Logical anti-exceptionalism and theoretical equivalence

Self Cite

This paper addresses a recent debate as to whether logical anti‐exceptionalists should understand logical theories in syntactic or semantic terms. In Wigglesworth (2017), I propose a purely semantic approach, while Woods (2018) has argued in favor of a purely syntactic approach. Here, I argue that neither of these approaches is satisfactory, as both treat arguably distinct logics as equivalent logical theories. I argue instead for an approach that combines syntactic and semantic components. The specific approach to a combined account of logical theories is based on the category‐theoretic notion of an institution.

Section: Subject Area: Philosophy Of Logicmentioning

confidence: 99%

T_{S}^{normalℒ}

.…”

Section: Subject Area: Philosophy Of Logicmentioning

confidence: 99%

Section: Subject Area: Philosophy Of Logicmentioning

confidence: 99%

T_{S}^{ℒ_{1}}

and

T_{S}^{ℒ_{2}}

, generated by a set of sentences, S , according to the logics ℒ 1 and ℒ 2 .…”

Section: Subject Area: Philosophy Of Logicmentioning

confidence: 99%

See 2 more Smart Citations

Individuating Logics

Wigglesworth

2019

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“…This because even the best syntactic accounts treat classical and intuitionistic logic as theoretically equivalent. Yet no two logical theories could be more obviously distinct than these (Wigglesworth ). His argument works against some syntactic accounts, but it doesn't work against them all.…”

mentioning

confidence: 99%

Intertranslatability, Theoretical Equivalence, and Perversion

Woods

2018

I investigate syntactic notions of theoretical equivalence between logical theories and a recent objection thereto. I show that this recent criticism of syntactic accounts, as extensionally inadequate, is unwarranted by developing an account which is plausibly extensionally adequate and more philosophically motivated. This is important for recent anti-exceptionalist treatments of logic since syntactic accounts require less theoretical baggage than semantic accounts.Keywords philosophy of logic; theoretical equivalence; anti-exceptionalism; revising logic; intuitionistic logic; non-classical logic DOI:10.1002/tht3.269It's increasingly common to claim that logic isn't special, that a logical theory is just a theory like any other (Hjortland 2017; Priest 2014; Russell 2014; Williamson 2017) These anti-exceptionalist views use theoretical virtues of alternative logics-simplicity, strength, etc.-in order to evaluate them analogously to how we evaluate scientific theories. 1 In doing so, it's helpful to know when two seemingly distinct theories are really differently formulated versions of the same theory, saying the same things in different ways. In other words, it's helpful to have an account of theoretical equivalence between logics.For example, axiomatic and natural deduction presentations of classical propositional logic initially look quite different even though they're intuitively theoretically equivalent. Now, natural deduction is less metatheoretically tractable while axiomatic accounts do worse at revealing obvious entailments. Neither disadvantage is problematic once we're justified in treating them as theoretically equivalent; perceived disadvantages of a logical theory that are merely presentational can be ignored in calculating its overall virtues.We have options when developing a notion of theoretical equivalence. One standard way uses semantic properties, like having the same set of models, to account for when two logical theories are equivalent. However, as the required model theory can only be developed by appealing to significant logical resources, many of which are in contention when choosing between logics, it's natural for anti-exceptionalists to prefer less theoretically taxing syntactic accounts of theoretical equivalence. Syntactic accounts require lighter metatheoretic resources (roughly a basic theory of syntax) which can often be developed

Not a Knot

Teijeiro

2020

Here, I examine the connective called Knot, which may be considered a threat to semanticists, but not to inferentialists. I argue that it constitutes a problem for neither, by showing, first, how to characterize it proof‐theoretically, and second, by showing how the issues it allegedly poses for the semanticist rest on an imprecise understanding of metainferences. I conclude that one should be careful in grounding philosophical disputes merely on formal tools.