Revising Carnap’s semantic conception of modality

Toby Meadows

Research output: Contribution to journalArticle

Abstract

I provide a tableau system and completeness proof for a revised version of Carnap’s semantics for quantified modal logic. For Carnap, a sentence is possible if it is true in some first order model. However, in a similar fashion to second order logic, no sound and complete proof theory can be provided for this semantics. This factor contributed to the ultimate disappearance of Carnapian modal logic from contemporary philosophical discussion. The proof theory I discuss comes close to Carnap’s semantic vision and provides an interesting counterpoint to mainstream approaches to modal logic. Despite its historical origins, my intention is to demonstrate that this approach to modal logic is worthy of contemporary attention and that current debate is the poorer for its absence.
Original languageEnglish
Pages (from-to)497-515
Number of pages19
JournalStudia Logica
Volume100
Issue number3
DOIs
Publication statusPublished - Jun 2012

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Modal Logic
Modality
Proof Theory
Second-order Logic
Tableau
Completeness
First-order
Semantics
Rudolf Carnap
Conception
Demonstrate
Model

Cite this

Revising Carnap’s semantic conception of modality. / Meadows, Toby.

In: Studia Logica, Vol. 100, No. 3, 06.2012, p. 497-515.

Research output: Contribution to journalArticle

Meadows, Toby. / Revising Carnap’s semantic conception of modality. In: Studia Logica. 2012 ; Vol. 100, No. 3. pp. 497-515.
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