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SUBJECT-MATTER AND INTENSIONAL OPERATORS III: STATE-SENSITIVE SUBJECT-MATTER AND TOPIC SUFFICIENCY

Part of: General logic

Published online by Cambridge University Press:  12 July 2023

THOMAS MACAULAY FERGUSON Open the ORCID record for THOMAS MACAULAY FERGUSON [Opens in a new window]
THOMAS MACAULAY FERGUSON*
Affiliation:
DEPARTMENT OF COGNITIVE SCIENCE RENSSELAER POLYTECHNIC INSTITUTE TROY, NY, USA and INSTITUTES OF PHILOSOPHY AND COMPUTER SCIENCE CZECH ACADEMY OF SCIENCES PRAGUE, CZECH REPUBLIC
*
E-mail: tferguson@gradcenter.cuny.edu
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Abstract

Logical frameworks that are sensitive to features of sentences’ subject-matter—like Berto’s topic-sensitive intentional modals (TSIMs)—demand a maximally faithful model of the topics of sentences. This is an especially difficult task in the case in which topics are assigned to intensional formulae. In two previous papers, a framework was developed whose model of intensional subject-matter could accommodate a wider range of intuitions about particular intensional conditionals. Although resolving a number of counterintuitive features, the work made an implicit assumption that the subject-matter of an intensional conditional is a function of the subject-matters of its subformulae. This assumption—which I will call a principle of topic sufficiency—runs counter to some natural intuitions concerning topic. In this paper, we will investigate topic sufficiency and offer a semantic account that is state-sensitive, providing an implementation through the introduction of topic-sensitive logics related to William Parry’s prototypical $\mathsf {PAI}$.

Keywords

subject-mattertopic-sensitive intentional modalsanalytic implicationcontainment logic

MSC classification

Primary: 03B20: Subsystems of classical logic (including intuitionistic logic) 03B47: Substructural logics (including relevance, entailment, linear logic, Lambek calculus, BCK and BCI logics)
Type
Research Article
Information
The Review of Symbolic Logic , First View , pp. 1 - 27
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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