Australasian Journal of Philosophy 78 (4):438 – 474 (2000)
AbstractOnly propositional logics are at issue here. Such a logic is contra-classical in a superficial sense if it is not a sublogic of classical logic, and in a deeper sense, if there is no way of translating its connectives, the result of which translation gives a sublogic of classical logic. After some motivating examples, we investigate the incidence of contra-classicality (in the deeper sense) in various logical frameworks. In Sections 3 and 4 we will encounter, originally as an example of what (in Section 2) we call a contra-classical modal logic, an unusual logic boasting a connective (" demi-negation" ) whose double application is equivalent to a single application of the negation connective. Pondering the example points the way to a general characterization of contra-classicality (Theorems 3.3 and 4.6). In an Appendix (Section 5), we look at one alternative to classical logic as the target for such translational assimilation, intuitionistic logic, calling logics which resist the assimilation, in this case, contra- intuitionistic. We will show that one such logic is classical logic itself, thereby strengthening a result of Wojcicki's to the effect that the consequence relation of classical logic cannot be faithfully embedded by any connective-by-connective translation into that of intuitionistic logic. (What the "faithfully" means here is that not only is the translation of anything provable in the 'source' logic..
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References found in this work
Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview.
Citations of this work
Shadows of Syntax: Revitalizing Logical and Mathematical Conventionalism.Jared Warren - 2020 - New York, USA: Oxford University Press.
Connexive Logics. An Overview and Current Trends.Hitoshi Omori & Heinrich Wansing - forthcoming - Logic and Logical Philosophy:1.
Substructural Logics, Pluralism and Collapse.Eduardo Alejandro Barrio, Federico Pailos & Damian Szmuc - 2018 - Synthese 198 (Suppl 20):4991-5007.
Intertranslatability, Theoretical Equivalence, and Perversion.Jack Woods - 2018 - Thought: A Journal of Philosophy 7 (1):58-68.
Change of Logic, Change of Meaning.Jared Warren - 2018 - Philosophy and Phenomenological Research 96 (2):421-442.
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