Models are of central importance in many scientific contexts. The centrality of models such as inflationary models in cosmology, general-circulation models of the global climate, the double-helix model of DNA, evolutionary models in biology, agent-based models in the social sciences, and general-equilibrium models of markets in their respective domains is a case in point (the Other Internet Resources section at the end of this entry contains links to online resources that discuss these models). Scientists spend significant amounts of time building, (...) testing, comparing, and revising models, and much journal space is dedicated to interpreting and discussing the implications of models. In short, models are one of the principal instruments of modern science. (shrink)

Recent years have seen an explosion of interest in the semantics of knowledge-attributing sentences, not just among epistemologists but among philosophers of language seeking a general understanding of linguistic context sensitivity. Despite all this critical attention, however, we are as far from consensus as ever. If we have learned anything, it is that each of the standard views—invariantism, contextualism, and sensitive invariantism—has its Achilles’ heel: a residuum of facts about our use of knowledge attributions that it can explain only with (...) special pleading. This is not surprising if, as I will argue, there is a grain of truth in each of these views. (shrink)

Paul Boghossian defends a meaning‐based approach to the apriority of the propositions of logic. His model is based on the idea that the logical constants are implicitly defined by some of the axioms and inference rules in which they are involved, thereby offering an alternative to those theories that deny that grasp of meaning can contribute to the explanation of a thinker's entitlement to a particular type of transition or belief.

Dialetheism is the view that some contradictions are true. This is a view which runs against orthodoxy in logic and metaphysics since Aristotle, and has implications for many of the core notions of philosophy. Doubt Truth to Be a Liar explores these implications for truth, rationality, negation, and the nature of logic, and develops further the defense of dialetheism first mounted in Priest's In Contradiction, a second edition of which is also available.

Attempts to clarify some issues about the use of hidden arguments to predicates of personal taste, and motivate an analysis which does not make use of such arguments.

In the course of the discussion, Professor Quine pinpoints the difficulties involved in translation, brings to light the anomalies and conflicts implicit in our ...

Willard Van Orman Quine begins this influential work by declaring, "Language is asocial art.

A collection of all but two of the author's philosophical essays and lectures originally published or presented before August 1976.

This is the first elementary book to employ the concept of infinitesimals.

The paper criticizes epistemological conceptions of analytic or conceptual truth, on which assent to such truths is a necessary condition of understanding them. The critique involves no Quinean scepticism about meaning. Rather, even granted that a paradigmatic candidate for analyticity is synonymy with a logical truth, both the former and the latter can be intelligibly doubted by linguistically competent deviant logicians, who, although mistaken, still constitute counterexamples to the claim that assent is necessary for understanding. There are no analytic or (...) conceptual truths in the epistemological sense. The critique is extended to purportedly analytic inference rules. An alternative account is sketched on which understanding a word is a matter of participation in a linguistic practice, while synonymy and concept identity consist in sameness of truth-conditional semantic properties. Although there are philosophical questions about concepts, the idea that philosophical questions in general are conceptual questions generates only an illusion of insight into philosophical methodology. (shrink)

The paper challenges the inferentialist account of concept possession that Paul Boghossian takes as a premise in his account of the transmission of justification by deductive reasoning in his paper 'Blind Reasoning'. Unorthodox speakers who reject the inferences in an alleged possession condition can still have the concept by understanding a word for it. In that sense, the inferences are not analytic. Inferentialist accounts of logical constants, theoretical terms (using the Ramsey-Carnap-Lewis method) and pejorative expressions such as 'Boche' are examined (...) and rejected. It is suggested that epistemological questions cannot be reduced to questions in the theory of thought and meaning. (shrink)

The paper criticizes epistemological conceptions of analytic or conceptual truth, on which assent to such truths is a necessary condition of understanding them. The critique involves no Quinean scepticism about meaning. Rather, even granted that a paradigmatic candidate for analyticity is synonymy with a logical truth, both the former and the latter can be intelligibly doubted by linguistically competent deviant logicians, who, although mistaken, still constitute counterexamples to the claim that assent is necessary for understanding. There are no analytic or (...) conceptual truths in the epistemological sense. The critique is extended to purportedly analytic inference rules. An alternative account is sketched on which understanding a word is a matter of participation in a linguistic practice, while synonymy and concept identity consist in sameness of truth-conditional semantic properties. Although there are philosophical questions about concepts, the idea that philosophical questions in general are conceptual questions generates only an illusion of insight into philosophical methodology. (shrink)

[Paul Boghossian] The paper asks under what conditions deductive reasoning transmits justification from its premises to its conclusion. It argues that both standard externalist and standard internalist accounts of this phenomenon fail. The nature of this failure is taken to indicate the way forward: basic forms of deductive reasoning must justify by being instances of ’blind but blameless’ reasoning. Finally, the paper explores the suggestion that an inferentialist account of the logical constants can help explain how such reasoning is possible. (...) /// [Timothy Williamson] The paper challenges the inferentialist account of concept possession that Paul Boghossian takes as a premise in his account of the transmission of justification by deductive reasoning in his paper ’Blind Reasoning’. Unorthodox speakers who reject the inferences in an alleged possession condition can still have the concept by understanding a word for it. In that sense, the inferences are not analytic. Inferentialist accounts of logical constants, theoretical terms (using the Ramsey-Carnap-Lewis method) and pejorative expressions such as ’Boche’ are examined and rejected. It is suggested that epistemological questions cannot be reduced to questions in the theory of thought and meaning. (shrink)

We investigate axiomatizations of Kripke's theory of truth based on the Strong Kleene evaluation scheme for treating sentences lacking a truth value. Feferman's axiomatization KF formulated in classical logic is an indirect approach, because it is not sound with respect to Kripke's semantics in the straightforward sense: only the sentences that can be proved to be true in KF are valid in Kripke's partial models. Reinhardt proposed to focus just on the sentences that can be proved to be true in (...) KF and conjectured that the detour through classical logic in KF is dispensable. We refute Reinhardt's Conjecture, and provide a direct axiomatization PKF of Kripke's theory in partial logic. We argue that any natural axiomatization of Kripke's theory in Strong Kleene logic has the same proof-theoretic strength as PKF, namely the strength of the system RA< ωω ramified analysis or a system of Tarskian ramified truth up to ωω. Thus any such axiomatization is much weaker than Feferman's axiomatization KF in classical logic, which is equivalent to the system RA<ε₀ of ramified analysis up to ε₀. (shrink)

I examine Paul Boghossian's recent attempt to argue for scepticism about logical rules. I argue that certain rule- and proof-theoretic considerations can avert such scepticism. Boghossian's 'Tonk Argument' seeks to justify the rule of tonk-introduction by using the rule itself. The argument is subjected here to more detailed proof-theoretic scrutiny than Boghossian undertook. Its sole axiom, the so-called Meaning Postulate for tonk, is shown to be false or devoid of content. It is also shown that the rules of Disquotation and (...) of Semantic Ascent cannot be derived for sentences with tonk dominant. These considerations deprive Boghossian's scepticism of its support. (shrink)

I examine Paul Boghossian's recent attempt to argue for scepticism about logical rules. I argue that certain rule- and proof-theoretic considerations can avert such scepticism. Boghossian's 'Tonk Argument' seeks to justify the rule of tonk-introduction by using the rule itself. The argument is subjected here to more detailed proof-theoretic scrutiny than Boghossian undertook. Its sole axiom, the so-called Meaning Postulate for tonk, is shown to be false or devoid of content. It is also shown that the rules of Disquotation and (...) of Semantic Ascent cannot be derived for sentences with tonk dominant. These considerations deprive Boghossian's scepticism of its support. (shrink)

Jason Stanley's "Knowledge and Practical Interests" is a brilliant book, combining insights about knowledge with a careful examination of how recent views in epistemology fit with the best of recent linguistic semantics. Although I am largely convinced by Stanley's objections to epistemic contextualism, I will try in what follows to formulate a version that might have some prospect of escaping his powerful critique.

This is a defense and extension of Stephen Yablo's claim that self-reference is completely inessential to the liar paradox. An infinite sequence of sentences of the form 'None of these subsequent sentences are true' generates the same instability in assigning truth values. I argue Yablo's technique of substituting infinity for self-reference applies to all so-called 'self-referential' paradoxes. A representative sample is provided which includes counterparts of the preface paradox, Pseudo-Scotus's validity paradox, the Knower, and other enigmas of the genre. I (...) rebut objections that Yablo's paradox is not a genuine liar by constructing a sequence of liars that blend into Yablo's paradox. I rebut objections that Yablo's liar has hidden self-reference with a distinction between attributive and referential self-reference and appeals to Gregory Chaitin's algorithmic information theory. The paper concludes with comments on the mystique of self-reference. (shrink)

Part one attempts to diffuse five different forms of truth skepticism, broadly conceived: the view that truth is indefinable, that it is unknowable, that it is inextricably metaphysical, that there is no such thing as truth, and the view that truth is inherently paradoxical, and so must either be abandoned, or revised. An intriguing formulation of the last of these views is due to Alfred Tarski, who argued that the Liar paradox shows natural languages to be inconsistent because they contain (...) defective, and ultimately incoherent, truth predicates. I argue in response that on a plausible interpretation of his puzzling notion of an inconsistent language, Tarski’s argument turns out to be logically valid, but almost certainly unsound, since one of its premises can be seen to be indefensible. Similar results are achieved for other forms of truth skepticism. (shrink)

There is a standard objection against purported explanations of how a language L can express the notion of being a true sentence of L. According to this objection, such explanations avoid one paradox (the Liar) only to succumb to another of the same kind. Even if L can contain its own truth predicate, we can identify another notion it cannot express, on pain of contradiction via Liar-like reasoning. This paper seeks to undermine such ‘revenge’ by arguing that it presupposes a (...) dubious assumption about the linguistic expression of concepts. Successful revenge would require that there be a notion other than truth that plays the same role with respect to concept-expression that truth is naturally thought to play before we are confronted with the Liar paradox. (shrink)

This essay proposes a theory of the nature and logic of truth on which truth is an inconsistent concept that should be replaced for certain theoretical purposes. The paradoxes associated with truth (for example, the liar) and the pattern of failures in our attempts to deal with them suggest that truth is an inconsistent concept. The first part of the essay describes a pair of replacement concepts, which the essay dubs ascending truth and descending truth, along with an axiomatic theory (...) of them and an empirical interpretation of the theory. The essay shows how to use these replacements in a familiar truth-conditional semantics as well. The second part of the essay offers a descriptive theory of our natural language truth predicate that takes it to be assessment sensitive, which means that it has the same content in every context of utterance, but its extension (that is, the set of things that are true) depends on a context of assessment. Contexts of assessment model situations in which a person interprets someone's utterance. From different contexts of assessment, the truth predicate has different extensions. The descriptive theory employs the concepts of ascending truth and descending truth, and they determine how the extension of the truth predicate varies across contexts of assessment. This assessment-sensitive theory of truth solves the liar and other paradoxes, it is compatible with classical logic and all the expressive resources we have in natural language, and it does not give rise to any new paradoxes. (shrink)

Of the dozens of purported solutions to the liar paradox published in the past fifty years, the vast majority are "traditional" in the sense that they reject one of the premises or inference rules that are used to derive the paradoxical conclusion. Over the years, however, several philosophers have developed an alternative to the traditional approaches; according to them, our very competence with the concept of truth leads us to accept that the reasoning used to derive the paradox is sound. (...) That is, our conceptual competence leads us into inconsistency. I call this alternative the inconsistency approach to the liar. Although this approach has many positive features, I argue that several of the well-developed versions of it that have appeared recently are unacceptable. In particular, they do not recognize that if truth is an inconsistent concept, then we should replace it with new concepts that do the work of truth without giving rise to paradoxes. I outline an inconsistency approach to the liar paradox that satisfies this condition. (shrink)

Alfred Tarski (1944) wrote that "the condition of the 'essential richness' of the metalanguage proves to be, not only necessary, but also sufficient for the construction of a satisfactory definition of truth." But it has remained unclear what Tarski meant by an 'essentially richer' metalanguage. Moreover, DeVidi and Solomon (1999) have argued in this Journal that there is nothing that Tarski could have meant by that phrase which would make his pronouncement true. We develop an answer to the historical question (...) of what Tarski meant by 'essentially richer' and pinpoint the general result that stands behind his essential richness claim. In defense of Tarski, we then show that each of the several arguments of DeVidi and Solomon are either moot or mistaken. One of the fruits of our investigation is the reclamation of what Tarski took to be his central result on truth. This is a reclamation since: (i) if one does not understand 'essential richness', one does not know what that result is, and (ii) we must unearth a heretofore unrecognized change that occurs in Tarski's view - an alteration of his main thesis in light of a failing he discovered in it. (shrink)

Modern empiricism has been conditioned in large part by two dogmas. One is a belief in some fundamental cleavage between truths which are analytic, or grounded in meanings independently of matters of fact, and truth which are synthetic, or grounded in fact. The other dogma is reductionism: the belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience. Both dogmas, I shall argue, are ill founded. One effect of abandoning them is, as (...) we shall see, a blurring of the supposed boundary between speculative metaphysics and natural science. Another effect is a shift toward pragmatism. (shrink)

In Contradiction advocates and defends the view that there are true contradictions, a view that flies in the face of orthodoxy in Western philosophy since Aristotle. The book has been at the center of the controversies surrounding dialetheism ever since its first publication in 1987. This second edition of the book substantially expands upon the original in various ways, and also contains the author’s reflections on developments over the last two decades. Further aspects of dialetheism are discussed in the companion (...) volume, Doubt Truth to be a Liar, also published by Oxford University Press in 2006. (shrink)

We have seen that proofs of soundness of (Boolean) DS, EFQ and of ABS — and hence the legitimation of these inferences — can be achieved only be appealing to the very form of reasoning in question. But this by no means implies that we have to fall back on classical reasoning willy-nilly. Many logical theories can provide the relevant boot-strapping. Decision between them has, therefore, to be made on other grounds. The grounds include the many criteria familiar from the (...) philosophy of science: theoretical integrity (e.g., paucity of ad hoc hypotheses), adequacy to the data (explaining the data of inference —all inferences, not just those chosen from consistent domains!) and so on. This paper has not attempted to address these issues in general. All it demonstrates is that the charge that a dialetheist solution to the semantic paradoxes can be maintained only by making some intelligible notion ineffable cannot be made to stick. The dialetheist has a coherent position, endorsing the T-scheme, but rejecting DS, EFQ (even Boolean DS and EFQ) and ABS. And any argument to the effect that the relevant notions are both ineffable and intelligible begs the question. The case against consistent “solutions” to the semantic paradoxes therefore remains intact. (shrink)

I argue that truth is relative (in the sense recently defended by some prominent analytical philosophers) by focusing on some semantic issues raised by Einstein's theory of relativity together with our ordinary attributions of truth.

In this ingenious and powerfully argued book Tim Maudlin sets out a novel account of logic and semantics which allows him to deal with certain notorious paradoxes which have bedevilled philosophical theories of truth. All philosophers interested in logic and language will find this a stimulating read.

In Confusion: A Study in the Theory of Knowledge, Joseph Camp argues that the reasoning of a person who has confused two objects in her thought and talk ought to be appraised using a four-valued relevance logic. I discuss two key moves in Camp’s argument: the assumption that charity to the reasoner requires recognition of her arguments as valid, and the argument that validity for a truth-valueless discourse should not be defined in terms of truth preservation. I then question whether (...) Camp’s four-valued semantics satisfies his own desiderata for a logic of confusion. -/- . (shrink)

The relativist's central objection to contextualism is that it fails to account for the disagreement we perceive in discourse about "subjective" matters, such as whether stewed prunes are delicious. If we are to adjudicate between contextualism and relativism, then, we must first get clear about what it is for two people to disagree. This question turns out to be surprisingly difficult to answer. A partial answer is given here; although it is incomplete, it does help shape what the relativist must (...) say if she is to do better than the contextualist in securing genuine disagreement. (shrink)

The goal of this paper is to make sense of relativism about truth. There are two key ideas. (1) To be a relativist about truth is to allow that a sentence or proposition might be assessment-sensitive: that is, its truth value might vary with the context of assessment as well as the context of use. (2) Making sense of relativism is a matter of understanding what it would be to commit oneself to the truth of an assessment-sensitive sentence or proposition.

Recent arguments for relativist semantic theories have centered on the phenomenon of “faultless disagreement.” This paper offers independent motivation for such theories, based on the interpretation of predicates of personal taste in certain attitude contexts and presuppositional constructions. It is argued that the correct interpretation falls out naturally from a relativist theory, but requires special stipulation in a theory which appeals instead to the use of hidden indexicals; and that a hidden indexical analysis presents problems for contemporary syntactic theory.

This paper argues that truth values of sentences containing predicates of “personal taste” such as fun or tasty must be relativized to individuals. This relativization is of truth value only, and does not involve a relativization of semantic content: If you say roller coasters are fun, and I say they are not, I am negating the same content which you assert, and directly contradicting you. Nonetheless, both our utterances can be true (relative to their separate contexts). A formal semantic theory (...) is presented which gives this result by introducing an individual index, analogous to the world and time indices commonly used, and by treating the pragmatic context as supplying a particular value for this index. The context supplies this value in the derivation of truth values from content, not in the derivation of content from character. Predicates of personal taste therefore display a kind of contextual variation in interpretation which is unlike the familiar variation exhibited by pronouns and other indexicals. (shrink)

The paper argues that the theory of Implicit Definition cannot give an account of knowledge of logical principles. According to this theory, the meanings of certain expressions are determined such that they make certain principles containing them true; this is supposed to explain our knowledge of the principles as derived from our knowledge of what the expressions mean. The paper argues that this explanation succeeds only if Implicit Definition can account for our understanding of the logical constants, and that fully (...) understanding a logical constant in turn requires the ability to apply it correctly in particular cases. It is shown, however, that Implicit Definition cannot account for this ability, even if it draws on introduction rules for the logical constants. In particular, Implicit Definition cannot account for our ability to apply negation in particular cases. Owing to constraints relating to the unique characterisation of logical constants, invoking the notion of rejection does not remedy the situation. Given its failure to explain knowledge of logic, the prospects of Implicit Definition to explain other kinds of a priori knowledge are even worse. (shrink)