The Harmony of Identity

Klev, Ansten

doi:10.1007/s10992-018-09499-0

Cited by 7 publications

(10 citation statements)

References 10 publications

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“…Both seem to assume that (LL) permits us to infer more from a heteronymous a = b than is justified given that the introduction rule is (Refl). We argued that the real trouble is 24 This argument parallels Klev's [3] distinct argument that definitional identities should not figure in the identity-introduction rules. 25 We are not denying that identity is the finest equivalence relationit is.…”

Section: Discussionmentioning

confidence: 64%

“…Since (&I) is the only introduction rule, we can infer Q from the side-premises together with any of the grounds for A & B that are licensed by the introduction rules. 3 So the rules satisfy (H1). Second, suppose we can infer a conjunction-free Q from any grounds for A & B given some side premises.…”

Section: Harmonymentioning

confidence: 93%

“…Congr;Congr 0 s for every s. 12 [5]: 115 (our emphasis). 13 [3]: 869. equivalent to the traditional ones, Griffiths's argument implies that they fall short of harmony in the same way.…”

Section: Griffiths On Harmony and Identitymentioning

confidence: 99%

“…of the formulas canvassed by the elimination rule (Leibniz's law). In response, Read [5,8] and Klev [3] amend the standard approach, either directly amending the rules (Read) or changing the background against which they function (Klev).…”

mentioning

confidence: 99%

“…[3]: 876.22 Klev uses Martin-Löf's elimination rule, which licenses derivation of A(t, u) from A(x, x) and t = u. This is equivalent to (LL) given the rules for implication and the universal quantifier ([3]: 868-9).…”

mentioning

confidence: 99%

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Introducing Identity

Griffiths

Ahmed²

2021

J Philos Logic

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The best-known syntactic account of the logical constants is inferentialism . Following Wittgenstein’s thought that meaning is use, inferentialists argue that meanings of expressions are given by introduction and elimination rules. This is especially plausible for the logical constants, where standard presentations divide inference rules in just this way. But not just any rules will do, as we’ve learnt from Prior’s famous example of tonk, and the usual extra constraint is harmony. Where does this leave identity? It’s usually taken as a logical constant but it doesn’t seem harmonious: standardly, the introduction rule (reflexivity) only concerns a subset of the formulas canvassed by the elimination rule (Leibniz’s law). In response, Read [5, 8] and Klev [3] amend the standard approach. We argue that both attempts fail, in part because of a misconception regarding inferentialism and identity that we aim to identify and clear up.

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Section: Discussionmentioning

confidence: 64%

Section: Harmonymentioning

confidence: 93%

“…Congr;Congr 0 s for every s. 12 [5]: 115 (our emphasis). 13 [3]: 869. equivalent to the traditional ones, Griffiths's argument implies that they fall short of harmony in the same way.…”

Section: Griffiths On Harmony and Identitymentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Introducing Identity

Griffiths

Ahmed²

2021

J Philos Logic

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The Logicality of Equality

Indrzejczak

2024

Outstanding Contributions to Logic

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The status of the equality predicate as a logical constant is problematic. In the paper we look at the problem from the proof-theoretic standpoint and survey several ways of treating equality in formal systems of different sorts. In particular, we focus on the framework of sequent calculus and examine equality in the light of criteria of logicality proposed by Hacking and Došen. Both attempts were formulated in terms of sequent calculus rules, although in the case of Došen it has a nonstandard character. It will be shown that equality can be characterised in a way which satisfies Došen's criteria of logicality. In the case of Hacking's approach the fully satisfying result can be obtained only for languages with a nonempty, finite set of predicate constants other than equality. Otherwise, cut elimination theorem fails to hold.

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Identity and Harmony and Modality

Schlöder

2023

J Philos Logic

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The Harmony of Identity

Cited by 7 publications

References 10 publications

Introducing Identity

Introducing Identity

The Logicality of Equality

Identity and Harmony and Modality

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