Une théorie davidsonienne de la signification pour une langue L prend la forme d'une theorie tarskienne de la véeritée-dans-L. Une telle théeorie sera absolument radicale s'il est possible d'éetablir qu'elle est tarskienne, c'est-à-dire conforme à la convention T de Tarski, en n'utilisant que des donnéees empiriques dont la description ne fait intervenir aucun concept linguistique, tandis qu'elle sera relativement radicale s'il est possible d'éetablir qu'elle est tarskienne en n'utilisant que des donnéees empiriques dont la description ne fait intervenir aucun concept (...) linguistique propre à L. (shrink)

In their (2008) article Liar-Like Paradox and Object Language Features C.S. Jenkins and Daniel Nolan (henceforth, JN) argue that it is possible to construct Liar-like paradox in a metalanguage even though its object language is not semantically closed. I do not take issue with this claim. I find fault though with the following points contained in JN’s article: First, that it is possible to construct Liar-like paradox in a metalanguage, even though this metalanguage is not semantically closed. Second, that the (...) presented examples of Liar-like paradox are supposed to be counterexamples to Tarski’s diagnosis of the classic Liar paradox. Third, that JN fail to notice Tarski’s postulate. And finally, that JN fail to recognize that the world they are pondering is not among the possible worlds. (shrink)

Presupposition, vagueness, and oddness can lead to some sentences failing to have a clear truth value. The homogeneity property of plural predication with definite descriptions may also create truth-value gaps: The books are written in Dutch is true if all relevant books are in Dutch, false if none of them are, and neither true nor false if, say, half of the books are written in Dutch. We study the projection property of homogeneity by deploying methods of general interest to identify (...) truth-value gaps. Method A consists in collecting both truth judgments and, independently, falsity judgments. The second method, employed in experiment series B and C, is based on one-shot ternary judgments: completely true vs. completely false vs. neither. After a calibration of these methods, we use them to demonstrate that homogeneity projects out of negation, the scope of universal sentences and the scope of non-monotonic quantifiers such as exactly two, to some extent. We assess our results in light of different theoretical approaches to homogeneity—approaches based on presuppositions, scalar implicatures, and something like supervaluations, respectively. We identify free parameters in these theories and assess various variants of them based on our results. Our experimental paradigms may be of broader significance insofar as they can be applied to other phenomena which result in the failure of a sentence to have a definite truth value. (shrink)

This is a commentary on MM McCabe's "First Chop your logos... Socrates and the sophists on language, logic, and development". In her paper MM analyses Plato's Euthydemos, in which Plato tackles the problem of falsity in a way that takes into account the speaker and complements the Sophist's discussion of what is said. The dialogue looks as if it is merely a demonstration of the silly consequences of eristic combat. And so it is. But a main point of MM's paper (...) is that there is serious philosophy in the Euthydemos, too. MM argues that to counter the sophist brothers Euthydemos and Dionysodoros, Socrates points out that that there are different aspects to the verb 'to say' that run in parallel to the different aspects of the very 'to learn'. So just as there is continuity rather than ambiguity between 'to learn' and 'to understand', so there is continuity between the different aspects of saying. Thus Socrates puts forward a teleological account of both learning and meaning. Following up on some of MM's thoughts, I argue that the sophists subscribe, despite appearance, to a theory of meaning that respects serious and widely accepted philosophical theses on meaning. -/- Forthcoming in the Australasian Philosophical Review. The curator of the volume is Fiona Leigh, and the committee also has Hugh Benson and Tim Clarke. You can find MM's paper as well as the commentaries by Nicholas Denyer and Russell E. Jones and Ravi Sharma (and myself) by registering. (shrink)

This paper explores applications of concepts from argumentation theory to mathematical proofs. Note is taken of the various contexts in which proofs occur and of the various objectives they may serve. Examples of strategic maneuvering are discussed when surveying, in proofs, the four stages of argumentation distinguished by pragma-dialectics. Derailments of strategies (fallacies) are seen to encompass more than logical fallacies and to occur both in alleged proofs that are completely out of bounds and in alleged proofs that are at (...) least mathematical arguments. These considerations lead to a dialectical and rhetorical view of proofs. (shrink)

We shall try to defend two non-standard views that run counter to two well-entrenched familiar views. The standard views are the universal and existential quantifiers of first-order logic are not modal operators, and the quantifiers are extensional. If that is correct then the counterclaims create genuine problems for some traditional philosophical doctrines.

What exactly does conceptual analysis consist in? Is it empirical or a priori? How does it support philosophical theses? and What kinds of thesis are these? There is no consensus on these questions in contemporary philosophy. This study aims to defend conceptual analysis by showing that it comprises a number of different methods and by explaining their importance in philosophy. After setting out an initial dilemma for conceptual analysis, the study outlines a minimal ecumenical account of concepts, as well as (...) an account of concept possession and concept employment. On the basis of these accounts, the study then argues that there are both empirical and a priori forms of conceptual analysis, and that each can be defended as legitimate methods. The philosophical interest of conceptual analysis, however, resides in relying on all three types of method in the service of answering philosophical concerns. This is illustrated by three sample cases. (shrink)

In this article, I am concerned with the ethical foundations of behavior therapy, that is, with the normative ethics and the meta-ethics underlying behavior therapy. In particular, I am concerned with questions concerning the very possibility of providing an ethical justification for things done in the context of therapy. Because behavior therapists must be able to provide an ethical justification for various actions (if the need arises), certain meta-ethical views widely accepted by behavior therapists must be abandoned: in particular, one (...) must give up ethical subjectivism, ethical skepticism, and ethical relativism. An additional task is to show how it is possible to provide a nonsubjective, nonskeptical, and nonrelativistic moral justification for an ethical statement. Although this is a monumental task, I provide a rough sketch of such a model, one that is congenial to the value judgments underlying behavior therapy. (shrink)

Tarski's definition of truth has rehabilitated the application of the word "true" to sentences of formalized languages. But a correspondence theory according to which a sentence is true if, And only if, It is related in the peculiar way of correspondence to the facts, Is incompatible with tarski's definition. Actually no theory of truth, Which claims to make proper assertions about sentences when calling them true, Is compatible with tarski's definition. Hence they all have to find their own solution to (...) the problem of the semantical antinomies and have to explain what it means to say that sentences are true. (shrink)

Science progresses if we succeed in rendering the objects of scientific inquiry more comprehensively or more precisely. Popper tries to formalize this venerable idea. According to him the most comprehensive and most precise description of the world is given by the set T of all true statements. A hypothesis comes the closer to T, or has the more verisimilitude, the more true consequences and the fewer false consequences it implies. Popper proposes to order hypotheses by the inclusion relations between the (...) sets of their true and of their false consequences ("truth contents" and "falsity contents"). A partial ordering would permit one to decide whether the substitution of theory t 1 by t 2 represents scientific progress. But because of the logical relations between the elements of the sets of logical consequences, or contents, false hypotheses cannot be compared. As our theories usually turn out to be false sooner or later, they can seldom be compared as to their verisimilitude and when they can, the result depends only on which theory implies the other and on their truth-values. Popper even tries to define a measure of verisimilitude on the partial ordering. It has to fail for the same reason. In addition he tries to relativize the concept of a content and fails. What is more, any attempt at defining a measure of better or worse correspondence to the whole truth must fail, as there is no justification for saying that any true primitive sentence asserts as much about reality as some other primitive sentence, or more. (shrink)

This book is a running commentary of Tarski’s momentous monograph ‘The Concept of Truth in Formalized Languages’, published in Polish in 1933, with special focus on discrepancies...

The category-theoretic representation of quantum event structures provides a canonical setting for confronting the fundamental problem of truth valuation in quantum mechanics as exemplified, in particular, by Kochen–Specker’s theorem. In the present study, this is realized on the basis of the existence of a categorical adjunction between the category of sheaves of variable local Boolean frames, constituting a topos, and the category of quantum event algebras. We show explicitly that the latter category is equipped with an object of truth values, (...) or classifying object, which constitutes the appropriate tool for assigning truth values to propositions describing the behavior of quantum systems. Effectively, this category-theoretic representation scheme circumvents consistently the semantic ambiguity with respect to truth valuation that is inherent in conventional quantum mechanics by inducing an objective contextual account of truth in the quantum domain of discourse. The philosophical implications of the resulting account are analyzed. We argue that it subscribes neither to a pragmatic instrumental nor to a relative notion of truth. Such an account essentially denies that there can be a universal context of reference or an Archimedean standpoint from which to evaluate logically the totality of facts of nature. (shrink)

We give a survey on truth theories for applicative theories. It comprises Frege structures, universes for Frege structures, and a theory of supervaluation. We present the proof-theoretic results for these theories and show their syntactical expressive power. In particular, we present as a novelty a syntactical interpretation of ID1 in a applicative truth theory based on supervaluation.

John Etchemendy has argued that it is but "a fortuitous accident" that Tarski's work on truth has any signifance at all for semantics. I argue, in response, that Etchemendy and others, such as Scott Soames and Hilary Putnam, have been misled by Tarski's emphasis on definitions of truth rather than theories of truth and that, once we appreciate how Tarski understood the relation between these, we can answer Etchemendy's implicit and explicit criticisms of neo-Davidsonian semantics.

This article discusses two coextensive concepts of logical consequence that are implicit in the two fundamental logical practices of establishing validity and invalidity for premise-conclusion arguments. The premises and conclusion of an argument have information content (they ?say? something), and they have subject matter (they are ?about? something). The asymmetry between establishing validity and establishing invalidity has long been noted: validity is established through an information-processing procedure exhibiting a step-by-step deduction of the conclusion from the premise-set. Invalidity is established by (...) exhibiting a countermodel satisfying the premises but not the conclusion. The process of establishing validity focuses on information content; the process of establishing invalidity focuses on subject matter. Corcoran's information-theoretic concept of logical consequence corresponds to the former. Tarski's model-theoretic concept of logical consequence formulated in his famous 1936 no-countermodels definition corresponds to the latter. Both are found to be indispensable for understanding the rationale of the deductive method and each complements the other. This study discusses the ontic question of the nature of logical consequence and the epistemic question of the human capabilities presupposed by practical applications of these two concepts as they make validity and invalidity accessible to human knowledge. (shrink)

Each science has its own domain of investigation, but one and the same science can be formalized in different languages with different universes of discourse. The concept of the domain of a science and the concept of the universe of discourse of a formalization of a science are distinct, although they often coincide in extension. In order to analyse the presuppositions and implications of choices of domain and universe, this article discusses the treatment of omega arguments in three very different (...) formalizations of arithmetic. In Peano's formalization the domain is a restricted class of individuals, while the universe of discourse is the unrestricted class of all individuals. In Gödel's formalization the domain is a restricted class of individuals as in Peano's formalization, but the universe of discourse coincides with the domain. In Whitehead-Russell's formalization the domain is a class of logical notions in Tarski's sense, that are necessarily not individuals, whereas the universe of discourse is the unrestricted class of individuals as in Peano's formalization. The present approach emphasizes the viewpoint that the universe of discourse of a given discourse is important in determining which propositions are expressed by which sentences. (shrink)

Review: Ippoliti, Emiliano, Sterpetti, Fabio, Nickles Thomas : Models and Inferences in Science.

Contra Lewis, it is argued that the correspondence theory is a genuine rival theory of truth: it goes beyond the redundancy theory; it competes with other theories of truth; it is aptly summarized by the slogan 'truth is correspondence to fact'; and it really is a theory of truth.

Tarski avoids the liar paradox by relativizing truth and falsehood to particular languages and forbidding the predication to sentences in a language of truth or falsehood by any sentences belonging to the same language. The Tarski truth-schemata stratify an object-language and indefinitely ascending hierarchy of meta-languages in which the truth or falsehood of sentences in a language can only be asserted or denied in a higher-order meta-language. However, Tarski’s statement of the truth-schemata themselves involve general truth functions, and in particular (...) the biconditional, defined in terms of truth conditions involving truth values standardly displayed in a truth table. Consistently with his semantic program, all such truth values should also be relativized to particular languages for Tarski. The objection thus points toward the more interesting problem of Tarski’s concept of the exact status of truth predications in a general logic of sentential connectives. Tarski’s three-part solution to the circularity objection which he anticipates is discussed and refuted in detail. (shrink)

Network motifs are small patterns of connections, found over‐represented in gene regulatory networks. An example is the negative feedback loop (e.g. factor A represses itself). This opposes its own state so that when ‘on’ it tends towards ‘off’ – and vice versa. Here, we argue that such self‐opposition, if considered dimensionlessly, is analogous to the liar paradox: ‘This statement is false’. When ‘true’ it implies ‘false’ – and vice versa. Such logical constructs have provided philosophical consternation for over 2000 years. (...) Extending the analogy, other network topologies give strikingly varying outputs over different dimensions. For example, the motif ‘A activates B and A. B inhibits A’ can give switches or oscillators with time only, or can lead to Turing‐type patterns with both space and time (spots, stripes or waves). It is argued here that the dimensionless form reduces to a variant of ‘The following statement is true. The preceding statement is false’. Thus, merely having a static topological description of a gene network can lead to a liar paradox. Network diagrams are only snapshots of dynamic biological processes and apparent paradoxes can reveal important biological mechanisms that are far from paradoxical when considered explicitly in time and space. (shrink)

Logical form has always been a prime concern for philosophers belonging to the analytic tradition. For at least one century, the study of logical form has been widely adopted as a method of investigation, relying on its capacity to reveal the structure of thoughts or the constitution of facts. This book focuses on the very idea of logical form, which is directly relevant to any principled reflection on that method. Its central thesis is that there is no such thing as (...) a correct answer to the question of what is logical form: two significantly different notions of logical form are needed to fulfil two major theoretical roles that pertain respectively to logic and to semantics. This thesis has a negative and a positive side. The negative side is that a deeply rooted presumption about logical form turns out to be overly optimistic: there is no unique notion of logical form that can play both roles. The positive side is that the distinction between two notions of logical form, once properly spelled out, sheds light on some fundamental issues concerning the relation between logic and language. (shrink)

The paper argues that the liar paradox teaches us these lessons about English. First, the paradox-yielding sentence is a sentence of English that is neither true nor false in English. Second, there is no English name for any such thing as a set of all and only true sentences of English. Third, ‘is true in English’ does not satisfy the axiom of comprehension.

The significance of the semantical paradoxes for natural languages is examined. If Tarski’s reflections on the issue are correct, English is inconsistent. Paul Ziff responds to Tarskian reflections by arguing to the conclusion that no natural language is or can be inconsistent. The authors reject Ziff’s argument, but they defend something similar to its conclusion: no language, natural or otherwise, is or can be inconsistent in the way that Tarski holds languages capable of formulating the Epimenides are inconsistent.

Tarski's theorem essentially says that the Liar paradox is paradoxical in the minimal reflexive frame. We generalise this result to the Liar-like paradox $\lambda^\alpha$ for all ordinal $\alpha\geq 1$. The main result is that for any positive integer $n = 2^i(2j+1)$, the paradox $\lambda^n$ is paradoxical in a frame iff this frame contains at least a cycle the depth of which is not divisible by $2^{i+1}$; and for any ordinal $\alpha \geq \omega$, the paradox $\lambda^\alpha$ is paradoxical in a frame (...) iff this frame contains at least an infinite walk which has an arbitrarily large depth. We thus get that $\lambda^n$ has a degree of paradoxicality no more than $\lambda^m$ iff the multiplicity of 2 in the (unique) prime factorisation of $n$ is no more than that in the prime factorisation of $m$; and all tranfinite $\lambda^\alpha$ has the same degree of paradoxcality but has a higher degree of paradoxicality than any $\lambda^n$. (shrink)

A relativized version of Tarski's T-scheme is introduced as a new principle of the truth predicate. Under the relativized T-scheme, the paradoxical objects, such as the Liar sentence and Jourdain's card sequence, are found to have certain relative contradictoriness. That is, they are contradictory only in some frames in the sense that any valuation admissible for them in these frames will lead to a contradiction. It is proved that for any positive integer n, the n-jump liar sentence is contradictory in (...) and only in those frames containing at least an n-jump odd cycle. In particular, the Liar sentence is contradictory in and only in those frames containing at least an odd cycle. The Liar sentence is also proved to be less contradictory than Jourdain's card sequence: the latter must be contradictory in those frames where the former is so, but not vice versa. Generally, the relative contradictoriness is the common characteristic of the paradoxical objects, but different paradoxical objects may have different relative contradictoriness. (shrink)

Even though disquotationalism is not correct as it is usually formulated, a deep insight lies behind it. Specifically, it can be argued that, modulo implicit commitment to reflection principles, all there is to the notion of truth is given by a simple, natural collection of truth-biconditionals.

The present paper discusses a proposal which says,roughly and with several qualifications, that thecollection of mathematical truths is identical withthe set of theorems of ZFC. It is argued that thisproposal is not as easily dismissed as outright falseor philosophically incoherent as one might think. Some morals of this are drawn for the concept ofmathematical knowledge.

Philosophical analysis was the central preoccupation of 20th-century analytic philosophy. In the contemporary methodological debate, however, it faces a number of pressing external and internal challenges. While external challenges, like those from experimental philosophy or semantic externalism, have been extensively discussed, internal challenges to philosophical analysis have received much less attention. One especially vexing internal challenge is that the success conditions of philosophical analysis are deeply unclear. According to the standard textbook view, a philosophical analysis aims at a strict biconditional (...) that captures the necessary and sufficient conditions for membership in the relevant category. The textbook view arguably identifies a necessary condition on successful philosophical analyses, but understood as a sufficient condition it is untenable, as I will argue in this paper. To this end, I first uncover eight conditions of adequacy on successful philosophical analyses, some of which have rarely been spelled out in detail. As we shall see, even sophisticated alternatives to the textbook view fail to accommodate some of these conditions. I then propose the concept grounding view as a more promising account of philosophical analysis. According to this view, successful philosophical analyses require necessary biconditionals that are constrained by grounding relations among the concepts involved. Apart from providing a satisfactory account of philosophical analysis in its own right, the concept grounding view is also able to meet the challenge that the success conditions of philosophical analysis are problematically unclear. (shrink)

This article contains an overview of the main problems, themes and theories relating to the semantic paradoxes in the twentieth century. From this historical overview I tentatively draw some lessons about the way in which the field may evolve in the next decade.

According to Field’s influential incompleteness objection, Tarski’s semantic theory of truth is unsatisfactory since the definition that forms its basis is incomplete in two distinct senses: (1) it is physicalistically inadequate, and for this reason, (2) it is conceptually deficient. In this paper, I defend the semantic theory of truth against the incompleteness objection by conceding (1) but rejecting (2). After arguing that Davidson and McDowell’s reply to the incompleteness objection fails to pass muster, I argue that, within the constraints (...) of a non-reductive physicalism and a holism concerning the concepts of truth, reference and meaning, conceding Field’s physicalistic inadequacy conclusion while rejecting his conceptual deficiency conclusion is a promising reply to the incompleteness objection. (shrink)

Although there is a prima facie strong case for a close connection between the meaning and inferential role of certain expressions, this connection seems seriously threatened by the semantic and logical paradoxes which rely on these inferential roles. Some philosophers have drawn radical conclusions from the paradoxes for the theory of meaning in general, and for which sentences in our language are true. I criticize these overreactions, and instead propose to distinguish two conceptions of inferential role. This distinction is closely (...) tied to two conceptions of deductive logic, and it is the key, I argue, for understanding first the connection between meaning and inferential role, and second what the paradoxes show more generally. (shrink)

We consider two formalisations of the notion of a compositionalsemantics for a language, and find some equivalent statements in termsof substitutions. We prove a theorem stating necessary and sufficientconditions for the existence of a canonical compositional semanticsextending a given partial semantics, after discussing what features onewould want such an extension to have. The theorem involves someassumptions about semantical categories in the spirit of Husserl andTarski.

The paper analyses what is said and what is presupposed by thePrinciple of Compositionality for semantics, as it is commonly stated. ThePrinciple of Compositionality is an axiom which some semantics satisfy andsome don’t. It says essentially that if two expressions have the same meaning then they make the same contribution to the meanings of expressionscontaining them. This is a sensible axiom only if one combines it with aconverse, that if two expressions make the same contribution to the meanings of sentences (...) containing them, then they have the same meaning;and some assumption that two expressions which can’t meaningfully besubstituted for each other have different meanings. as a full abstraction principle, and as ‘Husserl’s principle’.) Moreoverthe Principle of Compositionality speaks only about when two expressionshave the same meaning; it adds nothing whatever about what that meaningmight be . Some recent discussions by writers in linguistics and logic are assessed. The paper finishes by reviewing thehistory of the notion of compositionality. (shrink)

In its first meaning, a logic is a collection of closely related artificial languages. There are certain languages called first‐order languages, and together they form first‐order logic. In the same spirit, there are several closely related languages called modal languages, and together they form modal logic. Likewise second‐order logic, deontic logic and so forth.

In many actual arguments, the conclusion seems intuitively to follow from the premisses, even though we cannot show that it follows logically. The traditional approach to evaluating such arguments is to suppose that they have an unstated premiss whose explicit addition will produce an argument where the conclusion does follow logically. But there are good reasons for doubting that people so frequently leave the premisses of their arguments unstated. The inclination to suppose that they do stems from the belief that (...) the only way in which an argument's conclusion can follow definitely from its premisses is to follow logically. I argue that this belief is mistaken. I propose a revision of the current generic conception of logical consequence, and its variant specifications, to avoid the paradoxes of strict implication. The revised conception can then be naturally extended to include also what we might call 'enthymematic consequence'. This concept is a kind of consequence, whose properties merit investigation. (shrink)

Within the context of the Quine–Putnam indispensability argument, one discussion about the status of mathematics is concerned with the ‘Enhanced Indispensability Argument’, which makes explicit in what way mathematics is supposed to be indispensable in science, namely explanatory. If there are genuine mathematical explanations of empirical phenomena, an argument for mathematical platonism could be extracted by using inference to the best explanation. The best explanation of the primeness of the life cycles of Periodical Cicadas is genuinely mathematical, according to Baker (...) :223–238, 2005; Br J Philos Sci 60:611–633, 2009). Furthermore, the result is then also used to strengthen the platonist position :779–793, 2017a). We pick up the circularity problem brought up by Leng Mathematical reasoning, heuristics and the development of mathematics, King’s College Publications, London, pp 167–189, 2005) and Bangu :13–20, 2008). We will argue that Baker’s attempt to solve this problem fails, if Hume’s Principle is analytic. We will also provide the opponent of the Enhanced Indispensability Argument with the so-called ‘interpretability strategy’, which can be used to come up with alternative explanations in case Hume’s Principle is non-analytic. (shrink)

We develop a point-free construction of the classical one- dimensional continuum, with an interval structure based on mereology and either a weak set theory or logic of plural quantification. In some respects this realizes ideas going back to Aristotle,although, unlike Aristotle, we make free use of classical "actual infinity". Also, in contrast to intuitionistic, Bishop, and smooth infinitesimal analysis, we follow classical analysis in allowing partitioning of our "gunky line" into mutually exclusive and exhaustive disjoint parts, thereby demonstrating the independence (...) of "indecomposability" from a non-punctiform conception. It is surprising that such simple axioms as ours already imply the Archimedean property and that they determine an isomorphism with the Dedekind-Cantor structure of R as a complete, separable, ordered field. We also present some simple topological models of our system, establishing consistency relative to classical analysis. Finally, after describing how to nominalize our theory, we close with comparisons with earlier efforts related to our own. (shrink)

We attempt here to trace the evolution of Frege’s thought about truth. What most frames the way we approach the problem is a recognition that hardly any of Frege’s most familiar claims about truth appear in his earliest work. We argue that Frege’s mature views about truth emerge from a fundamental re-thinking of the nature of logic instigated, in large part, by a sustained engagement with the work of George Boole and his followers, after the publication of Begriffsschrift and the (...) appearance of critical reviews by members of the Boolean school. (shrink)

In recent work on Frege, one of the most salient issues has been whether he was prepared to make serious use of semantical notions such as reference and truth. I argue here Frege did make very serious use of semantical concepts. I argue, first, that Frege had reason to be interested in the question how the axioms and rules of his formal theory might be justified and, second, that he explicitly commits himself to offering a justification that appeals to the (...) notion of reference. I then discuss the justifications Frege offered, focusing on his discussion of inferences involving free variables, in section 17 of Grundgesetze, and his argument, in sections 29-32, that every well-formed expression of his formal language has a unique reference. (shrink)

If, as it is usually understood, incommensurable theories must be compatible then one need never choose between two such theories. But if theories were incompatible and incommensurable one would have to choose between them. What if they are incompatible only outside the domain of observation? The fact that Darwin's biology can clash with Kelvin's physics (each with their respective auxiliary assumptions) regarding the age of the earth shows how commensurable theories may yet be incompatible. But it also shows that they (...) need not be alternatives--i.e. that one may not be able to simply and satisfactorily replace the other in our world view. But standard examples of scientific revolutions consist of the replacement of one theory by another in one's world view. These alternative theories must therefore be more than merely incompatible--what do they share if not content? (I.e. they must be commensurable.). (shrink)