Conditionals in Theories of Truth

Gupta, Anil; Standefer, Shawn

doi:10.1007/s10992-015-9393-3

Cited by 11 publications

(11 citation statements)

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“…This tracking can be accomplished also by a device internal to the language. We can view revision stages as possible situations, and we can add to the language a modal operator

□

that has the force of “it is true in the previous revision stage that ….” The details of this can be found in Gupta and Standefer () . The point I wish to note here is that the rules of inference governing definition

scriptD

are now captured by the principle: (Df

□

)

\forall x (G x \equiv □ A (x, G))

. …”

Section: A Logic Of Definitionsmentioning

confidence: 99%

In Praise of a Logic of Definitions That Tolerates Ω‐inconsistency

Gupta

2018

Philosophical Issues

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“…This tracking can be accomplished also by a device internal to the language. We can view revision stages as possible situations, and we can add to the language a modal operator

□

scriptD

are now captured by the principle: (Df

□

)

\forall x (G x \equiv □ A (x, G))

. …”

Section: A Logic Of Definitionsmentioning

confidence: 99%

In Praise of a Logic of Definitions That Tolerates Ω‐inconsistency

Gupta

2018

Philosophical Issues

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“…There has been work dealing with (partial) formalization of the theory both in axiomatic form (see [30]) and in sequent form (see [8]). In this direction, it is worth mentioning the recent paper [27] by Gupta and Standefer, who have studied the logic of the rule of revision via conditionals devised to reflect it. The paper also explores an interpretation of the proposed conditionals by means of a modal operator, a connection that had been considered already in [55], and which has been further investigated proof-theoretically in [57].…”

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Guest Editors’ Introduction

Bruni

Standefer

2018

J Philos Logic

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by Hans Herzberger, revision theory appears as a proposal to deal with a type-free concept of formal truth that preserves the classical scheme [7,20,28,29]. Though the story is well-known, we think it would be useful to recapitulate here, in a brief and obviously incomplete summary, some of the main events by means of which the original proposals developed into the current, broader field of investigation, to give the uninitiated reader a rough idea of the context for the contributions in this volume. 1 In his seminal work from the 1930's, Alfred Tarski proved the existence of a fundamental inconsistency emerging in a situation where: (i) there is a formal language L respecting some modest assumptions on its strength in expressive capabilities; (ii) the language contains a unary, unrestricted predicate T for (codes of) formulas working as a truth predicate, verifying natural principles that require that the formula T ( ϕ ) be equivalent to ϕ, for every sentence ϕ of L; (iii) a classical relation of satisfaction for formulas of L in any interpretation, or model M, is retained, therefore each sentence ϕ of L is assumed to take either semantic value 1 or 0. Tarski's contradiction took the form of a theorem about the (arithmetical) undefinability of such predicate T for any L, granted (i)-(iii). Tarski's theorem shows that no sufficiently expressive, classical formal language can consistently contain its own truth predicate. As a solution, he proposed a typed theory of formal truth, asserting that every language L for 1 The interested reader should consult [38] for a more detailed introduction to revision theory.

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“… See Martinez [2001] andGupta [2006].18 See, respectively,Field [2008] andBeall [2009]. For a criticism of (IP), seeGupta and Standefer [2016].Australasian Journal of Logic (14:1) 2017, Article no. 6…”

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“…SeeGupta and Belnap [1993, 253-255] for discussion. It has, however, recently been shown how to extend the revision theory with new biconditionals that validate versions of all the defining clauses; for details, seeStandefer [2015] andGupta and Standefer [2016].29 The following is based on the ccpo frameworks described in andVisser [2004].30 I will generally suppress mention of assignments to variables and use the notation A(d) to indicate evaluation under an assignment whose values on the free variables of A, x, are the objectsd.Australasian Journal of Logic (14:1) 2017, Article no. 6…”

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confidence: 99%