In most situations, the speakers of two different scientific languages, i.e., the languages of comprehensive scientific theories, can effectively understand one another’s language and successfully communicate with each other. However, in some cases, effective mutual understanding and communication are problematic, difficult, and even in some measure unattainable between two substantially distinct scientific languages.
A radical conceptual shift in a scientific theory can render its language largely unintelligible to a later age within the same cultural or intellectual tradition. This is what Thomas Kuhn experienced repeatedly when he attempted to understand some out-of-date scientific texts. As Kuhn observed:
A historian reading an out-of-date scientific text characteristically encounters passages that make no sense. That is an experience I have had repeatedly whether my subject was an Aristotle, a Newton, a Volta, a Bohr, or a Planck. It has been standard to ignore such passages or to dismiss them as the products of error, ignorance, or superstition, and that response is occasionally appropriate. More often, however, sympathetic contemplation of the troublesome passages suggests a different diagnosis. The apparent textual anomalies are artifacts, products of misreading. (1988, pp. 9-10)
Kuhn (1987)1 records vividly ‘a decisive episode’ in the summer of 1947, when he, in his struggle to make sense of Aristotle’s physics, first encountered what he characterized as the phenomenon of incommensurability fifteen years later—a communication breakdown between two successive competing scientific language communities. Kuhn was deeply perplexed. How could Aristotle have made so many obviously senseless and absurd, not just false, assertions about motion? He discovered that ‘Aristotle had known almost no mechanics at all’ (Kuhn, 1987, p. 9). But the discovery troubled Kuhn. He wondered ‘how could his characteristic talents have deserted him so systematically when he turned to the study of motion and mechanics? Equally, if his talents have so deserted him, why had his writings in physics been taken so seriously for so many centuries after his death?’ (Kuhn, 1987, p. 9) Eventually Kuhn suspected that the fault might be his reading of Aristotle (he approached Aristotle from the perspective of Newtonian mechanics).
After changing his way of reading Aristotle and continuing to puzzle over the text, his perplexities suddenly vanished during one memorable hot summer day, as Kuhn recalled vividly 40 years later.
I was sitting at my desk with the text of Aristotle’s Physics open in front of me and with a four colored pencil in my hand. Looking up, I gazed abstractly out the window of my room—the visual image is one I still retain. Suddenly the fragments in my head sorted themselves out in a new way, and fell into place together. My jaw dropped, for all at once Aristotle seemed a very good physicist indeed, but of a sort I’d never dreamed possible. Now I could understand why he had said what he’d said, and what his authority had been. (Kuhn, 1987, p. 9)
My attempt to discover what Aristotle had thought provided my first exposure to incommensurability, and I have encountered it repeatedly since, not only with ancient texts but with texts by figures as recent as Planck and Bohr. Experiences of this sort seemed to me, from the very start, to require explanation. They signal a break between older modes of thought and those now current, and that break must have significance both for the nature of knowledge and for the sense in which it can be said to progress. I changed my career plans in order to engage those issues. (Kuhn, 1999, p. 33)
Guided by these personal experiences, Kuhn found out further that when two successive competing scientific languages, such as the language of Newtonian mechanics and that of Aristotelian mechanics, are separated by a ‘scientific revolution’, their respective proponents are liable to experience a failure of mutual understanding. They often inevitably talk past one another when attempting to resolve their disagreements. In short, Kuhn was struck by the observation that when rival scientific theories or paradigms clash, we can from time to time identify a communication breakdown between their advocates.2
Kuhn’s personal experiences with reading old scientific texts are shared by many others. In canonical texts such as Descartes’ Le monde, Galileo’s writings, Bacon’s Advancement of Learning and Novum Organum, and Locke’s Essay Concerning Human Understanding, we find the writers claiming to be unable to understand some of the fundamental concepts of the Aristotelian. For example, in his Le monde, Descartes quoted Aristotle in Latin, claiming to do so because he was unable to understand the sense of his definitions otherwise. Galileo and his supporters were often skeptical about the very possibility of establishing a constructive dialogue with the Tuscan Aristotelians during the debate on buoyancy during 1611-1613 (Biagioli, 1990). I. Hacking (1983) concurs and points out that the medical theory of the well-known sixteenth-century Swiss alchemist and physician, Paracelsus—which exemplifies a host of hermetic interests within Northern European Renaissance tradition—is hardly intelligible to modern Westerners. For example, a Paracelsan assertion that mercury salve is good for syphilis because of the association of the metal mercury with the planet Mercury, the market place, and syphilis makes little sense to the ears of today’s physician.
By the same token, substantial semantic and/or conceptual disparities between two comprehensive theories and their languages embedded in two coexistent, distinct, intellectual/cultural traditions can create serious impediments to mutual understanding and communication. For example, Chinese medical theory is hardly intelligible to most Western physicians. They are very skeptical of Chinese medicine and even regard Chinese physicians as something like medicasters. Many Western physicians claim that Chinese medicine sounds strange and alien to them. As one complains, the sentence, ‘The loss of balance between the yin and the yang in the human body invites evils which lead to diseases’, sounds as nonsensical to him as the utterance, ‘ooh ee ooh ah ah’. When a Chinese physician diagnoses a disease as the excess of the yin over the yang within the spleen of a patient, a Western physician would be left in a fog.
A historian or philosopher of science close to the position of logical empiricism would say that these claims about the difficulty of communicating with competitors represent a mere rhetorical strategy. But the question of whether those claims of communication breakdowns are real or rhetorical is beside the point. As Kuhn and others have noticed, such a failure of cross-language understanding and communication breakdown between two scientific languages cannot be simply taken as evidence of the interpreter’s limitation of knowledge or lack of interpretative skills. In many cases, difficulty in understanding an alien language and the communication breakdown between the interpreter’s and an alien language are experienced by most members of a scientific community, not just by some individuals of the community. It is this failure of mutual understanding and a communication breakdown between two language communities as a whole, rather than between some individual speakers with different dialects, intentions, or conflicting interests, that calls for our attention. The problem clearly involves some deep semantic and/or conceptual obstructions between two substantially different languages that make effective mutual understanding and communication difficult and problematic.3
Deeply perplexed by apparent communication breakdown between two competing scientific language communities, Kuhn and Feyerabend set out to give a philosophical explication of this phenomenon that they dubbed ‘incommensurability’. Both Kuhn and Feyerabend started to use the term ‘incommensurability’ independently to describe the communication breakdown between two scientific language communities. Kuhn made this point bluntly clear in his first writing about incommensurability.
We have already seen several reasons why the proponents of competing paradigms must fail to make complete contact with each other’s viewpoints. Collectively these reasons have been described as the incommensurability of the pre- and post-revolutionary normal-scientific traditions .... Communication across the revolutionary divide is inevitably partial. (Kuhn, 1970a, pp. 148-9; my italics)
The term ‘incommensurability’ is borrowed from mathematics. In its original mathematical use, it means ‘no common measure’ between two irrational numbers. For example, the hypotenuse of an isosceles right-angled triangle is incommensurable with its side or the circumference of a circle with its radius in the sense that there is no unit of length contained without residue an integral number of times in each member of the pairs. The term ‘incommensurability’ is used metaphorically (Kuhn, 1983b, p. 670) in Kuhn’s and Feyerabend’s hands in trying to capture their strong intuition that the communication breakdown between two scientific communities is due to lack of some common measure between the two languages used. According to an innocent and widely accepted assumption, any successful communication between two language communities requires some appropriate common measure between the languages used;4 otherwise, communication between the language communities would break down.
However, the controversy arises as to what counts as an appropriate common measure necessary for successful communication between two scientific language communities. Kuhn spent more than thirty years (1960s-1996) trying to pin this measure down. By doing so, Kuhn wished to conceptualize, clarify, and refine his notion of incommensurability, and thus to argue for his celebrated thesis that the phenomenon of incommensurability, i.e., communication breakdown, does exist and that cases of it abound not only in the history of rational thought in general but in the history of sciences in particular. Although Kuhn’s position underwent dramatic changes during these years, there was a common thread through all the changes: He sought to identify a significant necessary common measure of cross-language communication, and perhaps primarily to deny that such an identified common measure exists, thereby identifying a certain kind of semantic obstruction between would-be communicants using two competing scientific languages.
Consider briefly the development of Kuhn’s thesis of incommensurability since the publication of his Structure of the Scientific Revolutions in 1962. Initially, Kuhn specified the common measure as a shared paradigm: the entire constellation of shared metaphysical commitments, shared problems to solve, shared methodological standards of adequacy, and shared perceptions. Faced with extensive criticism, Kuhn realized later that his concept of paradigm was too vague. He thereby concentrated on an essential part of the paradigm, namely, exemplars and similarity relationships among items determined by exemplars.5 He accordingly specified the common measure as shared similarity relationships (family resemblance) among objects or situations for categorization.6 However, the major problem with the identification of similarity relationships as a common measure between two competing languages is that a mere shift of similarity relationships does not necessarily cause a communication breakdown.
To further specify the structure of categorical frameworks of scientific languages and to explore their role in successful communication between two competing language communities constituted the central task of Kuhn’s explication of incommensurability until the last day of his life. After 1983,
[t]he phrase ‘no common measure’ became ‘no common language’. The claim that two theories are incommensurable is then the claim that there is no language, neutral or otherwise, into which both theories, conceived as sets of sentences, can be translated without residue or loss. (Kuhn, 1983b, p. 670)
Since 1987, Kuhn gave up the common language requirement as being too broad, and started to focus exclusively on one essential part of a language—its taxonomic structure.7 At this latest stage, the phrase ‘common measure’ became ‘shared lexical structure or taxonomy’ between two competing scientific languages.
It is clear that Kuhn’s different formulations of incommensurability evolved in the process of his efforts to specify a significant common measure of successful cross-language communication. The cross-language communication breakdown is the essential sense of Kuhn’s notion of incommensurability. To say that two scientific theories are incommensurable is, for Kuhn, to say that a necessary common measure of some sort is lacking between the languages employed by them and that thereby the successful cross-language communication between their advocates breaks down.
No one issue has dominated the landscape of contemporary philosophy of science as has the problem of incommensurability. In fact, any philosopher who takes more than a fleeting interest in the development of science, rational thought, and knowledge must, at some stage, confront the issue of incommensurability in one of its many manifestations. The problem of incommensurability has caught the attention of Anglo-American philosophy in the last quarter of the twentieth century because of its significant implications for many central issues in the philosophy of science, the philosophy of language, ethics, epistemology, and metaphysics. Among them, the problem of theory comparison, the problem of scientific rationality, the problem of scientific progress, and the issue of scientific realism/anti-realism are some important issues that are closely linked to the problem of incommensurability.
It has been widely held that whatever the origins and intentions of Kuhn’s and Feyerabend’s thesis of incommensurability may be, it is plain that the thesis has made problematic the debate on processes of theory comparison and choice, and has accordingly threatened to undermine our image of science as a rational, realistic, and progressive enterprise. Kuhn and Feyerabend gave fresh respectability to irrationalistic, subjective, and relativistic views about science and knowledge. Consequently, the thesis of incommensurability has met its double fates: On the one hand, the thesis has become ‘a modern myth’ among many. For many philosophers and theorists in related fields with a relativist bent, the notion often serves as a conceptual foundation for their pet theories, such as social constructionism, multiculturalism, feminism, and postmodernism. On the other hand, the notion and the thesis of incommensurability have become ‘a public enemy’ in some philosophy circles, especially among philosophers and theorists with an anti-relativist bent and the self-claimed champions of rationality, objectivity of science, and human thoughts. Most notably, Kuhn’s and Feyerabend’s notion of incommensurability was attacked fiercely by D. Davidson (1984) in conjunction with the very notion of conceptual schemes.
Further, the influence of the thesis of incommensurability has reached far beyond the professional circle of philosophy. Practitioners with a relativistic bent in numerous interpretative fields, such as sociology, anthropology and ethnography, psychology, law, education, political science, economics, cognitive science, decision theory, and linguistics, have been busy discovering similar phenomena in their fields. Through its popularization, the notion of incommensurability has been put on the cultural map, and even becomes part of the weekly glosses in many professional circles.8
Because of the above two reasons, the notion of incommensurability has been one of the most revolutionary and influential notions in recent philosophical investigations. Along with its significant impact on the philosophy of science and other related areas, it is one of the most intriguing ideas in recent philosophy. On the one hand, the topic has been so popularized to the extent that one can even claim that in the circle of the philosophy of science ‘the doctrine of incommensurability needs no introduction’ (Pearce, 1987, p. 1). On the other hand, however, the notion of incommensurability is the most controversial, most often abused notion within contemporary analytic philosophy. Although in the past four decades, philosophers approached it from different directions and presented many historically erudite and conceptually fine-grained analyses of it, we still do not have any clear theoretical conception of what incommensurability is.
The fact that the notion of incommensurability has not been subjected to a satisfactory conceptual clarification explains why hardly any significant progress has been made in the study of the issue of incommensurability in the past.9 A comment made by Feyerabend 30 years ago can still be used to describe the current research circumstances of incommensurability: ‘Apparently, everyone who enters the morass of this problem [referring to the problem of incommensurability] comes up with mud on his head’ (1977, p. 363). Kuhn and Feyerabend, two pioneers opening this uncultivated land for us, are no exception. It seems to me that philosophical discussion involving the notion of incommensurability, no matter whether for or against it, tends to come to a deadlock, and is hard to evaluate and often fallacious. There is a danger that, as D. Pearce (1987) pointed out 20 years ago, through popularization and abuse, the term ‘incommensurable’ would become long in the tooth and the thesis would lose its original bite. This danger has occurred, and it mainly comes from two directions based on two pervasive misconceptions of incommensurability. If incommensurability were interpreted as untranslatability, the thesis would degenerate into a trivial platitude; almost any kind of conceptual difference or conflict could amount to a case of incommensurability. Alternatively, the problem of incommensurability could turn out to be a pseudo-problem for many if incommensurability were reduced to incomparability.
There are many reasons responsible for this slow progress made in the investigation of incommensurability. I would like to mention the following two major reasons: incommensurability as a complex historical-anthropological phenomenon that manifests itself in many facets and ramifications, and the failure of the received interpretation of incommensurability. The first reason will be discussed in the following two sections. The second reason is the topic of chapter 2.
It is commonly held that part of the blame for the vagueness of the notion of incommensurability lies with Kuhn himself. Kuhn’s notion of incommensurability has often been misinterpreted and abused: partly due to Kuhn’s terminological confusion and his constant change of the expression of the notion, partly because many commentators have simply misunderstood Kuhn’s point. Kuhn had to clarify himself repeatedly after the publication of his Structure. In my opinion, there is a deeper reason responsible for this. When Kuhn and Feyerabend coined the term ‘incommensurable’ to describe the communication breakdowns that they encountered in the study of the history of sciences, they had nothing so precise in mind. For them, the notion of incommensurability was just a suitable language metaphor to reveal their deep insight gained in their experiences.10
The vagueness of the explanation of incommensurability is partially due to the fact that we are dealing with a complex historical-anthropological phenomenon extending beyond the area of philosophy, whose roots are deep in the basic mechanisms of cultures, forms of life, languages, and social institutions. Generally speaking, incommensurability has its natural home primarily in seven disciplinary settings: in intellectual history in general to contrast widely divergent perspectives of understanding different Weitanschauungen; in the history of sciences in particular to contrast and understand the conceptually distant explanatory frameworks; in descriptive sociology to contrast kinship systems or other mechanisms for categorizations and explanation of human affairs;11 in anthropology and cultural studies to contrast and understand totally different modes of justification;12 in linguistic study to contrast different categorization systems which create ‘pattern resistance’ to widely divergent points of views;13 in axiology to contrast and evaluate distinct value (ethical, aesthetical, and others) systems; and in philosophical epistemology to contrast fundamentally diverse perspectives—which start with conceptually disparate presuppositions—of treating explanatory issues. The phenomenon of incommensurability has been and will continue to be rediscovered and enhanced in different disciplinary settings (recently, in cognitive science, psychology, rhetoric, and economics). It is not an exaggeration to say that any philosopher, sociologist, anthropologist, or linguist who takes a comprehensive-historical stand toward the development of rational knowledge and human society would encounter the phenomenon of incommensurability in one way or another at some stage. In Kuhn’s words, ‘incommensurability has to be an essential component of any historical, developmental, or evolutionary view of scientific knowledge’ (1991, p. 3).
Feyerabend explicitly makes an analogy between the clarification of the notion of incommensurability and an anthropological discovery. The term ‘incommensurability’ is nothing but a ‘terminology for describing certain historical-anthropological phenomena which are only imperfectly understood rather than defining properties of logical systems that are specified in detail’ (1978, p. 269). Just like an anthropologist trying to infiltrate an unknown tribe, who must keep in check any eagerness for instant clarity and logical perfection. He or she should not try to make a concept clearer than what is suggested by the available material, keeping key notions vague and incomplete until more information is collected. Feyerabend assumes that such an anthropological method is appropriate for studying the phenomenon of incommensurability. Here, lack of clarity of the notion of incommensurability indicates the scarcity of right information rather than the vagueness of the logical intuitions of it. Therefore, ‘the vagueness of the explanation reflects the incompleteness and complexity of the material and invites articulation by further research’ (Feyerabend, 1978, p. 270). Feyerabend had even gone so far as to register doubt that, in its present stage of development, the incommensurability thesis was incapable in principle of being given the kind of precise formulation that would serve to satisfy ‘analytic’ philosophers. In a similar way, Kuhn clearly realized that his attempts to describe the central conception of incommensurability were extremely crude. In his words, ‘efforts to understand and refine it have been my primary and increasingly obsessive concern for thirty years’ (1993a, p. 315).
As a complex historical-anthropological phenomenon, the problem of incommensurability manifests itself in many facets and ramifications. The issue of incommensurability in fact is a set of problems, which comprises three interrelated problems: the nature of incommensurability, the sources of incommensurability, and the epistemological and metaphysical implications or consequences of incommensurability. My experience in reading and discussion has been that those either sympathetic or apathetic to the issue of incommensurability often confuse these three problems.
The general question, ‘What is incommensurability?’ is ambiguous. It can be understood as a question either about the nature or about the sources of incommensurability. For clarity, the question should be divided into two separate questions. First, ‘What is the essential nature of incommensurability?’ The answers will take the format, ‘incommensurability as ...’ (for example, incommensurability as untranslatability, incommensurability as incomparability, or incommensurability as communication breakdown). Second, ‘What are the real sources of incommensurability?’ The answers will take the format, ‘incommensurability due to ...’ The common alleged sources of incommensurability are, to mention only a few: incommensurability due to radical meaning/reference variance, incommensurability due to value, standard, or problem change, or incommensurability due to lexical structure change.
If we consider the alleged consequences brought about by the thesis of incommensurability, as we have mentioned above, the problem of incommensurability consists of a group of interrelated issues: logical compatibility and semantic comparability between scientific theories; language translation and interpretation; sense and reference of the terms of scientific theories; categorization and taxonomization of scientific language; justification and validity of scientific theories; scientific rationality and progress; value judgment and evaluation criteria; absolutism and relativism; and scientific realism and anti-realism, etc.
Much more importantly, the notion of incommensurability is a multiple-dimension concept that involves at least two different dimensions: the normative dimension and the semantic dimension. Accordingly, the concept can be approached from at least two perspectives, which I will call the normative perspective and the semantic perspective. According to the semantic perspective, the problem of incommensurability has something to do with the nature of a certain kind of semantic relation between the languages employed by competing scientific theories. Incommensurability can be characterized as a lack of a certain kind of semantic contact between the languages of two competing theories due to changes in either the semantic values (meaning or reference) of the non-logical constituents of sentences or the semantic values (factual meaning, truth-values, or truth-value status) of sentences themselves in these languages. Because of the lack of a certain desirable semantic contact, proponents of incommensurable theories inevitably talk past one another when attempting to resolve their disagreements. Following the convention, I will call the incommensurability identified in the semantic dimension semantic incommensurability.
Besides the semantic dimension that addresses linguistic, conceptual aspects of science, the problem of incommensurability arises within a nonlinguistic/conceptual dimension also. As far as the sources of incommensurability are concerned, there are, traditionally, at least three alleged nonlinguistic/conceptual grounds of incommensurability: (a) the change of problems to solve, (b) incompatible methodological standards of adequacy (such as scientific value judgments on what are sufficient criteria of a good scientific theory, what is an adequate solution to a scientific problem, etc. Some might prefer to call this methodological incommensurability), and (c) the Gestalt switch between the modes of scientific perceptions. We can observe all these alleged forms of incommensurability in the earlier Kuhn’s (before 1980s) exploration of incommensurability.14 These various interpretations of incommensurability reveal genuine ambiguities and tensions within the earlier Kuhn’s understanding of incommensurability. Incommensurability due to the lack of a certain kind of normative contact between two competing scientific theories because of changes in their normative expectations, I will refer to as normative incommensurability.
Although incommensurability does have some normative import, I will not be addressing this normative aspect here. My decision is based on the following considerations. First, the linguistic/conceptual aspect of incommensurability still lacks a satisfactory explanation and an adequate solution. Until progress can be made at the conceptual level, there is only a slim chance of achieving success at the normative level. This is because the linguistic/conceptual aspect is more fundamental than the non-linguistic/conceptual aspect. As Pearce points out:
Though an inquiry into values and standards may pay dividends in helping to forge commensurability in the wider sense, it cannot be the sole basis for understanding science as rational enterprise. Even if one would show that science makes a judicious choice of its instruments, if there is a rational gap at the level of concepts then there is a rational gap in science as a whole because the essential process of theory appraisal and choice is, in effect, undermined. (1987, pp. 3-4)
Second, the changes at the non-linguistic/conceptual level can be explained by means of the changes at the linguistic/conceptual level. For example, the perceptual switch observed in perceptual incommensurable cases can be interpreted as the shift between different taxonomies of natural kinds. And the variance in methodological standards of adequacy is caused by the variance in modes of reasoning. The latter is one of the metaphysical presuppositions of scientific languages, as I will argue later. Actually, Kuhn explicitly regards the differences in methods, problem-fields, and standards of solution as necessary consequences of the language-learning process (Kuhn 1983b, p. 648; 1988, p. 10).
Third, the normative interpretation found in the earlier Kuhn’s formulation is his premature explication of incommensurability. Kuhn himself gave up his early normative perspective in the 1980s. In Kuhn’s own words, ‘My original discussion described non-linguistic as well as linguistic forms of incommensurability. That I now take to have been an overextension resulting from failure to recognize how large a part of the apparently non-linguistic component was acquired with language during the learning process’ (1988, p. 10).
In conclusion, the linguistic/conceptual aspects of incommensurability are more essential than the normative ones. Although our account of incommensurability may miss some admittedly important features if we leave the normative aspects out, I prefer clarifying one phenomenon in some essential aspects to making only some very broad and vague explications in order to have an inclusive explanation.
According to the semantic perspective, the communication breakdown in the case of incommensurability can, and should, be attributed to the lack of a certain kind of desirable semantic relationship between the languages employed by two competing scientific theories due to changes of a certain desirable semantic value(s) of certain kinds of components (sentences or their constituents) of the languages in question. This seems incontrovertible within the framework of the semantic perspective. But controversy arises with what kind of semantic relation is supposed to be the determinant semantic relation between the languages of two incommensurable theories. To see this, we need to identify different kinds of carriers of semantic values and, accordingly, different semantic values associated with these carriers.
First of all, the carriers of semantic values could be some non-logical constituents of a sentence, such as terms—either singular terms including proper names and definite descriptions or general terms including natural kind-terms (water, gold) and concept terms (mass, force)—and predicates. For example, in a Ptolemaic sentence,
(1) The sun, the largest planet, revolves about the earth, which is a star,
‘the sun’ and ‘the earth’ are proper names; ‘planet’ and ‘star’ are general terms; ‘the largest planet’ is a definite description; ‘revolves about’ and ‘is a star’ are two-place or one-place predicates. On the other hand, the carrier of semantic values could be a sentence as a whole, for instance, sentence (1).
Secondly, different semantic values are accordingly associated with different kinds of carriers. For a term of a sentence (say, ‘the earth’ or ‘planet’), we can talk about its meaning (sense) or reference; for a predicate (say, ‘is a star’), we can talk about its extension. Alternatively, if we take a sentence as a whole as the carrier of semantic values, we can speak of meaning, factual meaning, truth-value (Frege’s reference of a sentence), or truth-value status of the sentence (whether a sentence has a truth-value). For example, the factual meaning of sentence (1) consists in its truth conditions. (1) is either true or false from the point of view of Ptolemaic astronomy, but neither true nor false from the point of view of Copernican astronomy.
Corresponding to the two different kinds of carriers of semantic values and the semantic values associated with them, there are at least two kinds of semantic relations, which could be identified as the determinant semantic relation between the languages of two competing scientific theories in the case of incommensurability. One can focus on parts of sentences and their associated semantic values. In this way, the meaning/reference relation between the languages of two competing scientific theories would be the determinant semantic relation in the case of incommensurability. By comparison, one can focus on sentences as a whole and their associated semantic values. Then the truth-value functional relation15 would be the determinant semantic relation between them.
Corresponding to which kind of semantic relation is identified as the determinant relation, there are two possible ways, within the semantic perspective, to characterize the problem of incommensurability. According to my presuppositional interpretation of incommensurability presented in this book, the carriers of semantic values in the case of incommensurability are the sentences of the languages of two rival scientific theories. The semantic values that concern us are the factual meanings and the truth-value status of the sentences in question. So it is the truth-value functional relationship between two competing languages that counts as the determinant semantic relationship in the case of incommensurability. To say that two scientific theories are incommensurable is to say that there is a truth-value gap (a substantial number of core sentences of one language is lack of truth-values when considered within the context of a competing language) between the languages employed by the theories, which results in a communication breakdown between their proponents. And such an occurrence of a truth-value gap is in turn due to incompatible metaphysical presuppositions underlying the two languages. In contrast, according to the received translation-failure interpretation of incommensurability, terms are the semantic carriers in the case of incommensurability. Accordingly, the semantic values, which play the central role in the incommensurable cases, are the meanings/references of the terms in question. Thus, it is the meaning/reference relationship between the languages of two competing scientific theories that should be identified as the determinant semantic relationship in the case of incommensurability. To say that two scientific theories are incommensurable is to say that the languages of the two theories are mutually untranslatable. The failure of mutual translation in turn is due to the absence of meaning/reference continuity because of the radical variance of meaning/reference.
The received translation-failure interpretation has dominated the discussion of incommensurability for the past four decades. With focus on the meaning/reference relation between two scientific languages, the notions of meaning, reference, and translation have been subjected to many historically erudite and conceptually finegrained analyses. However, until now no significant progress has been made to clarify the notion of incommensurability. The main reason responsible for such slow progress, in my judgment, is that the translation-failure interpretation is misleading. It cannot establish a tenable and integrated notion of incommensurability. Therefore, we have to go beyond the translation-failure interpretation. This is the conclusion that I draw from chapter 2 after a comprehensive critique of the translation-failure interpretation.
The doctrine of conceptual relativism and the thesis of incommensurability are twin positions that rise and fall together. Presumably, the notion of conceptual schemes and its underlying metaphysical dualism between scheme and content serve as the conceptual foundation of the thesis of incommensurability. This is why D. Davidson attacks both the notion of conceptual schemes and the thesis of incommensurability together in his influential essay, ‘On the Very Idea of a Conceptual Scheme’ (1984). Due to such a close affinity of the notion of conceptual schemes with that of incommensurability, we have to respond to Davidson’s criticism in defense of the thesis of incommensurability. In chapters 3 and 4, I argue that Davidson’s two lines of criticism of the notion of conceptual schemes fail to dismantle the notion of conceptual schemes and therefore do not undermine the thesis of incommensurability. In fact, what Davidson attacks fiercely, even if it were successful, is not ‘the very idea’ of conceptual schemes, but rather the Quinean notion of conceptual schemes and its underlying Kantian scheme-content dualism. The very notion of conceptual schemes, conceptual relativism, and the thesis of incommensurability escape unharmed from Davidson’s attack.
Incommensurability is typically regarded as a radical conceptual disparity between two competing scientific languages. It is taken to represent a lack of conceptual continuity between them due to some kind of semantic obstruction. A lack of conceptual continuity between two languages is supposed to explain why their proponents inevitably talk past one another. Various attempts to locate the semantic obstruction in the meaning/reference relation between two competing languages fail. The opponents of the thesis of incommensurability applaud the failure of the translation-failure interpretation, and take it tacitly as the failure of the thesis of incommensurability itself. The advocates of the thesis, in contrast, have tried to save it by proposing various remedial measures within the framework of the translation-failure interpretation. Both opponents and proponents of incommensurability, in my opinion, make the same mistake. They both take the translation-failure interpretation as the only valid path to explore incommensurability. To me, it is not the notion of incommensurability that has let us down, but rather a particular conception of how that notion is to be philosophically established, explained, and improved—namely, the received notion of incommensurability—fails us. The failure of the received interpretation of incommensurability does not indicate that there is no such semantic obstruction between two disparate scientific languages, but rather indicates that it could manifest itself in some other more profound way.
To identify such a semantic obstruction, I turn to two case studies in chapter 5, one taken from the history of Western science, i.e., the Newton-Leibniz debate on the absoluteness of space; the other from the comparison between contemporary Western medical theory and traditional Chinese medical theory. I find that those classical conceptual confrontations are not confrontations between two scientific languages with different distributions of truth-values over their assertions due to radical variance of the meanings/references of the terms involved so much as they are what is implied by both the translation-failure interpretation and the Quinean notion of conceptual schemes—both notions are rooted in bivalent semantics in which every declarative sentence is either true or false. In contrast, those classical confrontations are the confrontations between two scientific languages with different distributions of truth-value status over their sentences due to two incompatible sets of metaphysical presuppositions underlying them. Consequently, the communication breakdown is not signified by the untranslatability between two scientific languages, but is rather indicated by the occurrence of a truth-value gap between them.
A new interpretation of incommensurability emerges from the above case studies. The current discussion of incommensurability and its related topics—such as conceptual schemes, translation, and theory comparison—are based on a tacit assumption that every sentence in a scientific language has a determinate truth-value or is either true or false (the principle of bivalence: Each sentence is assertable). What makes two scientific theories incommensurable, on the received interpretation, is the redistribution of truth-values over their assertions. On the contrary, I argue that in the discussion of incommensurability and related issues, what should concern us is the truth-value status of the sentences used to make the assertions, and not truths or truth-values of assertions. Accordingly, what we should focus on in the study of incommensurability is the truth-value functional relation instead of the meaning/reference relation, since it is the former, not the latter, that is the dominant semantic relation in the case of incommensurability.
In chapter 6, based on the insights we collect from the case studies as well as I. Hacking’s and N. Rescher’s writings on conceptual schemes, I propose a notion of presuppositional language as an alternative to the Quinean notion of conceptual schemes. A presuppositional language is, roughly, an interpreted language whose core sentences share one or more absolute presuppositions. Those absolute presuppositions, which I call metaphysical presuppositions, are contingent factual presumptions about the world as perceived by the language community whose truth the community takes for granted. Scientific languages are paradigmatic presuppositional languages. According to P. Strawson’s notion of semantic presupposition, a sentence would be truth-valueless if one of its semantic presuppositions failed. The notion of presuppositional language is introduced primarily to explain the occurrence of a truth-value gap between two scientific languages, as we will observe in our case studies. When two presuppositional languages conflict with one another, it is likely that many core sentences of one language, when considered within the context of the other language, are truthvalueless due to the failure of some shared metaphysical presuppositions.
In chapter 7, I reconstruct the later Kuhn’s taxonomic interpretation of incommensurability. According to my reconstruction, two scientific languages are incommensurable when the core sentences of one language, which have truth-values when considered within their own context, lack truth-values when considered within the context of the other language due to the unmatchable taxonomic structures underlying them. So constructed, Kuhn’s mature interpretation of incommensurability does not depend upon the notion of truth-preserving (un)translatability, but rather depends on the notion of truth-value status preserving cross-language communication. Hence, the later Kuhn started to move toward the direction of the presuppositional interpretation.
However, it is a controversial issue as to whether truth-value gaps should be permissible semantically. For many philosophers, the notion of truth-value gap is highly suspect. The theoretical ground of the notion of truth-value gap, namely, the notion of semantic presupposition, has been under constant attack. But it is the very notion of semantic presupposition that is at the heart of my interpretation. To clarify and defend the notions of semantic presupposition and truth-valuelessness, in chapter 8, based on my formally coherent definition of the notion of semantic presupposition, I defend the two notions against some most damaging objections.
Based on the formal treatment of semantic presuppositions, I am ready, in chapter 9, to formalize two crucial notions that I introduce informally in the previous chapters, namely, truth-value gap and presuppositional language. I start with an important but often-ignored distinction between the notions of truth-value (whether an assertion is true or false) and truth-value status (whether a well-formed, meaningful sentence is a candidate for truth-or-falsity), and correspondingly, the distinction between truth conditions and truth-value conditions. Based on my definition of truth-value conditions, truth-value status is relative to a specific language. It is a language that creates the possibility of truth-or-falsehood. Therefore, it is possible for one sentence to be a candidate for truth-or-falsity in one language, but not in the other. In the second part of chapter 9, the formal structure of a presuppositional language is analyzed in detail.
The hallmark of a presuppositional language is its metaphysical presuppositions. In chapters 10 and 11, three kinds of metaphysical presuppositions are identified and illustrated in detail. They are existential presumptions about the existing entities in the world, universal principles about the existent state of the world, and categorical frameworks about the structure of the world around a language community. Since the essence of a presuppositional language consists in its metaphysical presuppositions, two presuppositional languages differ in just this regard, namely, by being laden with different types of metaphysical presuppositions. The metaphysical presuppositions of a presuppositional language determine the truth-value status of its sentences. If two presuppositional languages with incompatible metaphysical presuppositions confront one another, the embodied incompatible metaphysical presuppositions would conflict to the extent that they mutually exclude or suspend each other. Such a mutual violation of each other’s metaphysical presuppositions would lead to a rejection of the other language by casting doubt upon whether its ontology is fit to describe reality and suspending all the possible facts associated with it, and consequently causes an ontological gap between the two languages. At the same time, violation or suspension of the metaphysical presuppositions of a presuppositional language would lead to the occurrence of massive truth-valueless sentences when considered within the context of a competing language, and results in a truth-value gap between the two languages.
Incommensurability is a semantic phenomenon closely related to the issue of how two presuppositional language communities can effectively understand and successfully communicate with one another. We have found that the advocates of the two distinct presuppositional languages often experience a communication breakdown between them. One primary purpose of introducing the notion of presuppositional language is to explain those communication breakdowns, which Kuhn and Feyerabend dubbed as the phenomenon of incommensurability. To do so, I need to locate some essential semantic and/or conceptual obstructions between two competing presuppositional languages and thus to identify a significant necessary condition of effective cross-language understanding and that of successful communication between the two language communities. This becomes a main focus of the rest of the chapters.
I start with, in chapter 12, one extreme of the communication breakdown, i.e., failure of cross-language propositional understanding. I argue that the comprehension of the metaphysical presuppositions of an alien presuppositional language is necessary for understanding it effectively. This shows that truth-value status plays an essential role in effective understanding: An interpreter can effectively understand an alien language only if the sentences of the language, when considered within the context of the interpreter’s language, are (conceptually) true or false. When an interpreter encounters an alien language, the most common approach to understand it is to try to consider it within the context of his or her own language. In this case, the interpreter might easily and facilely project his or her own well-entrenched language (form of life, tradition, worldview, or framework) onto the alien’s. When the metaphysical presuppositions of the two languages in question are compatible, this projective way of understanding usually does not cause a problem that would hinder mutual understanding; but when they are incompatible, the would-be communicators will experience a complete communication breakdown due to the failure of effective understanding of the other’s language.
However, it is a mistake to assert that the would-be-communicators of two incommensurable languages cannot understand one another per se. Anything that can be said in one human language can be, with imagination and effort, understood by the speaker of another human language. The as-of-now communication breakdown only shows us that propositional understanding does not work in the case of incommensurability. It calls for a different way of understanding. However, what we need in the incommensurable cases is not the opposite approach to the projective understanding, namely, the adoptive way of understanding—to suppose that one can understand others only when one thinks, feels, and acts like others. The thesis of incommensurability does not necessarily lead to radical relativism. H.-G. Gadamer’s hermeneutic understanding provides us a way of going beyond both projective and adoptive ways of understanding, both of which are propositional understanding in nature. In chapter 13, I discuss the possibility of restoring mutual understanding between two competing presuppositional languages in terms of Gadamer’s hermeneutic understanding, and explore some hermeneutic dimensions of the thesis of incommensurability.
Even if hermeneutic understanding can overcome complete communication breakdown due to the failure of mutual propositional understanding, there still exist some much more significant cases of communication breakdowns between two competing presuppositional languages with incompatible metaphysical presuppositions. When the speakers of two competing languages can understand but cannot successfully communicate with one another, they experience a partial communication breakdown. In chapters 14, 15, and 16, I argue that such a partial communication breakdown is inevitable between two competing presuppositional languages with incompatible metaphysical presuppositions. It is the existence of such partial communication breakdown, i.e., communication breakdown per se, that establishes the metaphysical significance of the phenomenon of incommensurability.
Chapter 14 focuses on the received transmission model of linguistic communication (informative communication). Propositional understanding should be distinguished from informative communication. Understanding is necessary, but not sufficient for successful communication between two incommensurable presuppositional languages. Successful cross-language communication requires much more than mutual understanding. Even in the case that both sides are bilinguals who can understand one another’s language, they still cannot communicate successfully with each other if the metaphysical presuppositions of the two languages are incompatible. This is because successful informative communication between two presuppositional languages requires shared or compatible metaphysical presuppositions. Otherwise, the communication between them is inevitably partial.
Chapters 15 and 16 discuss the two versions of the dialogical model of communication, which uses conversation or discourse, rather than transmission of information, as the central metaphor. One is Gadamer’s conversation model based on his philosophical hermeneutics, and the other is J. Habermas’s discourse model derived from his theory of communicative action. For both Gadamer and Habermas, cross-language communication is essentially the process of coming to hermeneutic understanding oriented toward agreement or consensus—not simply comprehension as propositional understanding entails—in terms of either genuine conversation (Gadamer) or through argumentation in dialogue (Habermas). In chapter 15, through analysis and criticism of Gadamer’s common language requirement through a full fusion of horizons, I conclude that cross-language communication between two incompatible presuppositional languages is inevitably partial. After identifying three essential conditions of communication according to Habermas’s discourse model in chapter 16, I argue that those conditions can be met only if the metaphysical presuppositions of two presuppositional languages are compatible. Therefore, chapters 14, 15, and 16 eventually reach the same conclusion: Shared or compatible metaphysical presuppositions between two presuppositional languages are necessary for successful communication between two distinct presuppositional languages. In other words, the communication between two presuppositional languages with two incompatible metaphysical presuppositions is inevitably partial. It is such partial communication breakdown between two distinct presuppositional languages that gives the real theoretical thrust of the thesis of incommensurability as communication breakdown.
A communication breakdown between two language communities is semantically indicated by the occurrence of a truth-value gap between them. I contend that this kind of communication breakdown due to the occurrence of a truth-value gap signifies that the two languages are incommensurable. In light of the above considerations, it seems to me that it is much more appropriate to use the occurrence of a truth-value gap between two rival presuppositional languages, signified by a communication breakdown and caused by incompatible metaphysical presuppositions, as a touchstone of incommensurability. For two presuppositional languages to be incommensurable is for the core sentences of one language to lack truth-values when considered within the context of the other language. More precisely, corresponding to two degrees of communication breakdown—that is, partial or complete communication breakdown—we can identify two degrees of incommensurability: moderate versus radical incommensurability. The moderate incommensurability relation between two competing languages associated with partial communication is the incommensurability of real metaphysical significance. The above is what I argue in the final chapter.
The presuppositional interpretation is inspired by a few philosophers’ works on some related topics. H. Gaifman’s (1975, 1976, and 1984) works on Wittgenstein’s concept of ontology rescues me from the ‘morass’ of the problem of incommensurability and puts me on the right track. I. Hacking’s (1982, 1983) and N. Rescher’s (1980) emphases on the distinction between the notion of truth-value and the notion of truth-value status as well as their clarification of the notion of conceptual schemes on the basis of truth-value status set a basic semantic framework for my project. My new interpretation emerges from reading the above works. Taking such a new perspective, I first puzzled over Kuhn’s and Feyerabend’s mature works on incommensurability. To my surprise, I found out that both pioneers have already hinted at the new interpretation in many profound ways.
However, although those philosophers has expressed ideas of the presuppositional interpretation, in different ways, most of these are expressed implicitly when they deal with other related issues. There are only some scattered insights here and there, which have not been made as a full case. This is part of the reason why these insights on incommensurability have not gained their deserved attention up to now. My purpose is to develop these insights into a full case, to give them a clear and coherent formulation. I hope that this treatment will help the presuppositional interpretation of incommensurability gain the acceptance that it deserves. This would be not only good in itself—to establish the tenability of the notion of incommensurability—but the effect on other related issues would be quite beneficial, such as the notion of conceptual schemes, the issue of cross-language understanding and communication, and the notion of truth-value status and truth-value conditions.
Before we start our adventure of dipping into ‘the morass’ of the problem of incommensurability, let us clarify a few crucial concepts and related terminology conventions that I have been using above and will continue to use throughout the book.
If semantic incommensurability has something to do with the semantic relations between two radically disparate scientific texts, then which of the following candidates is/are the appropriate term(s) of such a relation: scientific theories or scientific languages?
The terms ‘scientific theory’ and ‘scientific language’ are often used interchangeably by many analytical philosophers, as in the writings of T. Kuhn, P. Feyerabend, W.V. Quine, D. Davidson, H. Putnam, N. Rescher, due to the conceptual affinity between the two notions. Although it does not matter much to many how one construes the notions of scientific theory, scientific language, and their interrelation, many confusions in the discussion of the issue of incommensurability and related matters, such as the notion of conceptual schemes, do arise because of a lack of reasonable distinction between scientific theory and scientific language. Therefore, a certain distinction between them is called on here.
The term ‘scientific theory’ can be used to refer to a specific individual theory whose core is a very specific set of related doctrines (hypotheses, axioms, or principles) that can be utilized for making specific experimental predictions and for giving detailed explanations of natural phenomena. Examples are Maxwell’s theory of electromagnetism, Wegener’s theory of continental drift, and Einstein’s theory of the photoelectric effect, etc. On the other hand, the term can be used to refer to a whole spectrum of individual theories. The core of such a scientific theory consists of much more general, much less easily testable, sets of assumptions or presuppositions. Following P. Feyerabend, I use the term ‘comprehensive scientific theory’, which roughly correspond to P. Feyerabend’s ‘background theories’, T. Kuhn’s ‘paradigms’, I. Lakatos’ ‘research programmes’, or L. Laudan’s ‘research traditions’, such as quantum theory (including quantum field theories, group theories, S-martix theory, and renormalized field theories), Newton’s mechanics, Aristotelian physics, Einstein’s relativity theory, traditional Chinese medical theory, etc. What we are concerned about in the discussion of incommensurability, as Kuhn and Feyerabend emphasized, is not restricted individual scientific theories, since restricted theories rarely lead to the needed conceptual revisions, but comprehensive scientific theories.
Feyerabend once pointed out that comprehensive scientific theories are sufficiently general, sufficiently ‘deep’, and have developed in sufficiently complex ways. They can be considered, to some extent, along the same lines as well-developed natural languages (Feyerabend, 1978, pp. 224-5). As I see it, we can link scientific theory with scientific language on the basis of a modified ‘semantic’ approach of Beth and van Fraassen’s (Fraassen, 1970, 1989). We can think of a scientific theory as a set of theoretical definitions plus a number of theoretical hypotheses. Divorced from the ‘syntactic’ approach of the classic view—the idea that underlying any scientific theory is a purely formal logical structure captured in a set of axioms formulated in an appropriate formal language—the semantic approach shifts the focus from the axioms (as linguistic entities) to the models of axioms (non-linguistic entities—any physical or conceptual entities and processes that satisfy the axioms). The important distinction between the two approaches consists in the idea that the semantic account takes models as fundamental while the syntactic account takes statements, particularly laws, as fundamental. Contrary to the syntactic approach, which identifies a theory (i.e., Newtonian physics) with a definite set of statements (i.e., Newton’s three laws plus the law of universal gravitation), scientific theories are, according to the semantic approach, not linguistic entities. Rather, theories must be some extra-linguistic structures standing in mapping relations to the world.
If so, a scientific theory has to be formulated in some theoretical language with a specific lexicon (such as Kuhn’s lexical structure), plus syntax and logic. The theoretical language of a scientific theory consists of a consistent set of sentences or statements while the theory formulated in the language is either these sentences marked as ‘believed’, or a distribution of degrees of beliefs, in Bayesian style, over the sentences. Adopting such a semantic approach leaves wide latitude in the choice of languages for formulating particular scientific theories. In principle, any language could be used to formulate a theory, including extensions of everyday natural languages constructed through pragmatic observations of the linguistic usage within a scientific community, not just formal languages. We can call the theoretical language employed by a scientific theory the language of that theory, such as the language of modern chemistry, the language of the Copernican theory of astronomy, or the language of the phlogiston theory of combustion. In general, I will call accompanying languages of scientific theories scientific languages.
We need to notice that the concept of language in the discussion of incommensurability has several different meanings, which sometimes leads to confusion, especially in the discussion of the untranslatability thesis. Some distinctions are necessary here. First, ‘a language’ can refer to either a scientific language or a natural language. Obviously, scientific language should be distinguished from natural language. On the one hand, scientists express their ideas and theories in extensions of natural languages. The very same scientific language (say, the language of Newtonian physics) used to formulate a scientific theory (Newtonian physics) could be embedded in, expressed by, or coded in different extended natural languages (say, English or German). On the other hand, two different scientific languages (say, the language of Newtonian physics and that of Aristotelian physics) can be couched in or recorded by the same natural language (English). For our later discussions, ‘language’ usually refers to ‘scientific language’ when the context is clear. Whenever it is necessary, I will make it clear which language, natural language or scientific language, is under consideration. Second, sometimes it is necessary to distinguish the object language (such as the Newtonian language versus the Aristotelian language) that we are discussing from the metalanguage that we use to do the discussion—in our case, it will be English.
These two distinctions are especially important when we discuss the issue of possible translation between two texts. We have to be clear about the terms of translation relation: translation between two scientific languages, between two natural languages, or between one scientific language and one natural language. According to the accepted translation-failure interpretation, the languages of two alleged incommensurable theories cannot be mutually translated into one another. However, this does not mean without further qualification that an out-of-date scientific language (say, the language of phlogiston theory) cannot be translated into a contemporary natural language (say, English).16
We are now in a position to identify the terms of incommensurability relations. According to common usage, incommensurability is supposed to be about the relation between two conceptually disparate scientific theories. We usually claim that two scientific theories are incommensurable. Whereas, it is the languages of two scientific theories that are incommensurable. Theories are incommensurable only in a derivative sense. According to my presuppositional interpretation, two scientific theories are incommensurable if there is a truth-value gap between the languages of the theories. Furthermore, according to the received translation-failure interpretation, to say that two theories are incommensurable is actually to say that they are formulated in languages that are not mutually translatable. Again, it is languages, not theories, that are the terms of incommensurability relations. Therefore, the proper terms of incommensurability relations should be scientific languages. For this reason, I will confine my investigation to the analysis of the notion of incommensurability between scientific languages. Although I will be talking about incommensurability between two scientific theories from time to time, this is only a conventional way of speaking.
The notion of incommensurability seems to deal exclusively with scientific theorizing. But this notion can be extended to apply to a broader linguistic phenomenon, such as possible incommensurability between two conceptually disparate natural languages. Many philosophers (Feyerabend, R. Rorty, and others) extend the domain of incommensurability even further to cover much broader non-linguistic entities, such as traditions, forms of life, worldviews, cultures, or cosmological points of view. Although I am sympathetic with such a broad use of the notion of incommensurability, I will primarily focus on the linguistic dimension of incommensurability in the following discussion.
Our discussion of the presuppositional interpretation of incommensurability will proceed within the framework of trivalent semantics, which will be presented and formalized in chapter 8. Nevertheless, the use of a very broad brush here on the difference between bivalent and trivalent semantics may be helpful for the reader.
In logic, a proposition that has a definite truth-value, either true or false, is called bivalent. In standard bivalent semantics, a declarative sentence has, by default, a definite truth-value. It could only be either true or false. No truth-valuelessnesss (neither-truth-nor-falsity) is permissible. That means that any declarative sentence is assertable as a statement (by definition, a statement or assertion is either true or false).
In contrast, within trivalent semantics, a declarative sentence (such as ‘the present king of France is bald’) could be true, false, or neither-true-nor-false. The standard bivalent semantics only deals with truth-or-falsity, not neither-truth-nor-falsity. Within a three-valued semantics, besides the classical truth-values (truth or falsity), we have to add one more kind of truth-related semantic value of declarative sentences, which I will dub ‘the truth-value status’. The notion of truth-value status concerns whether a declarative sentence has a (classical) truth-value or whether a sentence is a candidate for truth-or-falsity (this is never a question within standard bivalent semantics). A sentence has two different truth-value statuses: either-true-or-false versus neither-true-nor-false. If a sentence has a truth-value, we say that it has a positive truth-value status (being true-or-false); otherwise it has a negative truth-value status (being neither-true-nor-false).
Accordingly, the truth-related evaluation of a declarative sentence S involves two connected stages: First, we have to determine the truth-value status of the sentence based on some given truth-value conditions. The question is whether S has a truth-value when considered within a certain language L. Second, if the answer to the first question is positive (S has a truth-value), then we can go ahead to determine what S ‘s truth-value is (it is either true or false) based on some given truth conditions. If the answer to the first question were negative, S would be truthvalueless (having no classical truth-value) from the viewpoint of language L. In this case, there is a truth-value gap regarding S. If a substantial number of core sentences of a language Lb when considered within the context of a competing language L2, lack classical truth-values, or vice versa, then there is a truth-value gap between the two languages L1 and L2.
1 T. Kuhn recalled this life-altering event again in his later publication in 1999.
2 Kuhn, 1983b, p. 669; 1987, pp. 8-12; 1988, pp. 9-11; 1991, p. 4; 1999.
3 Kuhn, 1983b, p. 669; 1987, pp. 8-9; 1988, pp. 9-10; 1991, p. 4.
4 This assumption is a basic methodology of communication theory that is forced on us when we try to communicate with others who employ different languages. Our expression of the basic assumption is innocent since it does not specify the content of agreement. But at the same time, it is too vague to be useful in the process of communication.
5 Kuhn’s early position is represented in Kuhn, 1970a, 1970b, 1976, 1977b, and 1979.
6 See Kuhn, 1970a, pp. 200-201; 1970b, pp. 275-6; 1976, p. 195; 1979, p. 416; 1987, pp. 20-21.
7 Kuhn, 1983b, p. 683; 1988, pp. 9, 16; 1991, pp. 4-5, 9; 1993a, pp. 323-6.
8 To have a taste of the popularity and pervasiveness of the notion of incommensurability in other areas, simply go to Amazon.com and search for books on incommensurability. You will find a paper collection from Symposium: Law and Incommensurability (University of Pennsylvania, 1998), a psychology book entitled Toward a Unified Psychology: Incommensurability, Hermeneutics and Morality (Institute of Mind and Behavior, 2000), a book on political economy, Ordinary Choices. Individuals, Incommensurability and Democracy (Routledge, 2005), two books on rhetoric and communication, Rhetoric and Incommensurability (Parlor Press, 2005) and Judgment, Rhetoric, and the Problem of Incommensurability (University of South Carolina Press, 2001), and so on.
9 Attempts at further explications and even precise formulations of the semantic notion of incommensurability different from the received interpretation to be presented in chapter 2 can occasionally be found in the literature, such as W. Stegmülar, 1979, H. Hung, 1987, J. Hintikka, 1988, W. Balzer, 1989, B. Ramberg, 1989, among others. These attempts are not satisfactory for many different reasons.
10 See Kuhn, 1983b, pp. 669-70; 1988, p. 10; 1991, p. 4; 1999.
11 Please see P. Winch, 1958 for the manifestation of incommensurability in social sciences.
12 For a prize case study, please read Feyerabend’s analysis of the cosmology shift from archaic to classical Greece in his 1978, chapter 17.
13 SeeB. Whorf, 1956.
14 Kuhn, 1970a, pp. 103, 148, 111-20, 150, 109-10.
15 By a truth-value functional relation between two languages, I mean the semantic relation regarding the truth-value status of the sentences in these languages. This is intended to be distinguished from the familiar logical relation regarding truth-values of the sentences—namely, the truth functional relation between two languages. It is my task to clarify such a truth-value functional relation between the languages of two competing scientific languages in the case of incommensurability in the following chapters.
16 H. Putnam’s argument against the thesis of untranslatability is based on confusion between scientific language (as object language) and natural language (as metalanguage). See Putnam, 1981, p. 114.