Australasian Journal of Philosophy 78 (4):438 – 474 (2000)
Only 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..
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
References found in this work BETA
Relevant Logics and Their Rivals.Richard Routley, Val Plumwood, Robert K. Meyer & Ross T. Brady - 1982 - Ridgeview.
Citations of this work BETA
False Though Partly True – an Experiment in Logic.Lloyd Humberstone - 2003 - Journal of Philosophical Logic 32 (6):613-665.
Natural Deduction and Curry's Paradox.Susan Rogerson - 2007 - Journal of Philosophical Logic 36 (2):155 - 179.
Similar books and articles
Glivenko Theorems for Substructural Logics Over FL.Nikolaos Galatos & Hiroakira Ono - 2006 - Journal of Symbolic Logic 71 (4):1353 - 1384.
Identical Twins, Deduction Theorems, and Pattern Functions: Exploring the Implicative BCsK Fragment of S. [REVIEW]Lloyd Humberstone - 2006 - Journal of Philosophical Logic 35 (5):435 - 487.
The Pleasures of Anticipation: Enriching Intuitionistic Logic. [REVIEW]Lloyd Humberstone - 2001 - Journal of Philosophical Logic 30 (5):395-438.
Modal Translations in Substructural Logics.Kosta Došen - 1992 - Journal of Philosophical Logic 21 (3):283 - 336.
An Intuitionistic Characterization of Classical Logic.Ming Hsiung - 2008 - Journal of Philosophical Logic 37 (4):299 - 317.
Identical Twins, Deduction Theorems, and Pattern Functions: Exploring the Implicative BCsK Fragment of S. [REVIEW]Lloyd Humberstone - 2007 - Journal of Philosophical Logic 36 (5):435 - 487.
Added to index2009-01-28
Total downloads35 ( #147,590 of 2,171,797 )
Recent downloads (6 months)2 ( #173,730 of 2,171,797 )
How can I increase my downloads?