next article in this issue  |
|
Document Details : Title: A Logic's Proper Semantics Author(s): BATENS, Diederik Journal: Logique et Analyse Volume: 255 Date: 2021 Pages: 215-243 DOI: 10.2143/LEA.255.0.3290188 Abstract : Many logics are sound and complete with respect to a multiplicity of semantic systems that assign different sets of models to the logic. If all these semantic systems are equally ‘good’, a series of problems results, as will be shown in section 1. In this paper I present a method to define for each logic L (from a huge class, comprising all usual deductive logics) a unique ‘proper’ semantics and I argue that it is justified to consider this semantics as correctly describing the ‘situations’ that are possible according to L. This solves the problems referred to in the previous paragraph. Implications for the discussion on inferentialism are obvious. For some logics L, the proper semantics coincides with the Henkin semantics, the set of models obtained by applying the Henkin method to true statements Γ∀L A, given an enumeration L of the set of formulas. For other logics L, the proper semantics counts more models than the Henkin semantics (and, moreover, not all Henkin models are maximally L-non-trivial). I shall show that a certain change to the Henkin method is sufficient to turn all proper models into Henkin models. |
|
