Taking the presuppositional interpretation, I puzzled over Kuhn’s and Feyerabend’s mature works on incommensurability. To my surprise, I found out that both pioneers of the thesis of incommensurability had already alluded to many aspects of the new interpretation in a profound way. Especially, the later Kuhn’s works on taxonomic incommensurability seem to be on the edge of breaking through the barrier of the traditional way of thinking about incommensurability in Tarski’s truth-functional style. In this chapter I will survey Kuhn’s positions on incommensurability and reconstruct Kuhn’s taxonomic interpretation contained in his later works. Feyerabend’s related works will be discussed when I clarify the contents of metaphysical presuppositions in chapter 10.
Unlike Feyerabend, Kuhn’s positions on incommensurability had undergone some dramatic changes since the publication of his Structure of Scientific Revolutions in 1962. We can roughly divide the development of Kuhn’s thoughts on incommensurability into three stages associated with the three different bearers of incommensurability: paradigm, disciplinary matrix, and lexicon. The first two stages will be presented below. The third stage will be discussed separately in the next section.
It is well known that Kuhn divides the development of natural sciences into periods of ‘normal sciences’ punctuated at intervals by episodes of ‘scientific revolutions’. A pivotal notion, paradigm, is introduced to conceptualize this revolutionary approach toward the development of scientific knowledge. Normal science is a period of a stable development dominated by a single paradigm. A scientific revolution happens when ‘an older paradigm is replaced in whole or in part by an incompatible new one’ (Kuhn, 1970a, p. 92). It is at the point of a revolutionary transition between two paradigms that we encounter the phenomenon of incommensurability: ‘The proponents of competing paradigms are always at least slightly at cross-purpose ... [and] fail to make complete contact with each other’s viewpoints’ (Kuhn, 1970a, p. 148). Consequently, ‘the transition between competing paradigms cannot be made a step at a time, forced by logic and neutral experience’ (Kuhn, 1970a, p. 150).
The term ‘paradigm’ in Structure was used loosely in two different senses.
On the one hand, it stands for the entire constellation of beliefs, values, techniques, and so on shared by the members of a given community. On the other, it denotes one sort of element in that constellation, the concrete puzzle-solutions which, employed as models or examples, can replace explicit rules as a basis for the solution of the remaining puzzles of normal science. (Kuhn, 1970a, p. 175)
As such, Kuhn’s notion of paradigm is very inclusive, embracing almost all shared metaphysical, epistemic, methodological, and value commitments of a scientific community, including the components of the normative dimension, such as problems, standards, and perceptions, as well as the components of the semantic dimension, such as meaning variance. Accordingly, Kuhn’s notion of incommensurability at this stage has at least four different meanings, as follows.
Two paradigms could be incommensurable due to different normative expectations built into each paradigm. The early Kuhn identifies the following three aspects of normative incommensurability.
(i) Topic-incommensurability: One definite feature of Kuhn’s paradigm consists in its self-determination of what count as legitimate problems to solve. Rival paradigms do not identify the questions or problems that any adequate paradigm must solve in the same way. However, the fact that rival paradigms focus on different sets of problems, define the most basic problems differently, and assign the problems different weights of contribution to their own paradigm would not make the rivals incommensurable. To make two paradigms incommensurable, these differences have to be built into the very standards of explanatory adequacy. In this sense, topic-incommensurability is not an independent form of incommensurability. It needs to be associated with another form of incommensurability, criterial-incommensurability.
(ii) Criterial-incommensurability: According to Kuhn’s theory of paradigms, it is the methodological standards of adequacy, including standards of adequate solution and adequate explanation as well as standards of comparative evaluation and rational justification that determine which problems should be solved. Those standards of adequacy that each paradigm implicitly sets for itself are sufficiently disparate from one to the next, each favoring its own achievements and research program and unfavorable with respect to the work of its rivals. For example, a criterial conception of rationality—institutionalized norms that define what is, and is not, rationally acceptable—is internal to a paradigm. Because of this, a mode of rational justification acceptable in one paradigm may not be acceptable in the other. Thus, there is no rational comparison between two competing paradigms.
(iii) Perceptual-incommensurability: Each paradigm decides its own privileged range of observational data or perceptions such that different paradigms may not acknowledge the same observational data or receive the same modes of perception. Two rival paradigms always seek to explain different kinds of observational data and lead to different perceptions in response to different agendas of problems and in accordance with different standards of adequacy. Metaphorically, ‘the proponents of different paradigms practice their trade in different worlds’ (Kuhn, 1970a, p. 150). This is the most controversial aspect of Kuhn’s early explication of incommensurability.
Two paradigms are incommensurable due to meaning variance. Both sides will inevitably talk past each other when trying to resolve their conflicts since they do not speak in the same terms. This is actually the received translation-failure interpretation we have discussed in chapter 2, which I will not belabor here.
In sum, incommensurability related to the notion of paradigms is characterized as certain kinds of discontinuities between two paradigms divided by a scientific revolution. They are semantic discontinuities, topic discontinuities, criterial discontinuities, and perceptual discontinuities. The nature of these discontinuities at this stage is vague and needs further clarification. Are there any common characteristics among these different kinds of discontinuities?
In the late 1960s, Kuhn clarified his notion of paradigm by replacing it with the notion of disciplinary matrix. The constituents of a disciplinary matrix include most or all components of a paradigm, which Kuhn made more specific under the new name:
Among them would be: Shared symbolic generalizations, like ‘f = ma’, or ‘elements combine in constant proportion by weight’; Shared models, whether metaphysical, like atomoism, or heuristic, like the hydrodynamic model of the electric circuit; Shared values, like the emphasis on accuracy of prediction, discussed above; and other elements of the sort. Among the latter I would particularly emphasize concrete problem solutions, the sorts of standard examples of solved problems which scientists encounter first in student laboratories, in the problems at the end of chapters in science texts, and on examinations. ... I shall henceforth describe them as exemplars. (Kuhn, 1970b, pp. 271-2)
Almost all the forms of incommensurability occurring between two paradigms can be recaptured under this new notion. However, the switch of the bearers of incommensurability from paradigms to disciplinary matrices indicates Kuhn’s progress in exploring the essence of incommensurability. There are two new forms of incommensurability associated with the two essential components of a disciplinary matrix: models/metaphysical commitments and exemplars.
Kuhn explains his notion of models as follows:
Models ... are what provide the group with preferred analogies or, when deeply held, with an ontology. At one extreme they are heuristic: the electric circuit may fruitfully be regarded as a steady-state hydrodynamic system, or a gas behaves like a collection of microscopic billiard balls in random motion. At the other, they are the objects of metaphysical commitment: the heat of a body is the kinetic energy of its constituent particles, or, more obviously metaphysical, all perceptible phenomena are due to the motion and interaction of qualitatively neutral atoms in the void. (Kuhn, 1977b, p. 463)
Some other examples of metaphysical commitments would be the pre-Newtonian assumption that all forces act by contact, the post-Newtonian commitment to an infinite Euclidean space, and the pre-quantum mechanics commitment to the fundamental character of continuous and deterministic physical processes. The metaphysical commitments of a disciplinary matrix provide the theorists with an explicit or implicit ontology by providing answers to some fundamental questions, such as what kinds of entities exist in the domain to be explored, and how may they be expected to behave and interact with one another? Two different metaphysical commitments of two competing disciplinary matrices populate the world with different entities, properties, and different interactions. The occurrence of this kind of metaphysical discontinuity signifies communication breakdown and leads to incommensurability at a deep level, which I will call metaphysical incommensurability (incommensurability due to conflicting metaphysical commitments).
Up to now, we have explored several different forms of incommensurability in the early Kuhn’s writings. What is the relationship among these different forms of incommensurability? The answer consists in the function of a metaphysical commitment: to provide the participants of a disciplinary matrix with explicit or implicit methodological guidance, which tells them what is to count as a legitimate problem in the context of this ontology, what is to count as an adequate solution to a problem, and what is to count as a satisfactory explanation. Take the Aristotelian theory of motion as an example. According to a metaphysical assumption of the Aristotelian theory, motion requires a constant acting force. Such an Aristotelian concept of motion created the problem of how to account for projectiles. The assumption not only created a problem to solve, but also determined that a legitimate explanation of projectiles had to make use of the entities, forces, etc., recognized in the Physics. Guided by this assumption, Buridan solved the problem with his version of the impetus theory. In contrast, once this Aristotelian metaphysical assumption was abandoned, the problems surrounding projectiles that required the postulate of an impetus either disappeared or did not make sense any more. An alternative disciplinary matrix with different metaphysical assumptions has a different list of problems and different criteria of adequacy. Their proponents use key expressions with different purposes. Hence, if the key expressions used by two rival theories happen to be the same, (e.g., ‘motion’ for Aristotle as opposed to ‘motion’ for Newton), the meanings of those expressions will differ.
As Kuhn himself emphasizes, the most essential and novel constituent of the disciplinary matrix is exemplars. By ‘exemplars’, Kuhn means ‘shared examples’ that are concrete problem solutions accepted by a scientific community as paradigmatic. The central role of exemplars in Kuhn’s disciplinary matrix is to provide members of a scientific community with a set of compatible learned expectations—although they may differ from individual to individual—about the similarities (similarity as family resemblance) among the objects and situations that populate the world they perceive. Presented with exemplars repeatedly drawn from various kinds, any member of the community can gain a learned perception of similarity relationship among different tokens, which determines the categorical structure of the language used by the community.
Kuhn’s discussion on the role of exemplars in scientific categorization is in line with a new development of the studies in human categorization in cognitive science and psychology around the 1970s.1 The question of concern is, how are objects and situations to be brought together selectively to form a category? According to this new approach, a category need not contain defining properties as necessary and sufficient conditions for membership, as the classical approach believes. If the ‘categorical nature’ of categories is to be explained, it appears most likely to reside in family resemblance—in the sense of Wittgenstein’s2—among its members. Categories may be processed, formed, and evaluated in terms of their individual exemplars or prototypes.3 The membership of a category is determined by whether a token is sufficiently similar (family resemblance) to one or more of the category’s known exemplars. Accordingly, a category does not have a fixed structure with a clear-cut boundary in which all members are equivalent. Instead, a category possesses a graded structure in which the membership of each token varies in how good an example it is of the category. Of all the members, those highly similar to the prototype are typical, whereas those less similar to the prototype are less typical and those dissimilar are atypical. Thus, there are two decisive factors for each category: its prototypes and the similarity relationships (family resemblance) of instances to these prototypes. If either the prototypes or similarity relationships are different or changed, then we have different graded structures for the same category (as far as the name of a category is concerned) or even different categories (as far as the content of a category is concerned). Foremost, the studies show that our category systems and the graded structures within categories are unstable, varying widely across cultural, linguistic, societal, and historical contexts (this will be discussed in detail in chapter 10).
Kuhn draws similar conclusions from his studies in the history of science. Following Wittgenstein’s notion of family resemblance, Kuhn insists that acquisition of similarity relation does not depend upon any explicit articulated rules or criteria. The knowledge of similarity can be tacitly embodied in the exemplars without intervening abstraction of criteria or generalizations. Such a family resemblance relationship determined by exemplars holds a central position in Kuhn’s theory of categorization. Kuhn regards natural categories as family resemblance classes: A natural family is a class whose members resemble each other more closely than they resemble the members of the other natural families. Similarity relationships, as a tacit classification, group similar objects in a category and separate dissimilar objects to different categories.
Kuhn finds further from his studies that different scientific languages with different disciplinary matrices at some stage of development have different category systems due to holding different networks of similarity relations among objects and situations. For example, the sun is more typical than the earth within the category of ‘planet’ for the proponents of Ptolemaic astronomy, since the former bears a closer resemblance relation to the ideal exemplar of the category represented by the category concept developed within the Ptolemaic tradition. The sun and the earth resemble each other and belong to the same category because both bear sufficient family resemblance to the concept of ‘planet’ in Ptolemaic tradition. In contrast with Ptolemaic astronomy, the earth is typical and the sun is atypical for the category ‘planet’ from the point of view of Copernican astronomy. This is because one is similar and the other is dissimilar to the prototype of the category of ‘planet’ determined by the category concept of ‘planet’ within Copernican tradition. The similarity relationship between the sun and the earth was changed also during the transition from Ptolemaic to Copernican astronomy. The sun and the earth no longer belong to the same category.
The above instability of graded structure of categories due to the shift of the network of similarity relations is demonstrated in full during episodes of scientific revolution. Due to the change of prototypes and similarity relationships during a revolution, a natural family ceased to be natural. Its members were redistributed among pre-existing and new-born sets. The old category system was replaced by new one. For instance, ‘what had been paradigmatic exemplars of motion for Aristotle—acorn to oak or sickness to health—were not motions at all for Newton’ (Kuhn, 1987, p. 19). This sort of redistribution of individuals among natural families or kinds is the central feature of the episodes labeled scientific revolutions. In this sense, a scientific revolution is, for Kuhn, characterized as a shift of patterns of similarity relationships.
The practice of normal science depends on the ability, acquired from exemplars, to group objects and situations into similarity sets which are primitive in the sense that the grouping is done without an answer to the question, ‘similar with respect to what?’ One central aspect of any revolution is, then, that some of the similarity relations change. Objects that were grouped in the same set before are grouped in different ones afterward and vice versa. Think of the sun, moon, Mars, and earth before and after Copernicus; of free fall, pendulum, and planetary motion before and after Galileo; or of salts, alloys, and a sulpuhur-iron filing mix before and after Dalton. (Kuhn, 1970a, p. 200)
As Kuhn points out, one direct result of the shift of similarity relationships during a scientific revolution is a communication breakdown between two language communities involved.
Not surprisingly, therefore, when such redistributions occur [referring to the redistribution of objects into different categories due to the change of the similarity relations], two men whose discourse had previously proceeded with apparently full understanding may suddenly find themselves responding to the same stimulus with incompatible descriptions and generalizations. (Kuhn, 1970a, p. 201)
Especially if two category systems of two scientific languages before and after the shift of similarity relationships, which happens usually during the episodes of scientific revolutions, are incompatible—one cannot be incorporated or fully formulated in the other—then the communication breakdown between the two communities is inevitable; and a full communication between them cannot be restored. Therefore, the two languages are incommensurable. This explication of incommensurability due to change in similarity relationships is Kuhn’s new unitary and highly specific surrogate for his old mixture of different forms of incommensurability. The significance of this version of incommensurability will become clear when we proceed to unearth the later Kuhn’s explication of taxonomic incommensurability.
After 1983 (marked by the publication of Kuhn’s essay, ‘Commensurability, Comparability, Communicability’), especially after his unpublished Shearman lectures delivered in 1987 at London, Kuhn had made a series of significant progresses (in his own words, ‘a rapid series of significant breakthroughs’) on the explication of incommensurability. Those progresses were initiated by introducing a new bearer of incommensurability: the lexicon (the lexical structure, the taxonomy, or taxonomic structure) of a scientific language. Kuhn defines a lexicon of a scientific language as the conceptual/vocabulary structure shared by all members of the language community, or as a mental ‘module in which each member of a speech community stores the kind-terms and kind-concepts used by community members to describe and analyze the natural and social worlds’ (Kuhn, 1993a, p. 325). A lexicon provides the community with both shared taxonomic categories/kind-terms and shared similarity relationships among those categories/terms. The structure of a lexicon of a scientific language consists of two parts: taxonomic categories or kind-terms and similarity relationships among these categories. Using K to refer to the kind-terms and R to refer to the relationships, a lexical structure, LS, of a language L can be symbolized as: LSL = [ K, R ].4
The notion of lexicon is a further development of Kuhn’s understanding of the role of scientific categorization in scientific communication, an insight that Kuhn had been pursuing since he started to focus on the notion of exemplars in the 1970s. The most significant elements of Kuhn’s works on incommensurability, I believe, were originated and developed from his insight of exemplars. What the later Kuhn did, during about a quarter century of his later life, was to approach this central thesis—incommensurability due to change in similarity—from different angles, and to explore it at different levels. It is this central thesis that constitutes the spindle of Kuhn’s engine of incommensurability. It is not hard to see that the later Kuhn committed himself more explicitly to this categorical approach to incommensurability. As we have mentioned in chapter 2, kind-terms in a scientific taxonomy are clothed with some expectations about their referents. These expectations are nothing but the expectations about the similarity relationships between objects and situations. ‘That is the pattern of similarities that constitutes these phenomena a natural family, that places them in the same taxonomic category’ (Kuhn, 1987, p. 20). The primary function of expectations about the similarity relationships is to transmit and maintain a taxonomy by passing and preserving the taxonomic categories and the structural relationships between them.
Compared with the two previous bearers, namely, the paradigm and the disciplinary matrix, which are a combination of linguistic and non-linguistic components, the lexicon is primarily a linguistic notion concerning the conceptual category system of a scientific language. By focusing on this categorical aspect of scientific language (exemplars, similarity relations, lexicons), Kuhn started to reorient his studies of incommensurability from the discussion of multiple-dimensional incommensurability, including both the normative and the semantic dimensions, to the focus on semantic incommensurability only. Incommensurability thus becomes a thesis exclusively about scientific languages. During the same process, Kuhn’s formulation of semantic incommensurability was undergoing transition also. In his early formulation, semantic incommensurability between two scientific theories was attributed to change in meanings (sense and reference) of the shared terms (singular and general terms) employed by theories. The later Kuhn realized that change in the semantic values of terms is only a by-product of a deeper lexical change of the languages, that is, change in the taxonomic structures of scientific languages. As far as the taxonomic structure is concerned, moreover, what is at stake is not any terms (single and general terms), but kind-terms (especially high-level theoretical kind-terms) in the related taxonomies. In fact, the later Kuhn became more and more dissatisfied with the traditional meaning approach to incommensurability with which he was widely identified as a major advocate:
Far from supplying a solution, the phrase ‘meaning variance’ may supply only a new home for the problem presented by the concept of incommensurability. ... [I]t will then appear that ‘meaning’ is not the rubric under which incommensurability is best discussed. (Kuhn, 1983b, p. 671)
To substitute lexicons for meanings, Kuhn wanted to ‘provide an account of incommensurability that does not explicitly use even the idea of meaning’ (Hacking, 1993, p. 294). Consequently, the later Kuhn restricted his attentions to one essential aspect of semantic incommensurability: taxonomic incommensurability.
As we have pointed out, for Kuhn two scientific languages are incommensurable when a necessary common measure is lacking between them so that the cross-language communication between their advocates breaks down. Kuhn’s different formulations of incommensurability evolved in the process of identifying such a significant common measure of full cross-language communication. It was indeed long journey home. Beginning with both the normative aspects of scientific languages (the same set of problems, compatible methodological standards of adequacy, and shared modes of perceptions) and the semantic aspects (shared meanings), Kuhn gradually pinned down the common measure as the categorical aspect of language (shared exemplars and communal perceptions of similarity relationships for scientific categorization), and eventually identified it as lexicons of scientific languages. Kuhn concluded that ‘shared taxonomic categories, at least in an area under discussion, are prerequisite to unproblematic communication’ (Kuhn, 1991, p. 4).
The lexicons of the various members of a speech community may vary in the expectations they induce, but they must have the same structure. If they do not, then mutual incomprehension and an ultimate breakdown of communication will result. ... People who share a core, like those who share a lexical structure, can understand each other, communicate about their differences, and so on. If, on the other hand, cores or lexical structures differ, then what appears to be disagreement about fact (which kind does a particular item belong to?) proves to be incomprehension (the two are using the same name for different kinds). The would-be communicants have encountered incommensurability, and communication breaks down in an especially frustrating way. (Kuhn, 1993a, pp. 325-6)
Left unresolved however is an explanation of why a shared taxonomic structure is necessary for cross-language communication between two rival scientific language communities in the case of incommensurability. Presumably, to answer the question Kuhn needs to work out a theory of cross-language communication to explain the essential role of lexicons in scientific communication. Without such a theory Kuhn’s taxonomic explication of incommensurability is radically incomplete. However, Kuhn appeared to be of two minds when he tried to address the issue at hand. He was torn and thus swung between the received interpretation of incommensurability as untranslatability and his more promising new interpretation in line with Hacking’s.
Kuhn seemed to be reluctant to part with the received interpretation of incommensurability as untranslatability. He apparently thought of cross-language communication in terms of translation. In fact, as early as at the end of 1960s and during the 1970s, Kuhn, in subsequent development of his views, realized that ‘untranslatable’ (Quine’s term) is a better word than ‘incommensurable’ for what he had in mind when he spoke of a communication breakdown between two rival scientific languages.5
In applying the term ‘incommensurability’ to theories, I had intended only to insist that there was no common language within which both could be fully expressed and which could therefore be used in a point-by-point comparison between them. (Kuhn, 1976, p. 191)
‘If two theories are incommensurable, they must be stated in mutually untranslatable languages’ (Kuhn, 1983b, pp. 699-70). Thus, instead of saying that Aristotle’s physics and Newton’s physics are incommensurable, one should say that some Aristotelian statements are not translatable into Newtonian statements. Since then, in clarifying incommensurability, the issue of translation-failure between rival scientific languages became a dominant theme of Kuhn’s.
After 1983, by virtue of introducing a new semantic tool of taxonomic structures, Kuhn continued to rely heavily on the notion of untranslatability in his explication of incommensurability.6 ‘Incommensurability thus becomes a sort of untranslatability, localized to one or another area in which two lexical taxonomies differ’ (Kuhn, 1991, p. 5). More significantly, Kuhn seemed to rely on the notion of translatability to bridge shared taxonomic structures with cross-language communication.
Notice now that a lexical taxonomy of some sort must be in place before description of the world can begin. Shared taxonomic categories, at least in an area under discussion, are prerequisite to unproblematic communication, including the communication required for the evaluation of truth claims. If different speech communities have taxonomies that differ in some local area, then members of one of them can (and occasionally will) make statements that, though fully meaningful within that speech community, cannot in principle be articulated by members of the other. (Kuhn, 1991, p. 4)
We can concisely formulate this reading of Kuhn (as one face of Kuhn) as follows:
(a) Effective communication between the speakers of two competing scientific languages is possible only if translation between the languages can be carried out.7
(b) Translation between two scientific languages is possible only if there is a systematic reference-mapping of the corresponding kind-terms in the two languages.
(c) A systematic reference-mapping of the corresponding kind-terms between two scientific languages is possible only if the two languages share the same taxonomic structure.8
(d) Therefore, a shared taxonomic structure is necessary for successful communication between two scientific language communities.9
Clearly, the above reading of Kuhn’s taxonomic interpretation is one version of what we have identified as the translation-failure interpretation of incommensurability in chapter 2. According to it, incommensurability amounts to untranslatability due to radical variance of meanings of the terms in two competing scientific languages. We have argued that translation is neither sufficient nor necessary for cross-language communication. Therefore, reference to untranslatability neither identifies nor resolves the problem of incommensurability, but rather leads to confusion and misunderstanding.
There is another face of the later Kuhn which has been neglected. Although one may find many reconstructions or reinterpretations of Kuhn’s concept of incommensurability in the literature,10 none have paid much attention to this aspect of Kuhn’s interpretation of taxonomic incommensurability, which is arguably more coherent, tenable, and powerful. As I reread Kuhn’s later works (especially the works after 1987) from the perspective of the presuppositional interpretation, I found that Kuhn had developed implicitly a sort of truth-value conditional theory of communication, which provides a badly needed cognitive connection between taxonomic structures of languages and cross-language communication. So construed, Kuhn’s concept of incommensurability is seen not to depend upon the notion of untranslatability after all, but rather rely on a set of semantic conceptions such as taxonomic structure, truth-value status and truth-value gap, possible world, and cross-language communication.11
Following I. Hacking, Kuhn recognized the importance of the distinction between the notion of truth-value and the notion of truth-value status in his latest interpretation of incommensurability.
Since that time, I have been gradually realizing (the reformulation is still in process) that some of my central points are far better made without speaking of statements as themselves being true or as being false. Instead, the evaluation of a putatively scientific statement should be conceived as comprising two seldom-separated parts. First, determine the status of the statement: is it a candidate for true/false? To that question, as you’ll shortly see, the answer is lexicon-dependent. And second, supposing a positive answer to the first, is the statement rationally assertable? To that question, given a lexicon, the answer is properly found by something like the normal rules of evidence. (Kuhn, 1991, p. 9)
These two stages of theory evaluation roughly correspond to the two phases of scientific development as defined by the early Kuhn, namely, revolutionary science and normal science. The later Kuhn realized that the landmark of scientific revolutions (paradigm shifts) is not the redistribution of truth-values, but reassignment of truth-value-status.
Clearly, the later Kuhn adopted trivalent semantics in thinking of incommensurability. Recall that in trivalent semantics, a substantial number of core sentences of one scientific language, when considered within the context of a competing language, could lack classical truth-values. For Kuhn, the core sentences of a scientific language are those presupposing the lexicon of the language: ‘Element a contains more phlogiston than element b’ in the phlogiston theory, ‘A body without external forces on it tends to seek its natural place’ in Aristotelian physics, and ‘Planets revolve about the earth’ in the Ptolemaic astronomy, and so on. As Kuhn observes, this is what happens during scientific revolutions.
Each lexicon makes possible a corresponding form of life within which the truth or falsity of propositions may be both claimed and rationally justified. ... 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 within the Newtonian lexicon. (Kuhn, 1993a, pp. 330-31)
Newtonians find Aristotelian sentences hard to understand, not because they think Aristotle wrote falsely, but because they cannot attach truth or falsity to a great many of the Aristotelian core sentences since the Aristotelian lexicon presupposed by the sentences fails when considered within the Newtonian language. Consequently, a truth-value gap occurs between the Newtonian and the Aristotelian languages. Such occurrences of truth-value gaps abound in the history of science. ‘Though the originals were candidates for true/false, the historian’s later restatements—made by a bilingual speaking the language of one culture to the members of another—are not’ (Kuhn, 1991, p. 9).
Along the lines of Hacking’s and Rescher’s reorientation of thinking of conceptual schemes in terms of redistribution of truth-value status instead of redistribution of truth-values, Kuhn’s substitute for the Quinean notion of conceptual schemes is his notion of lexicons.
What I have been calling a lexical taxonomy might, that is, better be called a conceptual scheme, where the ‘very notion’ of a conceptual scheme is not that of a set of beliefs but of a particular operating mode of a mental module prerequisite to having beliefs, a mode that at once supplies and bounds the set of beliefs it is possible to conceive. (Kuhn, 1991, p. 5)
Like Hacking’s styles of reasoning and Rescher’s factual commitments, the lexicon of a scientific language determines the truth-value status of its sentences.
After admitting the existence of truth-value gaps between two competing scientific languages, Kuhn faces the same question that confronts Hacking and Rescher: How to explain the occurrences of truth-valuelessness or truth-value gaps based on his notion of lexicons? Unlike Hacking, Kuhn’s lexical approach avoids circularity by defining lexicons independently without appeal to the notion of truth-value status. The later Kuhn seemed to come up with, as I interpret him liberally, a sort of truth theory that can be used to explain how a lexicon determines the truth-value status of sentences in terms of sort of truth-value conditions.
The usual theories of truth, such as the correspondence theory, are semantic theories about truth conditions and can only be used to determine the truth-value of a statement.12 But at issue here is not whether a statement is true, but rather whether a given string of words is assertable (hence qualifying as a statement) or whether a sentence has a truth-value. What is needed is not a theory about truth conditions, but a theory about truth-value conditions (whether a sentence has a truth-value). A usual theory of truth does not help us with this. So as to distinguish such a theory of truth from the usual theories of truth, it is useful to dub the former a ‘theory of truth-value’. Kuhn did not work out a complete theory of truth-value, but rather provided some clues here and there. Based on these clues, the task remains to reconstruct a Kuhnian theory of truth-value.
Following the conventional possible-world semantics, Kuhn regards a possible world as a way our actual world might have been (Kuhn, 1988, p. 13). The problem is which concept of world is in play here. As P. Hoyningen-Huene argues persuasively, Kuhn uses the concept of world in more than one sense (Hoyningen-Huene, 1993, ch. 2). It could refer to a world that is ‘already perceptually and conceptually subdivided in a certain way’ (Kuhn, 1970a, p. 129), which may be called a ‘world-for-us’. A world-for-us has a certain conceptual structure imposed by a certain taxonomic structure. It is a world to which we actually have conceptual access. In another sense, the concept of world could refer to the world-in-itself, namely, what is left over after we subtract all perceptual and conceptual structures imposed by human contributions from a world-for-us. Different from Kant’s thing-in-itself, Kuhn stipulates the world-in-itself to be spatio-temporal, not undifferentiated, and in some sense causally efficacious. Beyond this, nothing can be said about this world.
In what sense does Kuhn use the concept of a possible world? Do possible worlds include worlds-for-us only or both worlds-for-us and the world-in-itself? Answering this question requires consideration of a controversial issue on the ontological status of possible worlds. What is the proper range of possible worlds over which quantification occurs? D. Lewis quantifies over the entire range of worlds that have been or might be conceived. S. Kripke, at the other extreme, quantifies over only the worlds that can be stipulated. Kuhn makes a general distinction between conceivable (possible) worlds from stipulatable (possible) worlds. On the one hand, not all the worlds stipulatable within a given lexicon are conceivable. A world containing square circles can be stipulated but not conceived. On the other hand, not all possible worlds conceivable by the speaker of a language are stipulatable in it. For instance, the possible worlds described by the Newtonian language are not stipulatable, although conceivable, in the language of relativity theory (Kuhn, 1988, p. 14f). Kuhn stands along with Kripke and contends that only a world that can be conceptually accessible in the sense that it can be stipulatable in some language can be a possible world (Kuhn 1988, p. 14). Since the world-in-itself is totally inaccessible conceptually to any language community, it is not a possible world in Kuhn’s sense. Accordingly, the actual world in which one scientific community lives and works is a possible world that they actually perceive to be.
Notice that in Kuhn’s concept of possible worlds, the alleged distinction between there being a possible world and it being conceptually accessible is blurred. For a world to be a possible world, it has to be conceptually accessible somehow by some language. Some lexical structures are prerequisite to the existence of, not just accessible to, any possible world. ‘Like Kantian categories, the lexicon supplies preconditions of possible experience’ (Kuhn, 1991, p. 12). To echo G. Berkeley’s famous expression ‘to be is to be perceived’, Kuhn would say that ‘to be a possible world is to be conceptually accessible’.
Nevertheless, this does not mean that a possible world is conceptually accessible to any language. To be a possible world is to be a world accessible to certain languages, but not to any language. This is because, according to Kuhn, there is a conceptual connection between the taxonomic structure of a certain language and its conceptual accessibility relation to certain possible worlds. First of all, Kuhn contends that acquisition of a certain taxonomic structure is prerequisite to gaining conceptual access to a certain possible world. Certain learned similarity-dissimilarity relationships, as the central feature of a certain taxonomic structure, is a language-conditioned way of perceiving a certain world. Until we have acquired them, we cannot perceive that world at all. Similarly, some set of kind-terms supplies necessary categories to describe a certain possible world. For example, in order to gain conceptual access to the Newtonian world, the taxonomic structure of Newtonian mechanics, especially the interrelated kind-terms like ‘force’, ‘mass’, and ‘weight’, must be possessed first.
Kuhn further specifies that only the possible worlds stipulatable in, or describable by, the lexicon of a language are conceptually accessible to the language community. This is because
[o]nly the possible worlds stipulatable in that language can be relevant to them. Extending quantification to include worlds accessible only by resort to other languages seems at best functionless, and in some applications it may be a source of error and confusion ... [T]he power and utility of possible-world arguments appears to require their restriction to the worlds accessible with a given lexicon, the world that can be stipulated by participants in a given language-community or culture. (Kuhn, 1988, p. 14)
The question arises: ‘Why must every aspect of a conceptually accessible possible world be stipulatable in a language? Some of the possible worlds we are interested in might have an unaccessed or inaccessible feature for which no vocabulary has been, or even could be, developed. But those possible worlds are conceivable. Presumably the actual world is like this.’ Obviously, this objection assumes that any conceivable world would be conceptually accessible.14 But if it is possible to conceive of there being possibilities that cannot be conceived of, then to equate conceivability with conceptual accessibility may make it impossible to deal with such cases. More to the point, the matter at issue here is a language’s not an individual interpreter’s, conceptual accessibility relation to a possible world. Whether a possible world is stipulatable in a language can be determined by its taxonomic structure. But conceivability usually refers to the mental state of an individual interpreter. Any possible world would be conceivable for an interpreter if he or she wills to learn and adopt other languages that provide conceptual access to that world. Therefore, the concept of conceivability cannot help us to clarify a language’s conceptual accessibility relation to a possible world. It is irrelevant for the purpose at hand.
Theoretically, a language’s taxonomic structure enables the community to gain conceptual access to many, even infinite, possible worlds that are stipulatable in it. Of course, of these conceptually accessible possible worlds, only a small fraction are evidently possible for the community, which can be confirmed with experiments and observations accepted by the community. Discovering evidently possible worlds is what each scientific community undertakes to do in the course of normal science. As time passes, more and more conceptually possible worlds are excluded by requirements of internal consistency or of conformity with empirical data. Eventually, each lexicon may identify a highly limited set of possible worlds—the possible worlds that are both stipulatable and verifiable within the lexicon—and eventually a single world that the language community conceives as the actual world.
The same possible world may be conceptually accessible using different, but compatible, lexicons. Languages with incompatible taxonomic structures have access to different possible worlds.
To possess a lexicon, a structured vocabulary, is to have access to the varied set of worlds which that lexicon can be used to describe. Different lexicons—those of different cultures or different historical periods, for example—give access to different sets of possible worlds, largely but never entirely overlapping. (Kuhn, 1988, p 11)
To sum up, according to Kuhn, conceptual accessibility to possible worlds is taxonomic-structure dependent. Only the possible worlds stipulatable in a language can be conceptually accessible to the language community. Only a world conceptually accessible to a language is a possible world for it. Since conceptual accessibility to a world is language dependent, a possible world is language dependent.15 Therefore, a world may be possible for one language, but not possible for another. By providing the language community with a network of possibilities, the taxonomic structure of a language determines what is genuinely possible for the language.
Following Putnam and many others, Kuhn contends that although the correspondence theory of truth (i.e., the idea that the substantial nature of truth consists in correspondence with the mind-independent world) has to be given up, the intuition behind it (i.e., the truth of a sentence is determined by its correspondence to a state of affairs external to the sentence) seems too obvious to be put to rest. Such an innocuous intuition can still remain at the heart of a theory of truth as long as ‘a world-for-us’ is substituted for ‘the mind-independent world’ at one side of the correspondence relationship (Kuhn, 1988, p. 24; 1991, pp. 6, 8).
If, as standard forms of realism suppose, a statement’s being true or false depends simply on whether or not it corresponds to the real world—independent of time, language, and culture—then the world itself must be somehow lexicon-dependent. (Kuhn, 1988, p. 24)
More precisely, following the Wittgenstein concept of fact-ontology that the world is the totality of facts,16 we could treat a Kuhnian possible world as a set of internally related possible facts. Since a Kuhnian possible world is taxonomic-structure dependent, the possible facts are taxonomic-structure dependent. It is possible that some state of affairs counts as a possible fact in one language, but not in another with a sufficiently different taxonomic structure. Accordingly, a fact can be defined as the actualization of a possible fact or a possible fact verified in the actual world perceived by a language community. If a fact is the actualization of a possible fact and a possible fact is language dependent, then a fact seems to be inevitably language dependent. A fact so defined is relative to a language and subsists in a world specified by the language. There are no mind-independent facts out there waiting to be discovered.
According to the fact-based interpretation of the correspondence theory, a statement is true if and only if it corresponds to a fact. Because whether a state of affairs counts as a fact is dependent upon the taxonomic structure of a language; the same state of affairs may count as a fact in one language but not in another. Therefore, ‘evaluation of a statement’s truth values is, in fact, an activity that can be conducted only with a lexicon already in place, and its outcome depends upon that lexicon’ (Kuhn, 1988, p. 24). Consequently, evaluation of the truth-value of a statement or a truth claim of a sentence is a correlate of a taxonomic structure (Kuhn, 1991, p. 4).17
It is time to answer the question as to why some sentences that have truth-values in one scientific language lose their truth-values in another. Kuhn does not address this question explicitly. Nevertheless, based on his semantics of possible worlds and his adoption of a modified correspondence notion of truth as I have presented above, I think Kuhn would accept the following solution.
As pointed out earlier, the truth claim of a sentence P in a language L with a taxonomic structure TS consists in correspondence to a fact in the actual world perceived by TS. More precisely, take the designate of sentences as ‘states of affairs’. The truth-value of P consists in whether the state of affairs designated by P corresponds to a fact admitted by L. A fact admitted by L is at least a possible fact from the viewpoint of L. Then, in order for P to have a truth-value in L, the state of affairs designated by P has to correspond to a possible fact in a possible world specified by TS of L. For Kuhn, a possible fact from the viewpoint of L has to be conceptually accessible by TS. Thus the truth-value status of P9 when considered within L, is determined by whether the state of affairs designated by P corresponds to a possible fact from the point of view of L. If it does, then P is a candidate for truth-or-falsity; if it does not, then P is not a candidate for truth-or-falsity. Furthermore, if the state of affairs designated by P is not only a possible fact but also a fact specified by L, then P is true. Otherwise, it is false.
This establishes that the truth-value status of sentences is internalized within the taxonomic structure of a scientific language and becomes taxonomic-structure dependent. This is why Kuhn claims:
Each lexicon makes possible a corresponding form of life within which the truth or falsity of propositions may be both claimed and rationally justified. (Kuhn, 1993a, p. 330)
Where the lexicons of the parties to discourse differ, a given string of words will sometimes make different statements for each. A statement may be a candidate for truth/falsity with one lexicon without having that status in the others. And even when it does, the two statements will not be the same: though identically phrased, strong evidence for one need not be evidence for the other. (Kuhn, 1991, p. 9)
For instance, to assert the sentence,
(5) All diseases are due to the loss of the balance between the yin part and the yang part of the human body.
is to presuppose that there exist two natural forces ‘the yin’ and ‘the yang’. This state of affairs designated by (5) corresponds to a possible fact conceptually accessible by Chinese medical lexicon. (5) thus has a truth-value, no matter whether it is actually true or false, from the viewpoint of Chinese medical theory. However, the apparently same sentence is not conceptually accessible in terms of Western medical lexicon; thereby it does not correspond to any possible fact from the viewpoint of Western medical theory. Therefore, (5) is not simply false, but rather has no truth-value.
It has been argued so far that the truth-value status of sentences is, for Kuhn, taxonomic-structure dependent based on his theory of truth-value. However, Kuhn needs to explore further the role of truth-value status in cross-language communication in order to explain why, how, and in what sense a shared taxonomic structure between two scientific languages is necessary for successful communication between them.
To begin with, according to Davidson’s truth-conditional theory of understanding, to grasp the factual meaning (not just meaning in general) of a sentence is to know its truth conditions. To know the truth conditions of a sentence presupposes that the sentence has a truth-value. That means that having a truth-value is a prerequisite for a sentence to be factually meaningful. If a sentence lacks a truth-value when considered within a language, then it will become factually meaningless to its speakers. This explains why Kuhn has observed that ‘a historian reading an out-of-date scientific text characteristically encounters passages that make no sense’ (Kuhn, 1988, p 9). This is because these out-of-date sentences, which must have been either true or false in the original text, may be impossible to be stated as candidates for truth-or-falsity from today’s perspective.
Kuhn provides a different kind of argument for the necessity of truth-or-falsity in cross-language communication (Kuhn, 1991, pp. 8-10). Presumably, in order to achieve an informative use of a language, the language community has to adhere to some minimal rules of logic. Among them, the law of non-contradiction is crucial. The law claims that (S & ~S) is logically false for any sentence S in a language L, or in symbols, ├ L ~(S & ~S). The essential function of the law is to forbid accepting both a sentence and its contrary. The law requires a choice between acceptance and rejection of a sentence in discourse. For in normal discourse (something like the stage of Kuhn’s normal science), it is strongly desirable to make a choice between acceptance and rejection of a sentence in the face of evidences shared by both sides. For example, in Newtonian physics, we cannot assert both ‘Event e1 precedes event e2’ and ‘Event e2 precedes event e1’ at the same time. We cannot say that, in normal discourse, this paper is both white and not white. That is self-contradiction. Hence, it is reasonable to say that obedience to the law of non-contradiction to avoid self-contradiction is a minimal requirement for any successful linguistic communication. In this sense, the logical law of non-contradiction is one crucial minimal rule of any language game.
However, the proper function of the law of non-contradiction can be fulfilled only under some restrictions. When a sentence S has a truth-value within one language L1 ├ L1 ~(S & ~S) is valid. But if S is neither true nor false within another language L2, (S & ~S) is not false, but rather neither true nor false. The formula ├ L2 ~(S & ~S) thus is invalid since ~ (S & ~S) is untrue (neither true nor false) within L2. This shows that the law applies only to the sentences with (actual) truth-values. It requires that the sentences involved in discourse must have (actual) truth-values or be factually meaningful for one side to communicate successfully with the other. Actually, the law of non-contradiction can and should be understood as a hypothetical law. The law entails the positive truth-value status of the sentences involved. That is, ├ L ~(S & ~S) is valid—namely, (S & ~S) is logically false in L—only if S is either true or false. In this sense, to accept sentences in discourse as candidates for truth-or-falsity, which still allows for disagreement about their truth-values, constitutes the minimal rule of any successful linguistic communication. When one declares a sentence in discourse as a candidate for truth-or-falsity, one declares one’s commitment to the law of non-contradiction, and at the same time declares oneself as an active participant in linguistic communication.
On the contrary, the law prohibits the occurrence of truth-valueless sentences in normal discourse. To deny the sentences in discourse as candidates for truth-or-falsity is to violate the law of non-contradiction, and thereby to put communication at risk. If one breaks the rule by denying that the sentences in discourse have truth-values, then one declares oneself outside the language community. If a group of members of a language community denies that the core sentences of the language have truth-values but still try to continue to claim a place in the community, then the communication between them and the rest of the community breaks down. Neither side engages in successful communication even if they seem to talk to one another.
More significantly, it follows that if the core sentences in one scientific language, which are true or false in the language, have no truth-value when considered within another competing language, then there is a truth-value gap between them. The occurrence of such a truth-value gap indicates that the communication between the two language communities breaks down in a particularly frustrating way. A fully factually meaningful sentence within one language community sounds so strange in the other that it is not factually meaningful and thereby cannot be effectively understood in the latter. Therefore, the occurrence of a truth-value gap between two languages can be used as a strong linguistic correlate of a communication breakdown between them.
Based on the above consideration, Kuhn contends that all language games are no less than true-or-false games. For Kuhn, who endorses P. Horwich’s minimal theory of truth (Horwich, 1990), the truth predicates ‘is true’ and ‘is false’ exist primarily for the sake of such a logical need: to ensure that we stick to a language game. In Kuhn’s own words:
On this view [a version of the redundancy theory of truth], as I wish to employ it, the essential function of the concept of truth is to require choice between acceptance and rejection of a statement or a theory in the face of evidence shared by all. ... In this reformulation, to declare a statement a candidate for true/false is to accept as a counter in a language game whose rules forbid asserting both a statement and its contrary. ... In one form or another, the rules of the true/false game are thus universals for all human communities. (Kuhn, 1991, p. 9)
The idea that a language game is a true-or-false game can be viewed as one plausible interpretation of what Wittgenstein was driving at with his metaphor of conceptual schemes as ‘language games’. It is truth-value conditions, instead of truth conditions, that are ‘the rules of a language game’ in this interpretation. This assertion presents a striking contrast to conventional interpretations that focus on truth conditions, such as Davidson’s truth conditional theory of understanding.
It becomes clear now why shared or matchable taxonomic structures between two scientific languages are necessary for successful communication between them. But how can we know whether two taxonomic structures are matchable or not? Kuhn’s following passages provide a hint for such a distinction:
What members of a language community share is homology of lexical structure. Their criteria need not be the same, for those that can learn from each other as needed. But their taxonomic structures must match, for where structure is different, the world is different, language is private, and communication ceases until one party acquires the language of the other. (Kuhn, 1983b, p. 683)
Incommensurability thus becomes a sort of untranslatability,18 localized to one or another area in which two lexical taxonomies differ. The differences which produce it are not any old differences, but ones that violate either the no-overlap condition, the kind-label condition, or else a restriction on hierarchical relations that I cannot spell out here. Violations of those sorts do not bar intercommunity understanding. Members of one community can acquire the taxonomy employed by members of another, as the historian does in learning to understand old texts. But the process which permits understanding produces bilinguals, not translators, and bilingualism has a cost, which will be particularly important to what follows. The bilingual must always remember within which community discourse is occurring. The use of one taxonomy to make statements to someone who uses the other places communication at risk. (Kuhn, 1991, p. 5)
Full appreciation of these passages necessitates recollection of the two crucial features of Kuhn’s kind-terms: the projectibility principle and the no-overlap principle. According to the former, each kind-term is clothed with expectations about its extension or referents. The expectations about a kind-term’s referents are projectible in the sense that they enable members of a language community to postulate/project the use of the term to other unexamined situations, including counterfactual situations.19 The idea that kind-terms are projectible sounds like a tautology. To be a kind-term, a term must carry with it some generality on the application of the term to its tokens. However, we tend to ignore an important characteristic of the notion of projectibility because of its platitude: the limitation on the possible use of a kind-term. Although one can learn and understand the kind-terms in an old or an alien language, it does not mean that one can use them projectibly in one’s own language. One cannot speak an old or alien language while using the projectible kind-terms of the present language. Actually the same situation is faced by a bilingual who has to remind him or herself at all times of which language community he or she is in to avoid improper use of a kind-term of one language in the other language community. The no-overlap principle says that no two kind-terms at the same level of a (stable) taxonomic tree may overlap in their extensions (Kuhn, 1991, p. 4; 1993a, pp. 318-23).
The no-overlap principle is, in fact, the natural result of the projectibility principle. The expectations about a kind-term’s (e.g., ‘planet’s’) referents (e.g., planets) are usually learned in use.20 Presented with exemplars (e.g., the sun) drawn from various examined situations, the members of a language community (e.g., the Ptolemaic community) acquire a learned expectation about the similarity relationships between the objects or situations that populate the world perceived by them. In terms of these expectations about the similarity relationship among tokens, the members of the community can tell which presentations belong to which kind and which do not (e.g., Mars belongs to the kind of planets, but the earth does not in the Ptolemaic community). Since people can acquire the same kind-term in different ways, the expectations about the referents of the same kind-term may differ from individual to individual in a language community. However, within the same language community, these different expectations are compatible in the sense that they would eventually identify the same extension for the term by effectively learning each other’s expectations. On the other hand, some expectations about the referents of a kind-term may be so different in two competing language communities that they are incompatible with one another. In such a case, the members from one community (e.g., the Aristotelian community) will occasionally apply a kind-term (e.g., ‘motion’) to a token (e.g., the growth of an oak) to which the other (e.g., the Newtonian community) categorically denies that it applies. Usually, the non-identical extensions of the kind-term with incompatible expectations will overlap partially (e.g., for the movement of a physical object). If the speakers of the two communities use the term ‘motion’ separately in their own domain, no problem arises. But if they try to engage in an on-going dialogue, the difficulty arises in the region where both apply. Calling the same token ‘motion’ in the overlap region will always induce two conflicting expectations. Since these expectations are projectible, they cannot be only restricted within the overlap region and will be naturally extended to the respective non-overlap regions (e.g., to the growth of an oak). Therefore, ultimately the overlap is unstable and eventually only one kind-term remains within one language community (Kuhn, 1993a, p. 318).
The reason why two kind-terms at the same level of a (stable) taxonomic tree cannot overlap can be seen more clearly with some high-level theoretical kind-terms clothed with two incompatible expectations. Because these kind-terms figure importantly in fundamental laws about nature, they bring with them nomic expectations, i.e., exceptionless generalizations. In science, where they mainly function, these generalizations are usually laws of nature, such as Boyle’s law for gases or Newton’s laws of motion (Kuhn, 1993a, pp. 316-17). Then, if the extensions of such a kind-term with different concepts (e.g., ‘planets’ in Ptolemaic astronomy and in Copernican astronomy) overlap somehow and a token (e.g., ‘the earth’) lies in the overlap region, it would be subject to two exceptionless incompatible natural laws (e.g., Ptolemaic and Copernican laws of motion of celestial bodies). Similarly, the kind-term ‘mass’ in either Newton’s or Einstein’s language brings with it a nomic expectation in the form of a law of nature. Since the laws of nature built into the concept of mass in the Newtonian language and the Einsteinian language are incompatible, the respective expectations associated with the term are incompatible. These incompatible expectations will result in difficulties in the region where Newtonian ‘mass’ (massn) and Einsteinian ‘mass’ (masse) both apply. Calling some stuff in the overlap region ‘massn’ induces the nomic expectation associated with either the law of gravity or the second law of motion, while calling the same stuff ‘masse’ induces the incompatible nomic expectation associated with the new natural law in Einsteinian theory (general relativity theory). Hence such an overlap cannot remain stable over time (Kuhn 1988, pp. 14-23). For this reason,
periods in which a speech community does deploy overlapping kind-terms end in one of two ways: either one entirely displaces the other, or the community divides into two, a process not unlike speciation and one that I will later suggest is the reason for the ever-increasing specialization of the sciences. (Kuhn, 1993a, p. 319)
Following from the above reading of Kuhn’s insight, a primary type of unmatchable relationship between two taxonomic structures can be specified as follows:
Two taxonomic structures are unmatchable if the extensions of some shared theoretical kind-terms in the 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.
Classical unmatchable taxonomic structures are Ptolemaic vs Copernican astronomy (overlapping extensions of ‘planets’), Aristotelian vs Newtonian mechanics (overlapping extensions of’motion’), and so on.
Notice that the no-overlap prohibition only applies to the theoretical kind-terms with nomic expectations. The principle does not apply to the extensions of singular terms (names and definite descriptions) and must be weakened for low-level empirical kind-terms with normic expectations (the generalizations that admit exceptions). For low-level empirical kind-terms, only terms that belong to the same contrasting set are prohibited from overlapping in extensions. Therefore, the no-overlap prohibition is restricted within some local area of two overlapping taxonomies and leaves most parts of them open for possible overlapping. That means that a major overlap between two unmatchable taxonomies is still possible.
In addition to the above primary type of unmatchable relationships between two taxonomies, there exists at least another type:
Two taxonomic structures could be mismatched to such an extent that they are either totally disjointed or lack any major overlap.
Sometimes two competing languages may categorize a domain so differently that there is virtually no major overlapping between their taxonomies. B. Whorf has shown how different language communities might categorize the world around themselves in very different ways. Chinese medical theory and Western medical theory belong to such cases. It is hard to locate any major overlap between them since they employ two totally disjointed category systems at the theoretical level. Also, it is perfectly conceivable that two alien cultures may have two disjointed taxonomies although it is very unlikely that this will happen frequently.
It is time to put all the threads together for an overall picture of Kuhn’s taxonomic interpretation of incommensurability.
(a) Human categorization is determined by different contextual factors, such as cultural, historical, and linguistic factors, and varies widely across different contexts. The taxonomic structures of different scientific languages about the same subject matter can be totally different. The taxonomic structures of two successive rival scientific languages before and after a scientific revolution may change dramatically so that two structures become unmatchable.
(b) Different taxonomic structures gain conceptual access to different sets of possible worlds consisting of different possible facts. The truth-value status of sentence P of one scientific language L1 is determined by whether P, when considered within another competing scientific language L2, describes a possible fact in a possible world conceptually accessible by L2. Therefore, truth-value conditions of sentences are taxonomic-structure dependent.
(c) When the taxonomic structures of two competing scientific languages are unmatchable to one another, the two sets of possible worlds specified by them will be disjointed. Many possible facts within one set of possible worlds specified by one language would not count as possible facts when considered within the other language. Since the truth-value status of sentences is possible-fact dependent, there would be a truth-value gap occurring between the two languages. This is exactly what happens in the episodes of scientific revolutions. During these periods, scientific development turns out to depend on transitions to another disjointed set of possible worlds due to a switch to another unmatchable taxonomic structure. Is it, in these circumstances, appropriate to say that the members of the two communities live in different worlds? (Kuhn, 1988, pp. 13-15, 22-4)
(d) Accepting sentences in discourse as candidates for truth-or-falsity is an essential ingredient of any unproblematic linguistic communication. If there is a truth-value gap between two languages, this minimal logical rule of any language game is violated. Thus, the occurrence of a truth-value gap between two languages indicates that the communication between them is problematic and inevitably partial. ‘The would-be communicants have encountered incommensurability’ (Kuhn, 1993a, p. 326).
The above is the argument for a particular reconstruction of Kuhn’s new interpretation of incommensurability, which is a combination of a logical-semantic theory of taxonomy, a semantic theory of truth-value, and a truth-value conditional theory of communication. According to this truth-value interpretation of incommensurability, two scientific languages are incommensurable when core sentences of one language, which have truth-values when considered within its own context, lack truth-values when considered within the context of the other due to their unmatchable taxonomic structures.
1 To know more about this approach, please refer to E. Rosch, 1973, 1975, 1978; E. Rosch and C. Mervis, 1975; L. Barsalou, 1987; L. Barsalou and D. Sewell, 1984.
2 It is well known that Wittgenstein argues that the tokens of a type need not have common elements, from which a general rule or a set of criteria can be derived, in order for the type to be understood and used in the normal functioning of a language. He suggests that, rather, a family resemblance relation might be what linked the various tokens of a type into a similarity set (similarity in the sense of family resemblance). A so-called family resemblance relationship is a primitive relationship among items in which each item has at least one element in common with one or more other items, but no, or few, if any, elements are common to all items. For instance, a set of items consisting of the following different combinations of letters is a family resemblance set: ABC, BCD, CDE, DEF.
3 ‘Prototype’ is a term introduced by E. Rosch. By a prototype of a category, Rosch means the clearest cases of category membership defined operationally by people’s judgments of goodness of membership in the category. In Kuhn’s hands, ‘exemplar’ means originally ‘shared examples’ that are concrete problem solutions accepted by a scientific community as paradigmatic. In the case of categorization, ‘exemplar’ simply means the most typical token of a category according to a language community.
4 For a detailed explanation of Kuhn’s notion of lexicon or taxonomy, please refer to chapter 2 and I. Hacking, 1993.
5 See Kuhn, 1970a, 1970b, 1976, and 1979.
6 Kuhn, 1983b, pp. 669-70; 1988, p. 11; 1991, p. 5.
7 Kuhn, 1977a, p. 338; 1983b, p. 683; 1988; 1991, p. 5.
8 Kuhn, 1983b, p. 683; 1988, p. 22; 1991, p. 5, 1993a, p. 324.
9 Kuhn, 1988, p. 16; 1991, pp. 4-5; 1993a, pp. 325-6.
10 Such as W. Balzer, 1989, M. Biagioli, 1990, H. Brown, 1983, G. Doppelt, 1978, D. Fu, 1995, P. Hoyningen-Huene, 1990, H. Hung, 1987, M. Malone, 1993, B. Ramberg, 1989, and H. Sankey, 1991, to mention only a few.
11 Perhaps my following readings of Kuhn cannot be found explicitly in Kuhn’s writings. It is a reconstruction that uses various hints from Kuhn’s writings that, I think, reveal his mature understanding of incommensurability. What I try to do is to construct from these hints a reasonably clear and coherent theory of incommensurability. Inevitably, the reader will find that my interpretation of Kuhn is heavily influenced by my presuppositional perspective. Actually, maybe the contrary is true: My presuppositional interpretation is inspired by Kuhn’s insights revealed in his later writings.
12 Here we are only concerned with the so-called epistemic dimension of truth (about truth conditions), not about the semantic dimension of truth (about the metaphysical nature of truth). See M. Devitt, 1984 for the distinction.
13 Kuhn, 1970b, pp. 268, 270-71, 274; 1983b, p. 683; 1987, pp. 20-21; 1988, pp. 11, 13-14, 22-4; 1991, pp. 5, 10, 12; 1993a, pp. 319, 330-31.
14 Conceivability is at most (and should be) a necessary condition of conceptual accessibility. A world that cannot be conceived of, such as a world containing square circles, is not a conceptually accessible possible world.
15 Careful readers might notice some slippage between ‘there being a possible world’ and ‘it being conceptually accessible’. In fact, when I say ‘a possible world is language dependent’ or ‘a taxonomic structure specifies/determines a possible world’, I actually mean that ‘whether a possible world is conceptually accessible is language dependent’ or ‘a taxonomic structure specifies/determines whether a possible world is conceptually accessible to the language’. After this clarification, I will, for simplicity, continue to use the former way of speaking.
16 For a good defense of Wittgenstein’s fact-ontology as opposite to Aristotelian thing-ontology, see H. Gaifman, 1975 and 1976.
17 To claim that the evaluation of the truth-value of a statement or a truth claim is lexicon dependent does not mean that truth itself is relative to language. The core of Kuhn’s taxonomic relativist view can be fully preserved by the claim that incompatible taxonomic structures may yield different truth claims. Readers may profit from a similar interpretation, in S. Hacker, 1996, of conceptual relativism based on the distinction between truth itself and truth claims.
18 Although Kuhn continued to use the term ‘untranslatability’ in his explication of incommensurability after 1987, he used the term in a different sense from the traditional notion of truth-preserving translation. It is the notion of truth-value-preserving translation that the later Kuhn had in mind when he connected untranslatability with incommensurability.
19 Strictly speaking, to say that a kind-term is projectible is to say that the expectation about a kind-term’s referents, rather than the kind-term itself, is projectible.
20 Kuhn, 1987, pp. 20-21; 1988, pp. 14-23; 1993a, pp. 317-18, 325-6.