Disquotational Theory Research Articles

Аксиоматизация дисквотационной теории истины и аргумент неконсервативности

The paper considers the possibilities for the axiomatization of disquotational truth theory in perspective of the general S. Shapiro’s non-conservative argument against deflationary concept of truth. It shows that in a generalized formulation, Shapiro’s argument cannot be automatically extended to any axiomatic formulation of the disquotational theory. It also shows that the epistemological justification of the suitable class of substitutions for the T-scheme is the key to constructing an adequate axiomatic disquotational theory.

Minimalism and the generalisation problem: on Horwich\u2019s second solution

Disquotational theories of truth are often criticised for being too weak to prove interesting generalisations about truth. In this paper we will propose a certain formal theory to serve as a framework for a solution of the generalisation problem. In contrast with Horwich’s original proposal, our framework will eschew psychological notions altogether, replacing them with the epistemic notion of believability. The aim will be to explain why someone who accepts a given disquotational truth theory Th, should also accept various generalisations not provable in Th. The strategy will consist of the development of an axiomatic theory of believability, one permitting us to show how to derive the believability of generalisations from basic axioms that characterise the believability predicate, together with the information that Th is a theory of truth that we accept.

A Disquotational Theory of Truth as Strong as Z 2 − $Z_{2}^{-}$

T-biconditionals have often been regarded as insufficient as axioms for truth. This verdict is based on Tarski’s (1935) observation that the typed T-sentences suffer from deductive weakness. As indicated by McGee (1992), the situation might change radically if we consider type-free disquotational theories of truth. However, finding a well-motivated set of untyped T-biconditionals that is consistent and recursively enumerable has proven to be very difficult. Moreover, some authors (e.g. Glanzberg (2005)) have argued that any solution to the semantic paradoxes necessarily involves ‘inflationary’ means, thus spelling doom to deflationist and minimalist truth theories in particular. The situation is indeed worrisome as formal theories of minimalist truth are (almost) missing so far. This makes it very hard to properly evaluate the tenets of minimalism. In the present article, we will show how to find safe instances of the T-schema just by relying on syntactic features of the sentences of our language—in particular, we will explore Quine’s (1937) idea of stratification. Based on that, we will introduce some disquotational truth theories that are deductively very strong.

Pure Quotation

AbstractPure quotation, as in ‘cat’ has three letters, is a linguistic device designed for referring to linguistic expressions. I present a uniform reconstruction of the four classic philosophical accounts of the phenomenon: the proper name theory, the description theory, the demonstrative theory, and the disquotational theory. I evaluate the strengths and weaknesses of each proposal with respect to fundamental semantic properties like compositionality, productivity, and recursivity.

TRUTH AND SPEED-UP

AbstractIn this paper, we investigate the phenomenon ofspeed-upin the context of theories of truth. We focus on axiomatic theories of truth extending Peano arithmetic. We are particularly interested on whether conservative extensions of PA have speed-up and on how this relates to a deflationist account. We show that disquotational theories have no significant speed-up, in contrast to some compositional theories, and we briefly assess the philosophical implications of these results.

Naturalism and Abstract Entities

I argue that the most popular versions of naturalism imply nominalism in philosophy of mathematics. In particular, there is a conflict in Quine’s philosophy between naturalism and realism in mathematics. The argument starts from a consequence of naturalism on the nature of human cognitive subjects, physicalism about cognitive subjects, and concludes that this implies a version of nominalism, which I will carefully characterize. The indispensability of classical mathematics for the sciences and semantic/confirmation holism does not affect the argument. The disquotational theory of reference and truth is discussed but rejected. This argument differs from the Benacerrafian arguments against realism, because it does not rely on any specific assumption about the nature of knowledge or reference. It differs from the popular objections to the indispensability argument for realism as well, because it can admit both indispensability and holism. This argument motivates a new, radically naturalistic and nominalistic approach to philosophy of mathematics.

MINIMAL TRUTH AND INTERPRETABILITY

In this paper we will investigate different axiomatic theories of truth that are minimal in some sense. One criterion for minimality will be conservativity over Peano Arithmetic. We will then give a more fine-grained characterization by investigating some interpretability relations. We will show that disquotational theories of truth, as well as compositional theories of truth with restricted induction are relatively interpretable in Peano Arithmetic. Furthermore, we will give an example of a theory of truth that is a conservative extension of Peano Arithmetic but not interpretable in it. We will then use stricter versions of interpretations to compare weak theories of truth to subsystems of second-order arithmetic.

REDUCING COMPOSITIONAL TO DISQUOTATIONAL TRUTH

Disquotational theories of truth, that is, theories of truth based on the T-sentences or similar equivalences as axioms are often thought to be deductively weak. This view is correct if the truth predicate is allowed to apply only to sentences not containing the truth predicate. By taking a slightly more liberal approach toward the paradoxes, I obtain a disquotational theory of truth that is proof theoretically as strong as compositional theories such as the Kripke–Feferman theory, although it doesn’t probe the compositional axioms.

Two Arguments Against Disquotationalism

Attempts to argue that the disquotational theory of truth is somehow self-refuting have appeared largely unchallenged in the literature for some time now. Focusing on presentations by Anil Gupta and Crispin Wright, I contend that such arguments only undermine a view that nobody endorses. This done, I explain why it is fruitless to focus, as these arguments do, on deflationary accounts of the expressive function of the truth-predicate. I then suggest a strategy for arguing against disquotationalism and other forms of deflationism that focuses rather on the explanatory role of truth in accounts of meaning, in particular on the way that the theories of meaning compatible with deflationism handle embedded uses of sentences.

Correspondence and Disquotation: An Essay on the Nature of Truth.

Marian David defends the correspondence theory of truth against the disquotational theory of truth, its current major rival. The correspondence theory asserts that truth is a philosophically rich and profound notion which needs serious explanation. Disquotationalism is a radically deflationary philosophy of truth inspired by Tarski and propagated by Quine and others. It rejects the correspondence theory, insists truth is anemic, and advances an anti-theory of truth that is essentially a collection of platitudes: Snow is white is true only if snow is actually white; Grass is green is true only if grass is actually green. According to disquotationalists the only profound insight about truth is that it lacks profundity. David contrasts the correspondence theory with disquotationalism and then develops the latter position in rich detail - more than has been available in previous literature - to show its faults. He demonstrates that disquotationalism is not a tenable theory of truth, as it has too many absurd consequences.

The disquotational theory of truth is false

The disquotational theory of truth is false

Truth, Eliminativism, and Disquotationalism

The semantic concept of truth is naturally analyzed in terms of some notion of meaning. The so-called Disquotational Theory of Truth,' I propose, is best understood as a consequence of a physicalist and eliminativist attitude towards this notion: a physicalist who is an eliminativist with respect to the relevant notion of meaning is likely to adopt disquotationalism. I shall argue that disquotationalism is not a sensible theory about truth. It has too many unacceptable consequences. This result has at least an indirect bearing on eliminativism with respect to the relevant notion of meaning: if disquotationalism fails, eliminativism with respect to meaning becomes unattractive.