Abstract
Classical logic is usually viewed as a masterpiece of the human mind. It serves as the basic logic of classical mathematics and almost all other sciences. However, despite its long history and venerable reputation, it is not an ideal logic. It faces serious objections which demonstrate that as a practical tool, it is inadequate. A logic is an inadequate tool if its practical use generates counterintuitive and absurd situations that are highly incompatible with common sense and natural language. Classical logic and its modal extensions that we studied in the preceding chapter are just such logics. A few examples will suffice to prove the point.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anderson AR, Belnap ND, Jr. Entailment. The Logic of Relevance and Necessity. Vol. I. Princeton: Princeton University Press, 1975.
Anderson AR, Belnap ND, Jr., and Dunn JM. Entailment. The Logic of Relevance and Necessity. Vol. II. Princeton: Princeton University Press, 1992.
Arruda AI. On the imaginary logic of N.A. Vasil’év. In: Arruda AI, da Costa NCA, and Chuaqui R (eds.), Non-Classical Logic, Model Theory and Computability, pp. 3–24. Amsterdam: North-Holland Publishing Company, 1977.
Arruda AI. A survey of paraconsistent logic. In: Arruda AI, Chuaqui R, and da Costa NCA (eds.), Mathematical Logic in Latin America, pp. 3–41. Amsterdam: North-Holland Publishing Company, 1980.
Arruda AI. Aspects of the historical development of paraconsistent logic. In: Priest G, Routley R, and Norman J (eds.), Paraconsistent Logic. Essays on the Inconsistent, pp. 99–130. München: Philosophia Verlag, 1989.
Asenjo FG. A calculus of antinomies. Notre Dame Journal of Formal Logic 1966; 7:103–105.
Bimbó K. Relevance Logic. In: Jacquette D (ed.), Philosophy of Logic, pp. 723–789. Amsterdam: Elsevier, 2007.
Bochman A. Explanatory Nonmonotonic Reasoning. Singapore: World Scientific Publishing Company 2005.
Bremer M. An Introduction to Paraconsistent Logics. Frankfurt: Peter Lang, 2005.
Brouwer LEJ. On the Foundations of Mathematics. Thesis, Amsterdam; English translation in [Heyting, 1975], pp. 11–101.
Cavaliere F. L’Opera Di Hugh MacColl Alle Origini Delle Logiche Non-Classiche. Modern Logic 1996; 6:373–402.
da Costa NCA. Nota sobre o conceito de contradio. Anuário da Sociedade Paranaense de Mathemática 1958; 1:6–8.
da Costa NCA. Sistemas Formais Inconsistentes. Curitiba, Brazil: Universidade Federal do Parana, 1963.
da Costa NCA. On the theory of inconsistent formal systems. Notre Dame Journal of Formal Logic 1974; 15:497–510.
Dunn JM, and Restall G. Relevance Logic. In: Gabbay DM, and Guenthner F (eds.), Handbook of Philosophical Logic, 2nd Edition, Vol. 6, pp. 1–128. Dordrecht: Kluwer Academic Publishers, 2002.
Gottwald S. A Treatise on Many-Valued Logics. Baldock: Research Studies Press Ltd., 2001.
Gottwald S. Many-Valued Logics. In: Jacquette D (ed.), Philosophy of Logic, pp. 675–722. Amsterdam: Elsevier, 2007.
Grana N. Logica deontica paraconsistente. Naples: Liguori Editore, 1990.
Heyting A. Intuitionism: An Introduction. Third Revised Edition. Amsterdam: North-Holland Publishing Company, 1971.
Heyting A (ed.). L.E.J. Brouwer: Collected Works 1: Philosophy and Foundations of Mathematics. Amsterdam: Elsevier, 1975.
Jaśkowski S. Propositional calculus for contradictory deductive systems. Studia Logica 1969; 24:143–157. Originally published in Polish, in: Studia Societatis Scientiarum Torunensis 1948; Sectio A, Vol. I, Issue No. 5, pp. 55–77.
Kneale W, and Kneale M. The Development of Logic. Oxford: The Clarendon Press, 1968.
Łukasiewicz J. Philosophische Bemerkungen zu mehrwertigen Systemen des Aussagenkalküls. Comptes Rendus des Séances de la Société de Sciences et des Lettres de Varsovie, Classe III 1930; 23:51–77. (English translation in: McCall S (ed.), Polish Logic 1920–1939. With an Introduction by Tadeusz Kotarbinski, pp. 40–65. Oxford: Oxford University Press, 2005.)
Łukasiewicz J (1970). Selected Works, edited by L Borkowski. Amsterdam: North-Holland Publishing Company, 1970.
Marek VW, and Truszcyński M. Nonmonotonic Logic: Context-Depedent Reasoning. Berlin: Springer-Verlag 1993.
Post EL. Introduction to a general theory of elementary propositions. American Journal of Mathematics 1921; 43:163–185.
Priest G. In Contradiction. Dordrecht: Nijhoff, 1987.
Priest G. ‘Paraconsistent logic’. In: Gabbay DM, and Guenthner F (eds.), Handbook of Philosophical Logic, 2nd edition, Vol. 6, pp. 287–393. Dordrecht: Kluwer Academic Publishers, 2002.
Rescher N. Many-Valued Logic. New York: McGraw-Hill, 1969.
Stalanker R. A note on non-monotonic modal logic. Artificial Intelligence 1993; 64:183–196.
Van Dalen D. Intuitionistic Logic. In: Gabbay DM, and Guenthner F (eds.), Handbook of Philosophical Logic, Vol. III, pp. 225–339. Dordrecht: D. Reidel Publishing Company, 1986.
Wolter F, and Zakharyaschev M. Intuitionistic modal logics as fragments of classical bimodal logics. In: Orlowska E (ed.), Logic at Work, Essays in Honour of Helena Rasiowa, pp. 168–186. Heidelberg: Physica-Verlag, 1998.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Sadegh-Zadeh, K. (2012). Non-Classical Logics. In: Handbook of Analytic Philosophy of Medicine. Philosophy and Medicine(), vol 113. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2260-6_28
Download citation
DOI: https://doi.org/10.1007/978-94-007-2260-6_28
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-2259-0
Online ISBN: 978-94-007-2260-6
eBook Packages: Humanities, Social Sciences and LawPhilosophy and Religion (R0)