Modal logic

Paul Gochet
Table of contents

Standard elementary logic studies the deductive inferences which rest on two sets of logical constants: the connectives ‘not’, ‘and’, ‘either … or …’, ‘if … then …’ and the quantifiers ‘all’ and ‘some’. Modal logic extends the logical lexicon in order to account for the validity or non-validity of inferences which depends on the presence of modal terms such as ‘necessarily’ or ‘possibly’. With respect to arguments involving these terms, intuition cannot be trusted. Even the best logicians and philosophers fall prey to fallacies in this area. For instance, Etchemendy (1990: 87) discovered a hidden fallacious move in Tarski’s account of logical consequence, where he went from a statement of the form ‘Necessarily if p and q, then not r’ to a statement of the form ‘if p then necessarily if q then not r’. Anscombe (1959: 138) spotted another unsound move in a famous monograph on epistemology:

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