Wittgenstein's later rejection of the externalist Tractarian picture of logic according to which all rationally analysable discourse is properly understood as truth-functional rules out any conception of logic as the study of universal features of discourse. Given later references to 'the logic of our language', some conception of logic appears to survive even on Wittgenstein's later view. However, given his rejection of any conception of philosophical theory as explanatory or hypothetical, Wittgenstein seems to be forced into descriptivism. Despite these constraints, (...) I attempt to show that a valuable account of logic consistent with Wittgenstein's critique can be identified. That possibility raises the question: can any conception of formal logic as valuable modulo natural language survive Wittgenstein's later change of heart? Taking Wittgenstein's rejection of Tractarian conceptions seriously, logic is relativised to language-games in general and, perhaps, localised to particular language-games. Looking at logic in this way opens up the possibility of uncovering inferential structures distinct from those which form the traditional logical-epistemological dichotomy. Here I outline a formal logical framework consistent with all of the foregoing points in terms of which analogues of inferential structures (traditional and non-traditional) can be constructed. Taking third-person ascriptions of psychological predicates as a testcase, I try to show that the formal framework (a system of formal dialogue) has a flexibility which augurs well for future logical investigations into linguistic practices without presupposing knowledge of the kinds of inferential structures which such investigations might reveal. Hence, my claim that the system in question represents logic after (the later) Wittgenstein. (shrink)

Recasting important questions about truth and objectivity in new and helpful terms, his book will become a focus in the contemporary debates over realism, and ...

In epistemology, “contextualism” denotes a wide variety of more-or-less closely related positions according to which the issues of knowledge or justification are somehow relative to context. I will proceed by first explicating the position I call contextualism, and distinguishing that position from some closely related positions in epistemology, some of which sometimes also go by the name of “contextualism”. I’ll then present and answer what seems to many the most pressing of the objections to contextualism as I construe it, and (...) also indicate some of the main positive motivations for accepting the view. Among the epistemologists I’ve spoken with who have an opinion on the matter, I think it’s fair to say a majority reject contextualism. However, the resistance has to this point been largely underground, with little by way of sustained arguments against contextualism appearing in the journals,[i] though I have begun to see various papers in manuscript form which are critical of contextualism. Here, I’ll respond the criticism of contextualism that, in my travels, I have found to be the most pervasive in producing suspicion about the view. (shrink)

This paper treats entailment as a subrelation of classical consequence and deducibility. Working with a Gentzen set-sequent system, we define an entailment as a substitution instance of a valid sequent all of whose premisses and conclusions are necessary for its classical validity. We also define a sequent Proof as one in which there are no applications of cut or dilution. The main result is that the entailments are exactly the Provable sequents. There are several important corollaries. Every unsatisfiable set is (...) Provably inconsistent. Every logical consequence of a satisfiable set is Provable therefrom. Thus our system is adequate for ordinary mathematical practice. Moreover, transitivity of Proof fails upon accumulation of Proofs only when the newly combined premisses are inconsistent anyway, or the conclusion is a logical truth. In either case Proofs that show this can be effectively determined from the Proofs given. Thus transitivity fails where it least matters — arguably, where it ought to fail! We show also that entailments hold by virtue of logical form insufficient either to render the premisses inconsistent or to render the conclusion logically true. The Lewis paradoxes are not Provable. Our system is distinct from Anderson and Belnap''s system of first degree entailments, and Johansson''s minimal logic. Although the Curry set paradox is still Provable within naive set theory, our system offers the prospect of a more sensitive paraconsistent reconstruction of mathematics. It may also find applications within the logic of knowledge and belief. (shrink)

The logician's central concern is with the validity of argument. A logical theory ought, therefore, to provide a general criterion of validity. This book sets out to find such a criterion, and to describe the philosophical basis and the formal theory of a logic in which the premises of a valid argument are relevant to its conclusion. The notion of relevance required for this theory is obtained by an analysis of the grounds for asserting a formula in a proof.

What is truth. Paul Horwich advocates the controversial theory of minimalism, that is that the nature of truth is entirely captured in the trivial fact that each proposition specifies its own condition for being true, and that truth is therefore an entirely mundane and unpuzzling concept. The first edition of Truth, published in 1980, established itself as the best account of minimalism and as an excellent introduction to the debate for students. For this new edition, Horwich has refined and developed (...) his treatment of the subject in the light of subsequent discussions, while preserving the distinctive format that made the earlier edition so successful. (shrink)

In this book, Scott Soames illuminates the notion of truth and the role it plays in our ordinary thought as well as in our logical, philosophical, and scientific theories. Soames aims to integrate and deepen the most significant insights on truth from a variety of sources. He powerfully brings together the best technical work and the most important philosophical reflection on truth and shows how each can illuminate the other. Investigating such questions as whether we need a truth predicate at (...) all, what theoretical tasks it allows us to accomplish, and how we are to understand the content of any predicate capable of accomplishing these tasks, Soames organizes his discussion into three parts. Part I addresses crucial foundational issues as it identifies the bearers of truth, provides a basis for distinguishing truth from other notions, and formulates positive responses to well-known forms of truth-skepticism. Part II explicates the formal theories of Alfred Tarski and Saul Kripke and evaluates the philosophical significance of their work. It discusses their treatments of the Liar paradox, the relationship between truth and proof, the notion of a partially defined predicate, the concepts of logical truth and logical consequence, and the connection between truth and meaning. Part III extends important lessons drawn from Tarski and Kripke into new domains: vague predicates, the Sorites paradox, and the development of a larger, deflationary perspective on truth. Throughout the book, Soames examines a wide range of deflationary theories of truth, and attempts to separate what is correct and worth preserving in them from what is not. In doing so, he seeks to clear up many of the most significant philosophical doubts about truth. Written for a general audience while offering engaging material to the specialist, this rich study will be profitably read by both. (shrink)

Every student of English-speaking analytical metaphysics is taught that the early twentieth century philosophical debate about truth confronted the correspondence theory, supported by Russell, Moore, the early Wittgenstein and, later, J.L. Austin, with the coherence theory advocated by the British Idealists. Sometimes the pragmatist conception of truth deriving from Dewey, William James, and C.S. Peirce is regarded as a third player. And as befits a debate at the dawn of analytical philosophy, the matter in dispute is normally taken to have (...) been the proper analysis of the concept.No doubt this conception nicely explains some of the characteristic turns taken in the debate. Analysis, as traditionally conceived, has to consist in the provision of illuminating conceptual equivalences; and illumination will depend, according to the standard rules of play, on the analysans’ utilizing only concepts which, in the best case, are in some way prior to and independent of the notion being analyzed — or, if that's too much to ask, then concepts which at least permit of some form of explication which does not in turn take one straight back to that notion. (shrink)

All parties to the proceedings that follow concur with DS. The question is whether there is anything more to truth than can be gleaned from DS alone. Deflationism holds that there is nothing more to truth than this. Now it would appear that 'warrantedly assertible' can play the role of T in DS. Hence it would appear that the deflationist would be able to identify truth with warranted assertibility.

In Logics for Artificial Intelligence, Raymond Turner leads us on a whirl-wind tour of nonstandard logics and their general applications to Al and computer science.

(1998). Contextualist solutions to epistemological problems: Scepticism, Gettier, and the lottery. Australasian Journal of Philosophy: Vol. 76, No. 2, pp. 289-306. doi: 10.1080/00048409812348411.

Wittgenstein's later rejection of the externalist Tractarian picture of logic according to which all rationally analysable discourse is properly understood as truth-functional rules out any conception of logic as the study of universal features of discourse. Given later references to 'the logic of our language', some conception of logic appears to survive even on Wittgenstein's later view. However, given his rejection of any conception of philosophical theory as explanatory or hypothetical, Wittgenstein seems to be forced into descriptivism. Despite these constraints, (...) I attempt to show that a valuable account of logic consistent with Wittgenstein's critique can be identified. That possibility raises the question: can any conception of formal logic as valuable modulo natural language survive Wittgenstein's later change of heart? Taking Wittgenstein's rejection of Tractarian conceptions seriously, logic is relativised to language-games in general and, perhaps, localised to particular language-games. Looking at logic in this way opens up the possibility of uncovering inferential structures distinct from those which form the traditional logical-epistemological dichotomy. Here I outline a formal logical framework consistent with all of the foregoing points in terms of which analogues of inferential structures (traditional and non-traditional) can be constructed. Taking third-person ascriptions of psychological predicates as a testcase, I try to show that the formal framework (a system of formal dialogue) has a flexibility which augurs well for future logical investigations into linguistic practices without presupposing knowledge of the kinds of inferential structures which such investigations might reveal. Hence, my claim that the system in question represents logic after (the later) Wittgenstein. (shrink)

In this critical study I first summarize Crispin Wright's "Truth and Objectivity". Wright maintains (1) that truth- aptness of a given discourse is neutral about questions of realism and anti- realism concerning the discourse, but also (2) that such metaphysical questions largely turn on discourse- specific constraints governing the truth- predicate. I urge a distinction between (i) Wright's general approach to truth and objectivity, and (ii) his apparent inclination to implement and the approach by construing truth as a fundamentally epistemic (...) notion. I argue against an epistemically reductive implementation, and I briefly sketch an alternative way to implement the book's core ideas. (shrink)