What is the correct logic of necessity, actuality and apriority?

Journal article


Peter Fritz. (2014). What is the correct logic of necessity, actuality and apriority? Review of Symbolic Logic. 7(3), pp. 385-414. https://doi.org/10.1017/S1755020314000136
AuthorsPeter Fritz
Abstract

This paper is concerned with a propositional modal logic with operators for necessity, actuality and apriority. The logic is characterized by a class of relational structures defined according to ideas of epistemic two-dimensional semantics, and can therefore be seen as formalizing the relations between necessity, actuality and apriority according to epistemic two-dimensional semantics. We can ask whether this logic is correct, in the sense that its theorems are all and only the informally valid formulas. This paper gives outlines of two arguments that jointly show that this is the case. The first is intended to show that the logic is informally sound, in the sense that all of its theorems are informally valid. The second is intended to show that it is informally complete, in the sense that all informal validities are among its theorems. In order to give these arguments, a number of independently interesting results concerning the logic are proven. In particular, the soundness and completeness of two proof systems with respect to the semantics is proven (Theorems 2.11 and 2.15), as well as a normal form theorem (Theorem 3.2), an elimination theorem for the actuality operator (Corollary 3.6), and the decidability of the logic (Corollary 3.7). It turns out that the logic invalidates a plausible principle concerning the interaction of apriority and necessity; consequently, a variant semantics is briefly explored on which this principle is valid. The paper concludes by assessing the implications of these results for epistemic two-dimensional semantics.

Year2014
JournalReview of Symbolic Logic
Journal citation7 (3), pp. 385-414
PublisherCambridge University Press
ISSN1755-0203
Digital Object Identifier (DOI)https://doi.org/10.1017/S1755020314000136
Scopus EID2-s2.0-84916237823
Research or scholarlyResearch
Page range385-414
Publisher's version
License
All rights reserved
File Access Level
Controlled
Output statusPublished
Publication dates
Online12 May 2014
Publication process dates
Deposited24 Aug 2021
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