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’.

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References

Ackrill, J. L.
(ed.) 1963 Aristotle's Categories and De interpretatione. Oxford University Press. DOI logoGoogle Scholar
Aristotle
: see Ackrill (ed.) 1963 and Ross (ed.) 1928 Google Scholar
Barcan Marcus, R.
1946 A functional calculus of first order based on strict implication. The Journal of Symbolic Logic 11: 1–17. DOI logoGoogle Scholar
Bar-Hillel, Y.
1970 Aspects of Language. North Holland. Google Scholar
1971 Pragmatics of natural languages. Reidel. Google Scholar
Blackburn, P., M. De Rijke & Y. Venema
2001 Modal Logic. Cambridge University Press. DOI logoGoogle Scholar
Van Benthem, J.
1977 Tense logic and standard logic. Logique et Analyse 80: 395–437. Google Scholar
1983 The Logic of Time. A Model-Theoretic Investigation into the Varieties of Temporal Ontology and Temporal Discourse. Reidel. Google Scholar
Carnap, R.
1946 Modalities and Quantification. The Journal of Symbolic Logic 11: 33–64. DOI logoGoogle Scholar
1963 Carnap's Intellectual autobiography. In P. A. Schilpp (ed.) The Philosophy of Rudolf Carnap. Open Court. Google Scholar
Fitting, M. & R. Mendelsohn
1998 First-Order Modal Logic. Kluwer. DOI logoGoogle Scholar
Gabbay, D.
1974 Tense Logic and the Tenses of English. In J. Moravcsik (ed.) Logic and Philosophy for Linguists: 177–186. Mouton. Google Scholar
1976 Investigations in modal and tense logics. With applications to Problems in Philosophy and Linguistics. Reidel. DOI logoGoogle Scholar
Gabbay, D. & J. Woods
(eds.) 2006 The Handbook of History of Logic, vol. 7 Logic and the Modalities in the Twentieth Century. Elsevier. Google Scholar
Garson, J.
2006 Modal Logic for Philosophers. Cambridge University Press. DOI logoGoogle Scholar
Goranko, V.
1996 Hierarchies of Modal and Temporal Logic with Reference. The Journal of Logic, Language and Information 5: 1–24. DOI logoGoogle Scholar
Hughes, G. E. & M. J. Cresswell
1996 A new introduction to modal logic. Methuen. DOI logoGoogle Scholar
Kamp, H
1971 Formal Properties of ‘Now’. Theoria 37: 227–273. DOI logoGoogle Scholar
Lewis, I. & C. H. Langford
(1959) [1932] Symbolic logic. Dover. Google Scholar
Lyons, J.
1977 Semantics, vol. 2. Cambridge University Press. Google Scholar
Mctaggart, J. M. E.
1908 The Unreality of Time. Mind: 457–474. DOI logoGoogle Scholar
Moisil, G.
1972 Essai sur les logiques non chrysipiennes. Académie Socialiste de Roumanie. Google Scholar
Palmer, F.R
1979 Modality and the English modals. Longman. Google Scholar
Reichenbach, H.
(1974) [1947] Analysis of Conversational Language. In J. Moravcsik (ed.) Logic and Philosophy for Linguists: 122–141. Mouton. Google Scholar
Ross, W. D.
(ed.) 1928 The works of Aristotle: Analytica Priora. Clarendon. Google Scholar
Scott, D.
1971 On engendering an illusion of understanding. Journal of Philosophy 68(21): 787–807. DOI logoGoogle Scholar
Wolper, P.
1983 Temporal Logic Can Be More Expressive. Information and Control 56: 72–99. DOI logoGoogle Scholar