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’.
References
Ackrill, J.L.
(ed.)1963Aristotle's Categories and De interpretatione. Oxford University Press.
Aristotle
: see Ackrill(ed.)1963 and Ross (ed.) 1928
Barcan Marcus, R.
1946A functional calculus of first order based on strict implication. The Journal of Symbolic Logic 11: 1–17.