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PR EV IE W TRUTH-VALUE GAPS, ONTOLOGICAL COMMITMENTS, AND INCOMMENSURABILITY Xinli Wang, Ph.D. University of Connecticut, 1999 According to the accepted translation-failure interpretation, the problem of incommensurability involves the nature of the meaning-referential relation between scientific languages. The incommensurability thesis is that some competing scientific languages are mutually untranslatable due to the radical variance of meaning or/and reference of the terms they employ. I argue that this interpretation faces many difficulties and cannot give us a tenable, coherent, and integrated notion of incommensurability. It has to be rejected. On the basis of two case studies, I find that the confrontations between many classical incommensurable languages are not confrontations between two untranslatable languages with different distribution of truth values, but rather the confrontations between incompatible fundamental presuppositions at the ontological level. We can always identify a truth-value gap between two incommensurable languages. Such a truth-value gap indicates a communication breakdown between the two language communities on the one hand, and is caused by the incompatible fundamental presuppositions underlying them on the other. I thereby identify the truth-value functional relationship between sentences, instead of the meaning-referential relationship between terms, as the dominant semantic relation between two incommensurable languages. According to my presuppositional interpretation of incommensurability, the real secret of incommensurability lies in the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PR EV IE W Xinli Wang-University of Connecticut, 1999 ontological setup of two competing presuppositional languages. When two presuppositional languages with incompatible factual com m itm ents encounter with each other, the confrontation leads to a truth-value gap, and consequently a com m unication breakdown between them. Formally put, two scientific languages are incom m ensurable 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 an ontological gap between them. The presuppositional interpretation makes many significant contributions to the discussion of the issue of incommensurability and the related metaphysical and epistemological issues: (a) It confirms the existence of the phenomenon of incommensurability and makes it metaphysically and epistemologically significant, (b) It establishes the tenability and integrity of the notion of incommensurability, (c) It avoids many alleged unattractive epistemological and metaphysical consequences of the translation-failure interpretation. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PR EV IE W TRUTH-VALUE GAPS, ONTOLOGICAL COMMITMENTS, AND INCOMMENSURABILITY Xinli Wang B .S., Changchun Institute of Geology, P. R. China, 1982 M .A., Huazhong University of Science and Technology, P. R. China, 1988 A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy at the University of Connecticut 1999 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PR EV IE W UMI Number: 9926305 C o p y r ig h t 1 9 9 9 b y W ang, X i n l i All rights reserved. UMI Microform 9926305 Copyright 1999, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PR EV IE W Copyright by Xinli Wang 1999 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PR EV IE W APPROVAL PAGE Doctor of Philosophy Dissertation TRUTH-VALUE GAPS, ONTOLOGICAL COMMITMENTS, AND INCOMMENSURABILITY presented by Xinli Wang, B .S., M.A. Major Advisor _ Associate Advisor Associate Advisor Associate Advisor Anne Hiskes Scott Lehmann Austen Clark Samuel Wheeler ID University of Connecticut 1999 ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PR EV IE W Acknowledgments During the past five years, I have been fortunate to be under the guidance of the members of my dissertation commitment, i.e.. Professors Anne Hiskes, Austen Clark, Scott Lehmann, Samuel Wheeler HI. They are exceptionally perceptive philosophers and generous Mends. Their illuminating questions, detailed written comments, extensive criticisms, and insightful suggestions on each draft of the dissertation have enabled me to make considerable improvements on the earlier drafts. Without their helps and encouragement, I might still struggle in the "morass" of the issue of incommensurability or come up with much more "mud" on my head. I realize that most of them are unlikely to agree with my conclusions, but they can pride themselves on having diverted me from even sillier things that I might have said and helped me to bring my ideas and arguments into clearer focus. I owe an enormous intellectual debt and immense gratitude to them. iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PR EV IE W Table of Contents Chapter One: In troduction .....................................................................................1 1.1 The Current Research Status....................................................................................... 1 1.2 Many Faces of Incommensurability........................................................................... 4 1.3 The Normative Perspective......................................................................................... 11 1.4 The Presuppositional Interpretation of Incommensurability...................................... 18 1.5 Two Technical Issues.................................................................................................. 29 1.5.1 The Terms of Incommensurability Relations...................................................29 1.5.2 The Semantic Status of Cross-language Sentences..........................................33 Endnotes..............................................................................................................................38 Chapter Two: A Critique of the TransIation-Failure Interpretation.......................41 Introduction........................................................................................................................ 41 2.1 The Accepted Interpretation of the Thesis of Incommensurability........................... 41 2.2 An Influential Line of Criticism................................................................................. 46 2.3 Feyerabend's and Kuhn's Contextual Theory of Meaning......................................... 49 2.3.1 Feyerabend's Contextual Theory of Meaning................................................. 50 2.3.2 Kuhn's Lexical Theory of Reference................................................................54 2.4 Meaning-referential Continuity and Translatability.................................................. 57 2.5 Untranslatability and Incommensurability.................................................................63 2.5.1 The Notion of Truth-preserving Translation................................................... 65 2.5.2 Mutual Translation and Mutual Understanding...............................................72 2.5.3 Meaning-referential Continuity and Translation Again.................................. 76 2.6 Concluding Remarks...................................................................................................78 iv Reproduced with permission of the copyright owner. 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PR EV IE W Endnotes............................................................................................................................. 79 Chapter Three: Case Studies-The Emergence of Truth-Value G aps..................... 82 Introduction........................................................................................................................82 3.1 Traditional Chinese Medical Theory versus Contemporary Western Medical Theory....................................................................83 3.1.1 Paracelsus Medical Theory...............................................................................83 3.1.2 Traditional Chinese Medical Theory................................................................ 86 3.1.3 Is Untranslatability A Barrier o f the Cross-Language Understanding ? ....... 89 3.1.4 What Causes A Communication Breakdown?.................................................92 3.1.5 The Emergence of A Truth-value Gap............................................................. 97 3.2 Debates on the Absoluteness of Space and T im e..................................................... 100 3.2.1 The Newton-Leibniz Debate on the Absoluteness of Space............................100 3.2.2 The Newton-Einstein Debate on the Absoluteness of Time............................108 Endnotes............................................................................................................................. 110 Chapter Four: Semantic Presuppositions And Truth-Value Gaps...........................112 Introduction........................................................................................................................ 112 4.1 The Emergence of Truthvaluelessness.......................................................................114 4.2 Is The Notion of Semantic Presupposition Trivial?.................................................. 116 4.2.1 The Adequacy of the Notion of Semantic Presupposition...............................117 4.2.2 Schema P............................................................................................................118 4.2.3 A Trivalent Semantics...................................................................................... 119 4.2.4 A Definition of Semantic Presupposition........................................................ 125 4.3 Is the Notion of Semantic Presupposition Empty?..................................................... 132 4.3.1 A Dilemma: Internal and External Negation.................................................... 132 4.3.2 Counterexamples................................................................................................139 v Reproduced with permission of the copyright owner. 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PR EV IE W 4.4 Is the Notion of Truthvaluelessness Untenable?........................................................ 142 4.4.1 Truthvaluelessness and Falsity ......................................................................142 4.4.2 Truthvaluelessness and the Principle of Bivalence.......................................... 146 Endnotes................................................................................................................................ 150 Chapter Five: Presuppositional Languages....................................................................153 Introduction...........................................................................................................................153 5.1 A Theory of Truth-Value................................................................................................153 5.1.1 Truth Values versus Truth-Value Status.......................................................... 154 5.1.2 The Usual Theories of Truth.............................................................................154 5.1.3 Truth-Value Conditions..................................................................................... 157 5.2 The Occurrence of Truth-Value Gaps..........................................................................162 5.2.1 A Truth-Value Gap Regarding Individual Sentences...................................... 162 5.2.2 A Truth-Value Gap Between Two Languages.................................................164 5.3 Presuppositional Languages......................................................................................... 165 5.3.1 Introducing Presuppositional languages.............................................................165 5.3.2 The Structure of A Presuppositional Language................................................167 5.3.3 Core Sentences....................................................................................................177 5.4 Presuppositional Languages vs. Conceptual Schemes................................................178 Endnotes................................................................................................................................ 187 Chapter Six: Factual Commitments................................................................................ 189 Introduction...........................................................................................................................189 6.1 Existential Presumptions.............................................................................................. 189 6.2 Universal Principles......................................................................................................190 6.2.1 The Notion of Universal Principles..................................................................190 vi Reproduced with permission of the copyright owner. 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PR EV IE W 6.2.2 Universal Principles As State-of-Affairs Presuppositions............................. 195 6.3 Modes of Reasoning and Hidden Universal Principles.............................................. 197 6.3.1 The Notion of Modes of Reasoning..................................................................197 6.3.2 From Modes of Reasoning to Hidden Universal Principles............................ 200 6.3.3 The Pre-Modem Chinese Mode of Reasoning and Its Hidden Assumptions.............................................................................203 6.4 Categorical Frameworks.............................................................................................. 209 6.4.1 The Notion of Categorical Frameworks........................................................... 210 6.4.2 The Relativity of Lexical Taxonomies............................................................. 213 6.4.3 A Categorical Framework as A System of Sortal Presuppositions.................223 Endnotes.............................................................................................................................. 230 Chapter Seven: Factual Commitments, Cross-language Understanding and Communication............................................................................233 Introduction.........................................................................................................................233 7.1 Prepositional Understanding and Some Common Accounts.................................... 234 7.2 The Role of Factual Commitments In Cross-Language Understanding....................239 7.3 A Truth-Value Conditional Account of Understanding.............................................248 7.4 Truth-Value Gaps and The Failure of Effective Understanding............................... 254 7.5 Bilinguals and Cross-Language Communication....................................................... 257 7.6 Understanding versus Communication.......................................................................262 Endnotes.............................................................................................................................. 268 Chapter Eight: The Concept of Incommensurability..................................................270 Introduction.........................................................................................................................270 8.1 The Phenomenon of Incommensurability: Communication Breakdowns.................271 8.2 Compatible vs. Incompatible Factual Commitments.................................................277 Reproduced with permission of the copyright owner. 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PR EV IE W 8.2.1 The Distinction................................................................................................ 278 8 .2.2 Incompatible Category Systems.......................................................................280 8.3 Complete Communication Breakdowns.....................................................................287 8.4 Hermeneutic Understanding.......................................................................................290 8.5 Partial Communication Breakdowns..........................................................................297 8.6 Truth-Value Gaps and Communication Breakdowns............................................... 306 8.7 Truthvaluelessness With Ontological Significance................................................... 307 8.8 Conclusion: Incommensurability as the Occurrence of Truth-Value Gaps.............. 311 Endnotes.............................................................................................................................313 Chapter Nine: Incommensurability and Ontological Commitments.........................316 Introduction........................................................................................................................316 9.1 The World As the Totality of Facts.............................................................................317 9.2 Possible Facts............................................................................................................. 325 9.3 The Relativity of Facts...............................................................................................328 9.4 States of Affairs.......................................................................................................... 337 9.5 Ontological Commitments.........................................................................................340 9.6 Incommensurability Due to Ontological Incompatibility.......................................... 347 Endnotes.............................................................................................................................353 Chapter Ten: The Significance of the Presuppositional Interpretation.................. 356 10.1 The Advantages of the Presuppositional Interpretation Over the Translation-failure Interpretation........................................................................356 10.2 Incommensurability, Incompatibility, and Comparability.......................................363 Endnotes.............................................................................................................................373 Bibliography.....................................................................................................................374 viii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PR EV IE W Chapter One Introduction 1.1 The Current Research Status Incommensurability is a notion that for Thomas Kuhn and Paul Feyerabend emerged from attempts to understand some out-of-date scientific texts in their researches around 1950s. Like any other historian of sciences, for lack of an alternative at the beginning of studying, they had been trying to understand these texts as they would if the texts had occurred in contemporary discourse which they were familiar with. Approaching these texts in terms of their current scientific language, Kuhn and Feyerabend characteristically encountered passages that make no sense to them. That is an experience Kuhn had repeatedly whether his subject was an Aristotle, a Newton, A Volta, a Bohr, or a Planck. More significantly, they found that apparently nonsensical passages encountered in an old scientific text cannot be simply taken as evidence of the author's confused or mistaken beliefs, nor as evidence of the interpreter's personal limitation of knowledge or lack of skills of interpretation. It seems to involve some deep semantic obstruction between two different discourses.1 Guided by these personal experience, Kuhn and Feyerabend found out further that when two successive competing (comprehensive) scientific theories, such as Newtonian Mechanics and Aristotelian Mechanics, are separated by a so-called "scientific revolu- tion," the proponents of the two theories would inevitably talk past one another when attempting to resolve their disagreements.2 They were struck by the fact that when rival (comprehensive) scientific theories orparadigms-more general, rival cultures (Rorty), traditions (Gadamer), worldviews (Feyerabend), forms of life (Wittgenstein), or frameworks -clash, we can from time to time identify a communication breakdown between their advocates. Many assertions made in one body of discourse are unintelligible to those utilizing the other rival one. 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PR EV IE W 2 To illustrate such a communication breakdown between the advocates of two succes- sive scientific theories and to explore the presumably deep semantic obstruction between them, Kuhn and Feyerabend borrowed the term "incommensurability" from mathematics to describe such a phenomenon. In its original mathematical use "incommensurability" means "no common measure." By coining this term, Kuhn and Feyerabend initially meant to express their deep intuition that a communication breakdown between the advocates of two competing (comprehensive) scientific theories is due to lack of some common language into which both theories can be formulated; for the existence of a common language is necessary for successful communication between the advocates of the two theories.3 Kuhn had spent more than 30 years to conceptualize, clarify, and refine the notion of incommensurability, and to argue for his celebrated thesis that the phenomenon of incommensurability, i.e., communication breakdowns, does exist and cases of it abound not only in the history of science but also in the history of rational thought in general. The problem of incommensurability has caught the attention of the past three decades because of its significant implications for some central problems in the philosophy of science and other related areas, such as the philosophy of language, epistemology, and metaphysics. 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 or other of its many manifes- tations.4 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 which are supposed to be connected with the problem of incommensurability. It has been widely held that whatever the origins and intentions of Kuhn and Feyerabend's doctrine, it is plain that the thesis of incommensurability has problemized the debate on processes of theory-comparison and theory choice, and has Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PR EV IE W 3 accordingly threatened to undermine our image of science as a rational, realistic, and progressive enterprise. Consequently, Kuhn and Feyerabend gave fresh respectability to irrationalistic, subjective, and relativistic views about science and knowledge. Besides, the influence of the problem of incommensurability has reached far beyond the professional circle of the philosophy of science. Practitioners with a relativistic bent in numerous fields, such as sociology, anthropology and ethnography, psychology, education, political science, and linguistics, have been busy discovering similar phenom- ena in their fields. Through its popularization, the notion of incommensurability has been put on the cultural map, and even becomes the weekly glosses in many professional circles. Because of the above two reasons, the notion of incommensurability has been one of the most revolutionary and influential notions in recent philosophical investigation. This is why the issue of incommensurability is still very much alive today. Along with its significant impact on the philosophy of science and other related areas, the notion of incommensurability is one of the most intriguing ideas in recent philosophy. On the one hand, the topic has been so popularized that in the circle of the philosophy of science "the doctrine of incommensurability needs no introduction."5 On the other hand, however, the notion of incommensurability is the most controversial, most often abused notion in contemporary philosophy of science. Although philosophers, in the past 35 years, approached it from different directions and presented many historically erudite and conceptually fine grained analyses of it, "we do not have any clear theoretical conception of what incommensurability is."6 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 for the past.7 A comment made by Feyerabend 20 years ago can still be used to describe the current research situation of incommensurability. "Apparently, everyone who enters the morass of this problem (referring to the problem of incommensurability-author) comes up with mud on his Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PR EV IE W 4 o head." Kuhn and Feyerabend, two pioneers opening this uncultivated land, are not an exception either. It seems to me that philosophical discussion involving the notion of incommensurability, no matter whether for or against it, tends to come to a dead lock, and is hard to evaluate and often fallacious. There is a danger that, as D. Pearce pointed out 10 years ago, through popularization and abuse, the term "incommensurable" will become long in the tooth and the thesis will lose its original bite. This danger has occurred. The danger mainly comes from two direc- tions. On the one side, on the basis of some misconceptions of incommensurability, such as incommensurability as untranslatability, the thesis degenerates into a trivial platitude. According to this notion, almost any kind of conceptual difference or conflict amounts to a case of incommensurability. On the other side, the problem of incommensurability turns out to be a pseudo-problem if incommensurability equals or is reduced to incompara- bility. The following comment, made by Pearce in the late 80's, gives us a vivid descrip- tion of the present research situation on the issue of incommensurability. These days the virulence of the commensurability debates has faded, but it has left its marks on the shape of scientific philosophy and on science itself. Many philosophers currently pay lip service to 'the problem of incommensurability' by insisting on how seriously they take it; only to dismiss it subsequently in a few dipped phrases as being 'settled' and 'solved' (Pearce 1987, p. 2). 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: incom- mensurability as a complex historical-anthropological phenomenon which manifests itself in many facets and ramifications; the failure of the standard interpretation of incommen- surability. The first issue will be discussed in the following two sections. The second issue is the topic of chapter two. 1.2 Many Faces of Incommensurability It is commonly held that part of the blame for the vagueness of the notion of incomReproduced with permission of the copyright owner. Further reproduction prohibited without permission. PR EV IE W 5 mensurability 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 has to clarify himself again and again since 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 com- munication breakdowns which they encountered in the study of the history of sciences, they had nothing so precise in mind. For them, the notion of incommensurability is just a suitable language metaphor to reveal their deep insight gained in these researches.9 The vagueness of the explanation of incommensurability is partially due to the fact that we are dealing with a complex historical-anthropological phenomenon, whose roots are deep in the basic mechanisms of cultures, forms of life, languages, and social institu- tions. Generally speaking, incommensurability has its natural home primarily in five disciplinary settings: (a) 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 (such as Galenic and modem biochemical medicine); (b) in descriptive sociology to contrast kinship systems or other such mechanisms for categorizations and explanation of human affairs;10 (c) in anthropology to contrast and understand totally different modes of justification;11 (d) in linguistic study to contrast different categorization systems which create ''pattern resistance" to widely divergent points of views;12 (e) in philosophical epistemology to contrast fundamentally diverse perspectives-which start with concep- tually disparate presuppositions-of treating explanatory issues. The phenomenon of incommensurability has been and will continue to be rediscovered and enhanced in different disciplinary settings. It is not exaggerated 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 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PR EV IE W 6 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, develop- mental, or evolutionary view of scientific knowledge" (Kuhn 1991, p. 3). Feyerabend explicitly made 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" (Feyerabend 1978, p. 269). Just like an anthropologist trying to break into an unknown tribe, he/she must hold back his/her eagerness for instant clarity and logical perfection. He/She should not try to make a concept clearer than what is suggested by the available material. He/She must keep his/her key notions vague and incomplete until more information is collected. Feyerabend assumes that the anthropo- logical method is appropriate for studying the phenomenon of incommensurability. Here, lack of clarity of the notion of incommensurability indicates the scarcity of right informa- tion 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 has even gone so far as to register doubt that, in its present stage of development, the incommensurability thesis is capable in principle of being given the kind of precise formulation that would serve to satisfy 'analytic' philosophers. In a similar way, Kuhn clearly realizes that his attempts to describe the central conception of incommensurability were extremely crude. In his own words, "Efforts to understand and refine it have been my primary and increasingly obsessive concern for thirty years" (Kuhn 1993, p. 315). As a complex historical-anthropological phenomenon, the problem of incommen- surability manifests itself in many facets and ramifications. The issue of incommen- surability in fact is a set of problems which comprises three interrelated problems: (a) the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PR EV IE W 7 . • nature of incommensurability, (b) the sources of incommensurability, and (c) the episte- mological 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 and incomplete. It can be understood as a question either about the nature or about the sources of incom- mensurability. 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 a s ...," for example, incommensurability as untranslatability, incommensurability as incomparability, or incommensurability as communication break- downs. 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 and / or 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 incommen- surability, 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 which involves at least two different dimensions: the normative dimension and the semantic dimension. Accordingly, the concept can be approached from at least two perspectives corresponding to each dimension, which I will call the normative perspective Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PR EV IE W 8 and the semantic perspective. According to the semantic perspective, the problem of incommensurability has 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 (m eaning 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 incommensu- rable theories inevitably talk past one another when attempting to resolve their disagree- ments. I will call the incommensurability identified in the semantic dimension semantic incommensurability later. By contrast, according to the normative perspective, the problem of incommensurability has something to do with the nature of non-semantic relations between two competing theories, such as standards of adequacy, problem-field, or cognitive perceptions associated with each theory. So the rise of incommensurability can be attributed to the lack of a certain kind of normative contact between two competing scientific theories due to changes in their normative expectations. I will call the incommensurability located in the normative dimension normative incommensurability. 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 (semantic contact) between the languages employed by two competing scientific theories due to changes of a certain desirable semantic value(s) of certain kind of components (sentences themselves or their constituents) of the languages in question. This seems not to be in controversy within the framework of the semantic perspective. But the controversy arises with what kind o f 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 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PR EV IE W 9 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, (P) The sun, the largest planet, revolves about the earth, a star, "the sun" and "the earth" are proper names; "star" and "planet" 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 P. 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 or reference; for a predicate (say, "is a star"), we can talk about its extension. By contrast, if we take a sentence as a whole as the carrier of semantic values, we can speak of the meaning and factual meaning, truth values (Frege's reference of a sentence) and truth-value status of the sentence.13 For example, the factual meaning of sentence P consists in its truth conditions. P is either true or false from the point of view of Ptolemaic astronomy. But P is neither true nor false from the point of view of Copemican astronomy.14 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 meaningreferential relation between the languages of two competing scientific theories would be the determinant semantic relation in the case of incommensurability. By contrast, 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 the languages Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PR EV IE W 10 of two competing languages. Corresponding to which kind of semantic relations is identified as the determinant relation, there are two possible ways, within the semantic perspective, to characterize the problem of incommensurability. According to the presuppositional interpretation o f incommensurability, which I will present and defend, the carriers of semantic values in the case of incommensurability are the sentences of the languages of two rival scientific theories. The semantic values which concern us are factual meanings and truth-value status of 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 between the languages employed by the theories, which is signified by a communication breakdown between their proponents. And such an occur- rence of a truth-value gap is in turn due to incompatible ontological commitments underlying the two languages. By contrast, according to the accepted translation-failure interpretation o f 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 meaning or/and reference of terms in question. So it is the meaning-referential 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. And the failure of mutual translation in turn is due to the absence of meaning-referential continuity because of the radical variance of meaning or/and reference. I will argue in chapter two that the accepted interpretation is not an effective way to clarify the concept of incommensurability, but is rather misleading. As a substitute for it, I will present and defend the presuppositional interpretation of incommensurability in the remaining chapters. But before we move on, I need to consider in the next section the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. PR EV IE W