Review of Symbolic Logic 7 (3):385-414 (2014)
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.
|Keywords||Modal logic Necessity Apriority Actuality Two-Dimensional Semantics Nesting Problem|
|Categories||categorize this paper)|
References found in this work BETA
Epistemic Two-Dimensional Semantics.David J. Chalmers - 2004 - Philosophical Studies 118 (1-2):153-226.
Two Notions of Necessity.Martin Davies & Lloyd Humberstone - 1980 - Philosophical Studies 38 (1):1-31.
On the Concept of Following Logically.Alfred Tarski - 2002 - History and Philosophy of Logic 23 (3):155-196.
Citations of this work BETA
Actuality, Tableaux, and Two-Dimensional Modal Logic.Fabio Lampert - forthcoming - Erkenntnis:1-41.
Similar books and articles
Reference, Contingency, and the Two-Dimensional Framework.Martin Davies - 2004 - Philosophical Studies 118 (1-2):83-131.
The Logic of Historical Necessity as Founded on Two-Dimensional Modal Tense Logic.Lennart Åqvist - 1999 - Journal of Philosophical Logic 28 (4):329-369.
How to Kripke Brandom's Notion of Necessity.Benedikt Paul Göcke, Martin Pleitz & Hanno von Wulfen - 2008 - In Bernd Prien & David P. Schweikard (eds.), Robert Brandom. Analytic Pragmatist. ontos.
'Now' and 'Then' in Tense Logic.Ulrich Meyer - 2009 - Journal of Philosophical Logic 38 (2):229-247.
Inductive Logic with Causal Modalities: A Probabilistic Approach.Soshichi Uchii - 1972 - Philosophy of Science 39 (2):162-178.
Elementary Definability and Completeness in General and Positive Modal Logic.Ernst Zimmermann - 2003 - Journal of Logic, Language and Information 12 (1):99-117.
Necessities and Necessary Truths: A Prolegomenon to the Use of Modal Logic in the Analysis of Intensional Notions.V. Halbach & P. Welch - 2009 - Mind 118 (469):71-100.
Added to index2012-09-09
Total downloads391 ( #6,550 of 2,172,660 )
Recent downloads (6 months)74 ( #2,158 of 2,172,660 )
How can I increase my downloads?