To the axioms of Peano arithmetic formulated in a language with an additional unary predicate symbol T we add the rules of necessitation and conecessitation T and axioms stating that T commutes with the logical connectives and quantifiers. By a result of McGee this theory is -inconsistent, but it can be approximated by models obtained by a kind of rule-of-revision semantics. Furthermore we prove that FS is equivalent to a system already studied by Friedman and Sheard and give an analysis (...) of its proof theory. (shrink)

Is truth a substantial feature of truth-bearers? Correspondence theorists answer in the affirmative, deflationists in the negative. Correspondence theorists cite in their defense the dependence of truth on meaning or representational content. Deflationists in turn cite the conceptual centrality of simple equivalences such as ''Snow is white' is true iff snow is white'' and 'It is true that snow is white iff snow is white'. The apparent facts to which these theorists appeal correspond to some of our firmest and most (...) basic convictions about truth. An account of truth that fails to accommodate either sort of apparent fact is inadequate. The account presented in this essay attempts to avoid this inadequacy by 'deflating' truth for propositions but 'inflating' truth for entities that express propositions, thus drawing from the insights of both deflationists and correspondence theorists. (shrink)

A formal theory of truth, alternative to tarski's 'orthodox' theory, based on truth-value gaps, is presented. the theory is proposed as a fairly plausible model for natural language and as one which allows rigorous definitions to be given for various intuitive concepts, such as those of 'grounded' and 'paradoxical' sentences.

Deflationsism about truth is a pot-pourri, variously claiming that truth is redundant, or is constituted by the totality of 'T-sentences', or is a purely logical device (required solely for disquotational purposes or for re-expressing finitarily infinite conjunctions and/or disjunctions). In 1980, Hartry Field proposed what might be called a 'deflationary theory of mathematics', in which it is alleged that all uses of mathematics within science are dispensable. Field's criterion for the dispensability of mathematics turns on a property of theories, called (...) conservativeness. I present some technical results, some of which may be found in Tarski (1936), concerning the logical properties of truth theories; in particular, concerning the conservativeness of adding a truth theory for an object level language to any theory expressed in it. It transpires that various deflationary truth theories behave somewhat differently from the standard Tarskian truth theory. These results suggest that Tarskian theories of truth are not redundant or dispensable. Finally, I hint at an analogy between the behaviour of mathematical theories and of standard (Tarskian) theories of truth with respect to their indispensability to, as Quine would put, our 'scientific world-view'. (shrink)

The proof-theoretic results on axiomatic theories oftruth obtained by different authors in recent years are surveyed.In particular, the theories of truth are related to subsystems ofsecond-order analysis. On the basis of these results, thesuitability of axiomatic theories of truth for ontologicalreduction is evaluated.

Some axiomatic theories of truth and related subsystems of second-order arithmetic are surveyed and shown to be conservative over their respective base theory. In particular, it is shown by purely finitistically means that the theory PA ÷ "there is a satisfaction class" and the theory FS of [2] are conservative over PA.

To the axioms of Peano arithmetic formulated in a language with an additional unary predicate symbol T we add the rules of necessitation φ/Tφ and conecessitation T φ/φ and axioms stating that T commutes with the logical connectives and quantifiers. By a result of McGee this theory is w-inconsistent, but it can be approximated by models obtained by a kind of rule-of-revision semantics. Furthermore we prove that FS is equivalent to a system already studied by Friedman and Sheard and give (...) an analysis of its proof theory. (shrink)

Despite its centrality and its familiarity, W. V. Quine's dispute with Rudolf Carnap over the analytic/synthetic distinction has lacked a satisfactory analysis. The impasse is usually explained either by judging that Quine's arguments are in reality quite weak, or by concluding instead that Carnap was incapable of appreciating their strength. This is unsatisfactory, as is the fact that on these readings it is usually unclear why Quine's own position is not subject to some of the very same arguments. A satisfying (...) and surprising account is here presented that stiches together the puzzling pieces of this important philosophical exchange and that in turn leads to an explanation of why it is so difficult to say whether anything of substance is at stake. (shrink)

Despite its centrality and its familiarity, W. V. Quine's dispute with Rudolf Carnap over the analytic/synthetic distinction has lacked a satisfactory analysis. The impasse is usually explained either by judging that Quine's arguments are in reality quite weak, or by concluding instead that Carnap was incapable of appreciating their strength. This is unsatisfactory, as is the fact that on these readings it is usually unclear why Quine's own position is not subject to some of the very same arguments. A satisfying (...) and surprising account is here presented that stitches together the puzzling pieces of this important philosophical exchange and that in turn leads to an explanation of why it is so difficult to say whether anything of substance is at stake. (shrink)