Studia Logica

, Volume 74, Issue 3, pp 441-468

First online:

On Alternative Geometries, Arithmetics, and Logics; a Tribute to Łukasiewicz

  • Graham PriestAffiliated withDepartment of Philosophy, University of Melbourne

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The paper discusses the similarity between geometry, arithmetic, and logic, specifically with respect to the question of whether applied theories of each may be revised. It argues that they can - even when the revised logic is a paraconsistent one, or the revised arithmetic is an inconsistent one. Indeed, in the case of logic, it argues that logic is not only revisable, but, during its history, it has been revised. The paper also discusses Quine's well known argument against the possibility of “logical deviancy”.

Łukasiewicz revisability inconsistent arithmetics Traditional logic paraconsistency Quine