Béziau's Translation Paradox

Theoria 71 (2):138-181 (2005)
Lloyd Humberstone
Monash University
Jean-Yves Béziau (‘Classical Negation can be Expressed by One of its Halves’, Logic Journal of the IGPL 7 (1999), 145–151) has given an especially clear example of a phenomenon he considers a sufficiently puzzling to call the ‘paradox of translation’: the existence of pairs of logics, one logic being strictly weaker than another and yet such that the stronger logic can be embedded within it under a faithful translation. We elaborate on Béziau’s example, which concerns classical negation, as well as giving some additional background (especially from intuitionistic logic) to the example. Our interest is more on the logical exploration of the phenomenon Béziau’s case exemplifies than on the question of whether that phenomenon is (even prima facie ) paradoxical, though in Section 5 we do approach the latter question – somewhat obliquely – by considering an analogous phenomenon which it is hard to find puzzling.
Keywords definition  Connectives  translational embeddings  negation
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Reprint years 2008
DOI 10.1111/j.1755-2567.2005.tb01011.x
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References found in this work BETA

Modal Logic.Alexander Chagrov - 1997 - Oxford University Press.
Introduction to Mathematical Logic.Alonzo Church - 1956 - Princeton: Princeton University Press.
The Logic of Provability.George S. Boolos - 1995 - Cambridge University Press.

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