that are universal and necessary not for humanity as a whole, but only for a particular culture. So there are different ‘styles of cognition’ characteristic of certain cultures. Even mathematics is relative to certain civilizations. The mathematical formulae as such carry logical necessity; but their visualizable interpretation, which gives them meaning, is an expression of the ‘soul’ of the civilization that created them. In this sense, our scientific world picture is only of relative validity. The basic scientific concepts or categories, such as infinite space, force, energy, motion, etc., are expressions of our accidental type of mind, and do not necessarily hold for the world picture of other civilizations (L. Bertalanffy, 1955, pp. 251-3).
While Spengler was concerned with a small number of high cultures, American anthropologists took into account the cultures of primitive tribes and reached a similar conclusion. For example, as shown by L. Barsalou and D. Sewell (1984), people who have different cultural backgrounds often have different opinions about how typical of its category a certain instance is. ‘Groups of subjects taking different points of view generated substantially different graded structures for the same category. In birds, for example, the robin and eagle were typical from the American point of view, whereas the swan and peacock were typical from the Chinese point of view’ (L. Barsalou, 1987, p. 107).
Parallel to Spengler’s cultural relativism of the categories, B. Whorf developed his thesis of the dependence of categories on linguistic factors.6 It was a commonly held belief before Whorf that the cognitive process of all human beings possesses a common logical structure that operates prior to and independently of communication through languages. It follows that different languages are no more than merely different instruments for describing the same states of affairs or saying the same things differently. Whorf challenges this doctrine by proposing his hypothesis of linguistic relativity:
[T]he background linguistic system ... of each language is not merely a reproducing instrument for voicing ideas but rather is itself the shaper of ideas. ... We dissect nature along lines laid down by our native language. The categories and types that we isolate from the world of phenomena we do not find there because they stare every observer in the face; on the contrary, the world is presented in a kaleidoscopic flux of impressions which has to be organized by our minds—and this means ... by the linguistic system in our mind. (Whorf, 1956, pp. 211-13)
In other words, the structure of the language one habitually uses influences the manner in which one understands reality. Accordingly, the picture of the universe as perceived by users of different languages shifts from tongue to tongue.
According to Whorf, language affects thought by means of the kinds of classifications it ‘lays upon’ reality. Nature is, in reality, a kaleidoscopic continuum. The units that form the basis of the grammar and vocabulary of each language serve both to classify reality into corresponding units and to define the fundamental nature of those units. There are two basic forms of classification perpetuated by a language. One is overt classification made by language vocabulary at the level of lexicon. Any lexical difference between languages implies a difference in the thought content of the speakers. The other is covert classification at the grammar level. The most basic units of grammar, which Whorf claims formed the basis of the metaphysics of language, are none other than the most general grammatical classes of the language, such as nouns, adjectives, and verbs in English. Whorf speaks of the semantic correlates of grammatical classes as the ‘covert categories’ of the language that provide the speakers of a language with those covert classifications of reality. For example, in Indo-European languages, substantives, adjectives, and verbs appear as basic grammatical units. A sentence, which is essentially a combination of these basic grammatical units, contains a separable subject and a predicate. This scheme of a persisting entity (represented by the subject) separable from its properties (represented by the predicate) and active or passive behavior had a profound effect on the categories of occidental thinking, from Aristotle’s categories of ‘substance’, ‘attributes’, and ‘action’ to the antithesis of matter and force, mass, and energy in physics. By contrast, Indian languages (such as Nootka or Hopi) do not have these parts of speech or separable subject and predicate. Rather they signify an event as a whole. When we say, ‘A light flashed’, the Hopi use a single term, ‘flash (occurred)’. La Barre has vividly summarized this viewpoint:
Aristotelian Substance and Attribute look remarkably like Indo-European nouns and predicate adjectives. ... More modern science may well raise the question whether Kant’s Forms, or twin ‘spectacles’ of Time and Space are not on the one hand mere Indo-European verbal tense, and on the other hand human stereoscopy and kinaesthesis and life-process—which might be more economically expressed in terms of the c, or light-constant, of Einstein’s formula. But we must remember all the time that E = mc2 is also only a grammatical conception of reality in terms of Indo-European morphological categories of speech. A Hopi, Chinese, or Eskimo Einstein might discover via his grammatical habits wholly different mathematical conceptualizations with which to apperceive reality. (La Barre, 1954, p. 301)
The structure of a category system can also vary and shift with the development of human knowledge. The later Kuhn’s studies on taxonomic structures of scientific languages reach a similar conclusion as that of Spengler’s and Whorf s: the relativity of categories. Kuhn provides us with plenty of case studies from the history of sciences about how lexical taxonomies shift with different scientific theories. In particular, the Kuhnian thesis of the relativity of scientific taxonomies is essentially parallel to the Spenglerian thesis of cultural relativity of categories and the Whorfian thesis of linguistic relativity of categories. The Spenglerian thesis is based upon the few high cultures (civilizations) of history, the Whorfian thesis upon the linguistics of primitive tribes, and the Kuhnian thesis upon scientific development through different historical periods, especially during the periods of so-called scientific revolutions.
According to Kuhn, taxonomization is a process consisting of three interrelated variants: categorizing the domain into taxonomic categories; distributing items into pre-existing categories; and establishing the relationships between two categories in a taxonomy. The change of any one of these variants will change the taxonomic structure of a P-language.
Whorf has shown us in his empirical study of languages that different languages categorize the world in different ways. Sometimes two competing languages may categorize a common domain so differently that there is virtually no substantial overlap between their taxonomies. For instance, Chinese medical theory and Western medical theory classify a common domain in totally different ways and thus have totally disparate systems of medical categories. There is not any major overlap between the taxonomies of these two medical theories.
A new taxonomy may be created from an old one by removing some previous categories completely. For instance, the category ‘phlogiston’ in phlogiston theory disappeared completely from the oxygen theory. Such recategorization can crucially affect the extensions of interrelated categories, and thus change the lexical structure of the previous language.
As Kuhn illustrated below, during revolutionary transitions of scientific theories, a natural family could cease to be natural; its members were redistributed among pre-existing sets by transferring one or more singular objects or subcategories from one category to another, thus changing the membership of the categories.
The techniques of dubbing and of tracing lifelines permit astronomical individuals— say, the earth and moon, Mars and Venus—to be traced through episodes of theory change, in this case the one due to Copernicus. The lifelines of these four individuals were continuous during the passage from heliocentric to geocentric theory, but the four were differently distributed among natural families as a result of that change. The moon belonged to the family of planets before Copernicus, not afterwards; the earth to the family of planets afterwards, but not before. Eliminating the moon and adding the earth to the list of individuals that could be juxtaposed as paradigms for the term ‘planet’ changed the list of features salient to determining the referents of that term. Removing the moon to a contrasting family increased the effect. That sort of redistribution of individuals among natural families or kinds, with its consequent alteration of the features salient to reference, is, I now feel, a central (perhaps the central) feature of the episodes I have previously labeled scientific revolutions. (Kuhn, 1979, p. 417)
In the above case, what transferred in redistribution are singular objects, i.e. the moon and the earth, resulting in a change in the category of the high-level theoretical kind-term, ‘planet’. There is another kind of redistribution in which the categories of a pair of high-level theoretical kind-terms change due to switching a low-level empirical subcategory between them. For instance, the categories of the kind-terms ‘mixture’ and ‘compound’ altered because alloys were compounds before Dalton and were mixtures afterward.
As discussed in chapter 7, by focusing on the family resemblance relationship, Kuhn shows that two competing scientific communities at some stage of development many adopt different category systems due to holding different networks of similarity relations among objects and situations. For example, the similarity relationship between the sun and the earth was changed during the transition from Ptolemaic to Copernican astronomy. The sun and the earth were no longer put into the same category after Copernicus. Accompanying the shift of similarity relationships, the prototypes within taxonomic categories change. Due to the change of the prototype and the similarity relationship, a natural family or a taxonomic category ceases to be natural since its members are redistributed among pre-existing and newborn sets. Thus, the old category system is replaced by a new one.
Lastly, we have to emphasize that the three contextual factors we have identified above are not independent of one another. Culture and language are not two independent variables in the formation of a category system. It is impossible to separate a language from its cultural background. They are the two sides of the same coin. In some sense, we can say that a culture is reflected, in a concentrated form, in its language. A language is actually a micro-culture. Therefore, we should say that categories and their structures are found or bound in a culture and coded by the language of the culture. Furthermore, many taxonomies are not found in a culture all the time but rather found in a culture at a particular point in time. When we talk about a specific taxonomy found in a culture and coded in the language of that culture, we really mean the taxonomy, relative to the culture and its language, at a particular stage of the historical development of the culture and its language. Therefore, a language is not merely an abstract system of symbols outside cultural and historical contexts, but is an organic system of symbols embodied in a specific culture at a specific historical period. Considering a language in this sense, it is not an exaggeration say that each language has its own lexical taxonomy.
To sum up, human category systems do not remain stable across different contexts. Instead, human categorization is shaped by different contextual factors and varies widely across contexts. These findings challenge the traditional absolutistic view of categorization that found its foremost expression in Kantian conceptual absolutism. According to Kant, there are so-called forms of intuition (space and time) and the categories of the intellect (such as substance and causality), which are universally commitments for any rational beings. Accordingly, natural sciences based on these categories are equally universal. Physical science using these a priori categories—Euclidean space, Newtonian time, and strict deterministic causality—is essentially classical mechanics, which, therefore, is the absolute system of knowledge, applying to any phenomenon as well as to any mind as the observer. However, the development of natural sciences destroys the dream of absolutism. While categories (such as space) used to appear to be absolute for any rational observer, they now appear as changing with the advance of scientific knowledge (such as non-Euclidean spaces or the many-dimensional configuration spaces of quantum theory). Little is left of Kant’s supposedly a priori and absolute categories.
In chapter 8, I have formally clarified and defined logical presupposition, especially existential presupposition. A logical presupposition relation can be defined by logical implication within an uninterpreted language. However, the more interesting presupposition relations, which we encounter frequently in scientific languages, are so-called analytic presuppositions including sortal and state-of-affairs presuppositions. Since analytic presuppositions are meaning/interpretation dependent, they can only be defined by analytic implication within an interpreted language. It is hence hard to formally define analytic presuppositions that can apply to any interpreted language. Below, we will only focus on sortal presuppositions.
Our languages (both natural and scientific) are many-sorted languages. That is to say, all terms (names, descriptions, and variables) are classified into different sorts or categories. With every k-place predicate, P, a k-tuple of sorts or categories is associated: Whenever P (t1 ... , tk) occurs, it is required that the k-tuple of sorts or categories of {t1 ... , tk} should be the one associated with P. Put in another way, each predicate P in a possible world is assigned a specific set of objects, <Oi>, i = 1, 2, 3, ... to which the predicate P is applicable. We call this set of objects the category, sort, or significant range of the predicate P in question. For example, for a one-place predicate ‘ ... is red’, its category will be all sense-perceivable physical objects in our contemporary English speech community. Violation of this restriction will lead to so-called Ryle’s category mistakes, such as
(33) p is tuned to G sharp.
(34) My soul is red.
(35) The barn is grammatical.
(36) The earth is more honest than Mars.
According to Ryle’s original doctrine of ‘category mistake’, all sentences involving category mistakes are meaningless because they are ungrammatical or ill-formed. But the doctrine of literal meaninglessness of category mistakes is highly suspect. It is plain that sentences with category mistakes are different from gibberish such as ‘Three spadlaps sat on a bazzafrazz’ or ‘Umph the but g kreeplat blunk’. The sentences like (33)-(36) contain neither any non-word nor any other illicit surface-grammatical concatenation. Whether they are meaningful appears to be language dependent. For example, sentence (34) is truth-valueless for contemporary English speakers (call it language community E). However, the same sentence may be truth-valueful or actually describe a state of affairs when considered within another language community. Imagine a primitive tribe (call it language community T) whose people believe that each person’s soul is colored and that red color signifies courage. Then it is perfectly meaningful for a tribe’s warrior to declare proudly, ‘My soul is red’. The real problem with sentences involving category mistakes is not that they are meaningless or make no sense in general, but that they are truth-valueless or pointless for the user of a specific language community. For this reason, I side with J. Martin in attributing category mistakes to be the failure of sortal presuppositions.8
In fact, both (33) and (34) and their negations
(~33) p is not tuned to G sharp.
(~34) My soul is not red.
presuppose the following sentences, respectively:
(33a) p is capable of producing a musical tone.
(34a) My soul is capable of being colored.
Since these sortal presuppositions are held to be false for language community E, two presupposing sentences (33) and (34) are neither true nor false. More specifically, if an atomic sentence is thought to be made up of a subject and a predicate, such as
(23) S is P,
we can determine its truth-values in the following way. The extension of the predicate S must fall in the category of the predicate P. We define the extension of a predicate as a subset of its category. We can further assign truth-value status and truth-values to an atomic sentence (23) according to where its subject S falls: If S falls in the extension of P, then (23) is true; if S falls inside the category of P but outside the extension of P, then (23) is false; if S falls outside the category of P, then (23) is neither true nor false. Values for molecular sentences are then calculated according to Kleene’s strong matrix (refer to Table 8.3 in chapter 8). For example, since the subject ‘my soul’ of (34) is outside the category ‘is colored’ (all sense-perceivable objects), (34) is neither true nor false for language community E.
Like other types of presuppositions, a sentence may presuppose (necessarily) many different sortal presuppositions. For example, both sentence (34) and its negation (~34) presuppose (34a). Since a soul is a non-sense-perceivable entity (let us take this for granted for the sake of argument) for language community E, sentence (34a) in turn presupposes the sentence,
(34b) Some non-sense-perceivable entities are capable of being colored.
Based on rules of presuppositions CP2 and CP3 given in chapter 9, sentences (34a), (34b), and (34a and 34b) are all the presuppositions of (34). Of these different presuppositions, some of them are more fundamental than others in the sense that some presuppositions presuppose others without being presupposed by them. A sortal presupposition SP will be regarded as being more fundamental than another sortal presupposition SP*, if SP is presupposed by SP*. For instance, for sentence (34), presupposition (34b) is more fundamental than presupposition (34a) since (34a) presupposes (34b). Furthermore, if a sortal presupposition is so fundamental to a language that it sets (fully or partially) the boundary for the category (sort, or significant range) of a predicate in the language, then we will call it an absolute sortal presupposition for the language. For example, the category of the predicate, ‘ ... is red’, is the collection of all sense-perceivable physical objects in language community E. This category is determined by an absolute sortal presupposition in this language, namely,
(34c) Only sense-perceivable physical objects are capable of being colored.
This is the reason why (34) is neither true nor false when considered within community E, since a sortal presupposition of the sentence, i.e., (34b), directly contradicts the absolute sortal presupposition, (34c), of language community E. By contrast, the same sentence (34) would be either true or false when considered within language community T since the fundamental presupposition of the sentence, namely (34b), partially sets the category of the predicate ‘... is red’ that includes some immaterial entities like souls.
If the essential function of an absolute sortal presupposition is to determine (fully or partially) the category of a predicate in a language, then we can further assume that each language has its own system of shared absolute sortal presuppositions that set the boundaries for the categories of most predicates in the language (since the categories of most predicates in a language are relatively fixed). The existence of the system of shared absolute sortal presuppositions for each language is predicted by our formal theory of presupposition, although which specific absolute sortal presuppositions are held in a language cannot be identified by such a formal theory. Unlike logical presuppositions, which are defined by (formally) logical implication in an uninterpreted language, sortal presuppositions are analytic, and thus are defined by (formally) analytic implication in an interpreted language. While what a sentence logically presupposes can be determined by referring to the grammatical form of the sentence and is hence independent of the meaning of any particular descriptive term, what a sentence analytically presupposes cannot be determined by inspection of the grammar alone, but depends on the meaning of a particular descriptive term. The fact that ‘S is a cat’ and ‘S is not a cat’ presupposes ‘S is an animal’ depends on the meaning of ‘cat’ in a specific interpreted language. Therefore, it is the task of empirical semantics to identify the particular sortal presuppositions, including the absolute sortal presuppositions, of a specific language.
There is one effective way to identify the system of shared absolute sortal presuppositions of a language without appealing to a formal theory of presupposition. Consider the Ptolemaic sentence (19),
(19) Some planets travel around the earth.
(19) presupposes at least two assertions about the categorical status of the earth:
(19a) The earth is not a planet.
(19b) The earth is a star.
Here we take ‘revolve’ to mean a relation between two separate objects in that one object revolves around the center of gravity of the other. So (19a) is analytically implied by the verb ‘revolve’ in (19). (19b) can be derived from (19) based on the definition of ‘star’ (All the planets revolve around a star). (19a) is one absolute sortal presupposition of the Ptolemaic language about the category of the predicate, ‘... is a planet’, which excludes ‘the earth’ from the category of the kind-term ‘planets’. Similarly, (19b) is another absolute sortal presupposition of the Ptolemaic language about the category of the predicate ‘... is a star’ that includes ‘the earth’ in the category of the kind-term ‘stars’. In general, according to the category framework of Ptolemaic astronomy, the sun and moon were planets, like Mars, Venus, and Jupiter; the earth was not, but belonged to the natural family of stars. In contrast, after the transition from Ptolemaic to Copernican astronomy, the earth was a planet; the sun was a star; and the moon was a satellite.
The above case suggests that the categorical framework of each P-language actually functions as the system of shared absolute sortal presuppositions that sets the boundaries for the categories of most predicates in the language. Since each language has its own unique lexical taxonomy, it also has its own system of shared absolute sortal presuppositions. This conclusion is further supported by one key feature of the lexical taxonomy of a language, namely, the closure of lexical taxonomy: The lexical taxonomy of a language involves something like a ‘closure’—there are things that cannot be said without violating the lexical taxonomy in question. The closure of a taxonomy is implied by the Whorfian thesis. According to Whorf, the system of classifications of a language, especially the covert classifications, creates ‘patterned resistance to widely divergent points of view’ (Whorf, 1956, p. 247) (because of their subterranean nature they are ‘sensed rather than comprehended—awareness of [them] has an intuitive quality’ (Whorf, 1956, p. 70)). This patterned resistance may oppose not just the truth of the resisted alternatives but often the absolute sortal presuppositions underlying the system of classifications that an alternative has been presented.
Consider a familiar example. The Copernican system of classifications of celestial bodies (The earth is put into the category of planets) creates a ‘patterned resistance’ to the sortal presupposition (19a) or (19b) that is presupposed by the Ptolemaic sentence (19). The same is true for the Ptolemaic system of classification that creates a ‘patterned resistance’ to a sortal presupposition, say,
(37a) The sun is not a planet,
of many Copernican sentences, say,
(37) The planets revolve about the sun.
As a result, the Ptolemaic sentence (19), when considered within the Copernican language, is neither true nor false, since its sortal presupposition (19b) is held to be false within the Copernican language. Accordingly, the Copernican sentence (37), when considered within the Ptolemaic language, is neither true nor false, since its sortal presupposition (37a) is not held to be true within the language of Ptolemaic astronomy. It is clear that the Copernican (or the Ptolemaic) taxonomy not only sets the boundaries for the categories of predicates such as ‘... is a planet’ and ‘ ... is a star’, but actually determines the truth-value status of the sentences involved with these predicates. In this sense, we can say that the Copernican (the Ptolemaic) taxonomy constitutes its own unique system of absolute sortal presuppositions.
In general, if two different language communities have two different category systems that offer ‘patterned resistance’ to one another in the sense of suspending each other’s absolute sortal presuppositions, then the members of one community can use one sentence to make an assertion while the apparently same sentence cannot be used to make an assertion within the other community. Similarly,
with the Aristotelian lexicon in place it does make sense to speak of the truth or falsity of Aristotelian assertions in which terms like ‘force’ or ‘void’ play an essential role, but the truth-values arrived at need have no bearing on the truth or falsity of apparently similar assertions made with the Newtonian lexicon. (Kuhn, 1993a, p. 331)
This is because there is no way, even in an enriched Newtonian vocabulary, to convey Aristotelian assertions regularly misconstrued as asserting the proportionality of force and motion or the impossibility of void. In the Newtonian lexicon, these assertions cannot be expressed fully since to express them one has to invoke the Aristotelian lexicon, which is ‘patternedly’ resisted by the Newtonian lexicon.
Suppose that <MP1> and <MP2> are two distinct sets of M-presuppositions of two disparate P-languages PL1 and PL2. We can define a pair of compatible Mpresuppositions as:
<MP1> and <MP2> are compatible iff <MP1> and <MP2> are or could both be held to be true by the advocate of PL1 or PL2.
Consequently, the members of two language communities with compatible sets of M-presuppositions agree on the truth-value status of sentences of the other language, although they may differ in assigning truth-values to the same sentences. In contrast, two sets of M-presuppositions of two different P-languages are incompatible if the M-presuppositions of one language are categorically rejected by the advocate of the other. Two incompatible M-presuppositions assign opposite truth-value status to numerous core sentences of one language under consideration.
Accordingly, two P-languages PLj and PL2 are compatible if their M-presuppositions <MP1> and <MP2> are compatible with one another; otherwise the two languages are incompatible.
In the case in which one language is a subset of the other competing language, whether the two sets of M-presuppositions are compatible depends on the specific relation between them. Phlogiston theory was formed by adding the vocabulary and the universal principle of the existence of phlogiston to Aristotelian metaphysics such that the former was embedded within the Aristotelian language. Since the advocate of phlogiston theory accepts Aristotelian metaphysics and the Aristotelians could accept the existence of phlogiston, the two languages are compatible. In contrast, as shown in chapter 5, although the Newtonian language of space LN includes the Leibnizian language of space LZ as its sublanguage, the M-presuppositions of the two languages are still incompatible. This is because the Leibnizians are obliged to reject the M-presupposition of the Newtonian language, namely, the existence of Newtonian absolute space. Consequently, both languages assign different truth-value status to the sentences in the set SN-SL.
Among three types of M-presuppositions identified, our definition of the compatibility of M-presuppositions can be applied directly to existential presumptions and universal principles since they can be formulated as a set of countable statements. For example, the core sentences of Newtonian mechanics are underlain by the principle of construction. That is, properties such as shapes, masses, and periods are internal properties inherent in objects themselves and change only by direct physical interactions. But according to the theory of relativity, there are no such inherent properties (at least by the interpretation of Einstein and Bohr), for shapes, masses, and periods are relational properties between physical objects and co-ordinate systems. These properties could change even without any physical interaction between the objects in which those properties are supposed to inhere if the original coordinate system is replaced by another. From the viewpoint of the theory of relativity, the Newtonian principle of construction is simply false. Therefore, the universal principle of the Newtonian language and the corresponding universal principle of Einstein’s language (no matter what it is) are incompatible. A similar analysis can be easily applied to other P-languages with incompatible universal principles or existential presumptions. We will not belabor them here.
However, it seems difficult to apply our definition directly to categorical frameworks. Intuitively we cannot ask the question of whether a category system is true or false. We had better come up with a different criterion to test the compatibility of two competing category systems.
Consider the following hypothetical case study about color classification.9 Different languages may (and actually do) divide the spectrum in different ways and thereby have different color predicates. Imagine three sets, C1, C2, and C3, of color predicates in three different languages L1, L2, and L3. C1, C2, and C3 divide the spectrum in such a way that no color predicates of one set match up with the color predicates of any other set. Thus, we have three different category systems of color. Let us further suppose that C1 has ‘red’, ‘orange’, ‘yellow’, ‘green’, ‘blue’, and ‘purple’ as its finest-grained color predicates; C2 has ‘rorange’, ‘ygreen’, and ‘bpurple’; C3 has ‘red*’, ‘orange*’, ‘green*’, and ‘blue*’ at the corresponding level of discrimination. The extensions of C2 can be imagined to be distributed along the spectrum so that ‘rorange’ matches up with the shades of both ‘red’ and ‘orange’, ‘ygreen’ with both ‘yellow’ and ‘green’, and ‘bpurple’ with both ‘blue’ and ‘purple’ in C1. The extension of C3 can be imagined to be shifted along the spectrum to such a degree that ‘red*’ applies to some shades that C1 would call red and some shades that C1 would call orange; ‘orange*’ applies to some shades that C1 would call orange and the shade that C1 would call yellow, as well as others that C1 would call green; ‘green*’ applies to some shades that C1 would call green and some shades that C1 would call blue; ‘blue*’ applies to some shades that C1 would call blue and some that C1 would call purple.
The categorical mismatch between C1 and C2 is adjustable since each color predicate of C2 (namely, each color category) can be defined in C1. The predicate ‘x is rorange’ in C2 can be expressed as ‘x is either red or orange but not both’ (take ‘or’ in exclusive sense) in C1, ‘x is ygreen’ as ‘x is either yellow or green but not both’, and so on. In this way, C2 can be incorporated fully (without loss) into C1 although there are no shared categories between them. In this case, we say that C1 and C2 are two compatible category systems. By contrast, the mismatch between C1 and C3 is so disparate that it is impossible to define each color predicate of C3 in C1, and vice versa.
Perhaps one might suggest a possible formulation as follows: The speaker of L1 can interpret the speaker of L3 as having the concept ‘reddish-orange’, or ‘shades which overlap with red and orange’ for the concept ‘red*’ in C3. Similar formulations can be given for the concepts ‘orange*’, ‘green*’, and ‘blue*’ in C3. But this proposal faces at least one crucial objection. Since we have supposed that the color predicates in both C1 and C3 are the finest-grained in L1 and L3, the speaker of L1 has no way to identify the extension of the concept ‘reddish-orange’, and thereby the extension of the concept ‘red*’ is undetermined for the speaker of L1. Without the identification of the extension of the concept ‘red*’, any formulation of ‘red*’ (in L1) cannot be done. Therefore, it is clearly not the case that C3 can be incorporated without remainder into C1. In this case, we say that C1 and C3 are two incompatible category systems.
Based on the above illustration, we can formulate the following distinction between compatible and incompatible category systems:
Two category systems (or taxonomies) are compatible iff one overlaps substantially with the other10 to the extent to permit incorporating one into the other.
Of course, the relationship between C1 and C2 is not the only kind of possible compatibility relations between two category systems. It is, for instance, possible that taxonomy T1 may be included fully within taxonomy T2 because T2 is extended from T1. Recall the Newton-Leibniz debate on the absoluteness of space. Although Newton’s and Leibniz’s theories of space present different conceptions of space, both theories have ‘overlapping’ or ‘common parts’. We have shown that Newton and Leibniz have no disagreement about the truth-value status of the classical Euclidean language LE, which is a common language shared by both sides. Actually, Leibniz’s language of space LZ is an extension of LE. The taxonomy of LE is included fully within LZ. Therefore, the taxonomies of LE and LZ are compatible. As to the relation between Newton’s language LN and Leibniz’s language LZ, the situation is a Little different. LZ is a sublanguage of LN. Within the overlapping part (namely, within LZ), since both languages have identical taxonomies (more precisely, part of Newton’s taxonomy is identical with Leibniz’s), both have compatible taxonomies. The controversy arises when the speaker of Leibniz’s language goes beyond LZ and asks whether the sentences in the set SN-SL have factual meanings. For example, from Leibniz’s point of view, core Newtonian sentences (9) (‘The body b at time t could have located in a different place’) and (10) (‘Spatial location of the body b at time t1 is different from its location at time t2) are actually truth-valueless or factually meaningless. But such a controversy about the truth-value status of sentences in question is caused by an underlying universal principle (whether there exists Newtonian absolute space), not caused by incompatible taxonomies of the two languages.
However, one might think that the central expressions used in the above definition, i.e., ‘incorporated’ and ‘overlap substantially with’, are too vague to be useful to make an effective distinction. Fortunately, Kuhn has provided us with another criterion to identify two incompatible taxonomies based on the projectibility principle and the no-overlap principle of kind-terms: Two category systems or taxonomies are incompatible if the extensions of some shared theoretical kind-terms in two taxonomies overlap (but are not co-extensive) in some local area to such an extent that incorporating one into the other will directly violate the no-overlap principle. In addition, two category systems or taxonomies can be incompatible if they are mismatched to such an extent that they are either totally disjointed or lack any major overlap. Those two criteria have been presented earlier. We will not belabor them here.
1 See Kuhn, 1983b, pp. 682-3; 1988, p. 11; 1991, pp. 5, 11-12; 1993a, pp. 315, 325, 329.
2 In his discussion of kinds, Kuhn does not explicitly discuss the ontological status of kinds that concerns, for example, the problem of natural kinds (cosmic vs mundane natural kinds). However, from Kuhn’s position on the ontological status of similarity relations and his attitude toward metaphysical realism, it is reasonable to regard Kuhn as taking a conceptualist position on kinds: There are not any sets, kinds, universals, classes out there in the world that cut the nature at its joints. Kinds or universals can exist in particulars, but there are none priori to particulars. There are real things out there, and we divide them into kinds according to both nature’s way (the things in nature distinguishing themselves into various segmentation) and our conceptions (the lexicon, i.e., the module in which members of a speech community store the community’s kind-terms). See Kuhn, 1993a, pp. 315-16 and Hacking, 1993, pp. 277, 291.
3 There are a number of problems with this position. One is that such environmental factors are ultimately insufficient to account for the richness and diversity of human categorization.
4 The real problem with this position consists in its assumption that segmentations of the world are originally arbitrary. Taking this view, human categorization may become the arbitrary product of historical accident or even of whimsy.
5 Perceptual categories, such as the categories of color, may be universal. Even so, they still leave room for cultural differences.
6 In some sense, we can say that the Whorfian thesis of linguistic relativity is part of a general conception of cultural relativism developed in the first half of the twentieth century.
7 Kuhn, 1970b, pp. 269, 275-6; 1979, p. 417; 1987, pp. 8, 10.
8 See J. Martin, 1975, 1979 for a formal definition of sortal presupposition.
9 The following hypothetical case study is a modified version of a similar case study given by M. Khalidi (1991, pp. 73-8). I adopt this case for a very different purpose.
10 An overlap between two taxonomies is different from an overlap between two kind-terms (or two categories). The no-overlap principle only prohibits the overlap between two kind-terms or categories at the same level of a taxonomy, but does not prohibit the overlapping of two taxonomies.