What Is an Inconsistent Truth Table?

Weber, Zach; Badía, Guillermo; Girard, Patrick

doi:10.1080/00048402.2015.1093010

Cited by 53 publications

(19 citation statements)

References 31 publications

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“…The aim was said to be to "preach to the Gentiles in their own tongue", a description whose charm becomes especially apparent when we recall Meyer's own early days as a Christian missionary (in Japan). Among the items in the bibliography of the present paper for independent reasons in which this turn of phrase is quoted are (Read 1988) (as well as (Aberdein and Read 2009)) and (Weber, Badia and Girard 2016) -though there may be more. Read's own 'Scottish Plan' for the semantic of relevant logic (Read 1988, §7.3 and § §8.4-8.6) is, by contrast, not only metalogically relevant but treats all vocabulary homophonically.…”

Section: Introduction and Initial Difficultiesmentioning

confidence: 90%

“…49 ( (Girard and Weber 2018) also take as their basic logic BCK, with quantifiers added as well as multiplicative or intensional conjunction -see note 7 -but additive or extensional disjunction, on the other hand, and add modal operators with a view to treating them semantically using the Kripke model-theoretic truth-definition in the modal-free part of an analogous metalogic, paying special attention to the complications caused by the lack of contraction for this enterprise.) While on the subject of soundness, mention should be made of (Weber, Badia and Girard 2016), in which a paraconsistent metalogic is used in the semantic metatheory, the latter theory itself being inconsistent -and proudly so -with the authors establishing to their own satisfaction at least (p. 542) that the object logic is sound and not sound (as well as that the law of excluded middle is both valid and invalid). Hmm.…”

Section: Bacon and Othersmentioning

confidence: 99%

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Semantics without Toil? Brady and Rush Meet Hallden

Humberstone

2019

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The present discussion takes up an issue raised in Section 5 of Ross Brady and Penelope Rush's paper 'Four Basic Logical Issues' concerning the (claimed) triviality-in the sense of automatic availability-of soundness and completeness results for a logic in a metalanguage employing at least as much logical vocabulary as the object logic, where the metalogical behaviour of the common logical vocabulary is as in the object logic. We shall see-in Propositions 4.5-4.7-that this triviality claim faces difficulties in the face of Halldén incompleteness, for essentially the same reasons that Halldén thought this phenomenon raised semantic difficulties for the modal logics of C. I. Lewis exhibiting it. To counter any inclination to dismiss the phenomenon as providing at best a marginal range of counterexamples to the triviality claim, a Postscript assembles some reminders of the extent of-and the varied considerations favouring-Halldén incompleteness.

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Section: Introduction and Initial Difficultiesmentioning

confidence: 90%

Section: Bacon and Othersmentioning

confidence: 99%

Semantics without Toil? Brady and Rush Meet Hallden

Humberstone

2019

orgf

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“…• a ¬A iff a A For many relevant logics, one can add boolean negation conservatively, meaning that the addition of boolean negation brings with it no new theorems that lack 42. See Weber, Badia, and Girard (2016) for the development of a related idea with respect to truth tables.…”

Section: Issues In Metaphysicsmentioning

confidence: 99%

Actual Issues for Relevant Logics

Standefer¹

2020

Ergo, an Open Access Journal of Philosophy

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In this paper, I motivate the addition of an actuality operator to relevant logics. Straightforward ways of doing this are in tension with standard motivations for relevant logics, but I show how to add the operator in a way that permits one to maintain the intuitions behind relevant logics. I close by exploring some of the philosophical consequences of the addition. 1. See Dunn and Restall (2002) or Bimbó (2006) for reader-friendly overviews of relevant logics. 2. How to understand the connection at issue is a delicate matter. Anderson and Belnap (1975) suggest a kind of connection based on use. An alternative conception is the sufficiency view of Routley (1977: 895ff.). A different approach to relevance is offered by Tennant (2017).

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“…So the criticism would apply not just to the nontransitive approach. There are, of course, exceptions; some people do their metatheory in a nonclassical logic (Bacon ; Weber, Badia, and Girard ; Zardini , ). Let us assume that this is the way to go.…”

Section: A Problem With Expressing Admissibilitymentioning

confidence: 99%

The Cut-Free Approach and the Admissibility-Curry

Hlobil¹

2018

Thought: A Journal of Philosophy

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The perhaps most important criticism of the nontransitive approach to semantic paradoxes is that it cannot truthfully express exactly which metarules preserve validity. I argue that this criticism overlooks that the admissibility of metarules cannot be expressed in any logic that allows us to formulate validity-Curry sentences and that is formulated in a classical metalanguage. Hence, the criticism applies to all approaches that do their metatheory in classical logic. If we do the metatheory of nontransitive logics in a nontransitive logic, however, there is no reason to think that the argument behind the criticism goes through. In general, asking a logic to express its own admissible metarules may not be a good idea.Until recently, philosophical common sense had it that, on pain of triviality, you cannot accept all of classical logic, allow for self-reference and let your language contain its own truth predicate (satisfying all Tarski biconditionals). The nontransitive approach to semantic paradoxes has proved common sense wrong. It offers a supraclassical logic, called STT, with a transparent truth predicate (i.e., a truth predicate, T, such that A and T⟨A⟩ are everywhere intersubstitutable) and self-reference (Cobreros et al. 2012(Cobreros et al. , 2013Ripley 2012Ripley , 2013. Transitivity, that is, Cut, fails in STT. But it only fails for paradoxical sentences, like the liar sentence or Curry sentences. That seems like a small price to pay for the full strength of classical logic together with a transparent truth predicate. With that much to recommend itself, I think we should try to hold on to the nontransitive approach as long as we can. My goal in this paper is to show that, contrary to recent criticism (Barrio, Rosenblatt, and Tajer 2016; Rosenblatt 2017), we shouldn't reject the nontransitive approach because it cannot express the admissibility of its own metarules.Along the way, we can observe some general facts about the possibility of expressing, in the object language, which metarules are admissible. In particular, I point out that no one who does her metatheory in classical logic and allows for self-reference can allow her logic to truthfully express which metarules are admissible, according to her own logic.

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What Is an Inconsistent Truth Table?

Cited by 53 publications

References 31 publications

Semantics without Toil? Brady and Rush Meet Hallden

Semantics without Toil? Brady and Rush Meet Hallden

Actual Issues for Relevant Logics

The Cut-Free Approach and the Admissibility-Curry

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