The Collapse of Logical Contextualism

(Logic & Philosophy of Mathematics, English)

ollowing the publications of JC Beall and Greg Restall the position called 'logical pluralism' experienced a renaissance. The theory, crudely put, consists of two parts:

(1)_The core concept of validity is given by the Generalized Tarski Thesis (GTT) according to which ''an argument is valid(x) if and only if, in every case(x) in which the premises are true, so is the conclusion''.

(2)_There are at least two admissible instances of case(x).

The most prominent objection to Beall & Restall's logical pluralism is the collapse problem, which has been formulated by Priest (2001), Read (2006) and Keefe (2014). The question at its core is whether, given the acceptance of some set of premises A, one should accept the conclusion C. As GTT involves truth-preservation, any logic classifying the inference from A to C as valid guarantees that we cannot step from truth to untruth. Consequently, if any encompassed logic classifies the inference from A to C as valid, one should accept C, if one accepts A. This, in turn, implies that there is a single privileged consequence relation: any argument is valid simpliciter if and only if it is valid according to one of the encompassed logics. Logical Pluralism collapses.

Caret (2017) claims that the collapse problem can be overcome by adopting logical contextualism. Agreeing with Beall & Restall that the core of logical validity is given by GTT, Caret takes it that contexts choose deductive standards by which we judge the validity of arguments. The collapse problem, so Caret argues, is avoided as in each context only the logic that is selected for that context has any normative bearing.

I will argue that if no contextualism of truth is to be adopted, the collapse problem maintains its force for logical contextualism. Caret does not acknowledge the ground for the normativity of validity judgements, namely truth-preservation. As such, contextualism cannot escape collapse. Carets efforts to construe a logical contextualism, as I contend, are nonetheless fruitful as they point towards a direction logical pluralism should be understood.

Chair:

Time: 14:00-14:30, 18 September 2019 (Wednesday)

Location: SR 1.007

Timo Meier

(Johannes Gutenberg-University Mainz, Germany)

Timo Meier is a PhD candidate at the Johannes Gutenberg-Universität Mainz. His research interest lie in the philosophy of logic and metaphysics. Following his master thesis about the logic of fiction, his PhD thesis revolves around the objectivity of logic with particular focus on logical pluralism.

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