Graduate studies at Western
Australasian Journal of Philosophy 78 (4):438 – 474 (2000)
|Abstract||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)|
|Through your library||Configure|
Similar books and articles
Nikolaos Galatos & Hiroakira Ono (2006). Glivenko Theorems for Substructural Logics Over FL. Journal of Symbolic Logic 71 (4):1353 - 1384.
Lloyd Humberstone (2006). Identical Twins, Deduction Theorems, and Pattern Functions: Exploring the Implicative BCsK Fragment of S. [REVIEW] Journal of Philosophical Logic 35 (5):435 - 487.
Lloyd Humberstone (2008). Béziau's Translation Paradox. Theoria 71 (2):138-181.
Lloyd Humberstone (2001). The Pleasures of Anticipation: Enriching Intuitionistic Logic. [REVIEW] Journal of Philosophical Logic 30 (5):395-438.
Greg Restall (forthcoming). Substructural Logics. Stanford Encyclopedia of Philosophy.
Greg Restall (1997). Combining Possibilities and Negations. Studia Logica 59 (1):121-141.
Kosta Došen (1992). Modal Translations in Substructural Logics. Journal of Philosophical Logic 21 (3):283 - 336.
Ming Hsiung (2008). An Intuitionistic Characterization of Classical Logic. Journal of Philosophical Logic 37 (4):299 - 317.
Lloyd Humberstone (2007). Identical Twins, Deduction Theorems, and Pattern Functions: Exploring the Implicative BCsK Fragment of S. [REVIEW] Journal of Philosophical Logic 36 (5):435 - 487.
Added to index2009-01-28
Total downloads9 ( #122,562 of 738,577 )
Recent downloads (6 months)1 ( #61,778 of 738,577 )
How can I increase my downloads?