On alternative geometries, arithmetics, and logics; a tribute to Łukasiewicz
This paper was originally presented at a conference on Łukasiewicz. It attributes to him the idea that there might be rigorous logical systems in which sentences could be neither true nor false, and therefore hails him as the founder of modern nonclassical logic. The concept of alternative logics is rendered plausible by detailed comparison with the other two great a priori sciences in Kant's classification, geometry and (with an ingenious science fiction story) arithmetic; and by a description of the relations between the traditional logic (Aristotle's, as developed during the Middle Ages) and the classical logic of Frege and Russell, particularly the inconsistency of their judgements about the validity of Darapti and Camestros, and the argument (due to \textit{Len Goddard}, ``The inconsistency of Aristotelian logic?'', Australasian Journal of Philosophy 78, 434-437 (2000)) that traditional logic is inconsistent. Quine's argument that one who tries to adopt a deviant logic only changes the subject is shown to beg the question at issue as a defence of classical logic, and his claim that any translation manual must preserve classical logic is rejected. The paper concludes with the suggestion that Łukasiewicz may be seen as the Riemann of logic.
scientific article; zbMATH DE number 1972203