Abstract
Since Whitehead and Russell’s Principia Mathematica, explicit definitions are usually considered to be logically neutral. In this paper, we explore those explicit definitions which were called creative by the members of the Warsaw School. We explain why a definition can be necessary for the proofs of certain results in a formal system and why the eliminability of a definition does not imply its logical neutrality. For this purpose, we explore certain important but often neglected results about definitions established by Leśniewski, Łukasiewicz, and Tarski in the 1920s.
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References
Joray P.: Should Definitions be Internal? In Bilkova M., Behounek L. (eds). The Logica Yearbook 2004. Praha: Filosofia. 189–199 (2005).
Joray P.: What is wrong with creative definitions? Logika 23 ,Wrocław. 39–49 (2006).
Joray P.: La définition dans les systèmes logiques de Łukasiewicz, Leśniewski et Tarski. In Pouivet R., Rebuschi M. (eds). La philosophie en Pologne: 1918–1939. Paris: Vrin. 203–222 (2006).
Joray P.: Axiomatiques minimales et définitions : la thèse de Tarski sur le calcul biconditionnel. Travaux de Logique 20, Universités de Neuchâtel / Rennes. 57–83 (2011).
Leśniewski S.: Collected Works (2 vol.). Surma S. J., Srzednicki J. T., Barnett D. I. (eds). Warszawa: PWN / Dordrecht: Kluwer (1992).
Łukasiewicz J.: Rola definicyj w systemach dedukcyjnych (The role of definitions in deductive systems, French transl. by Blaszczyk M. in Joray [3], 221-222). Ruch Filozoficzny 11. 164 (1928).
Łukasiewicz J.: O definicyach w teoryi dedukcyi (On definitions in deductive systems, French transl. by Blaszczyk M. in Joray [3], 217-220). Ruch Filozoficzny 11. 177–178 (1928).
Łukasiewicz J.: Elements of Mathematical Logic. Oxford: Pergamon / Warsaw: PWN (1963).
Łukasiewicz J.: The Equivalential Calculus. In Borkowski L. (ed.) Jan Łukasiewicz : Selected Works. Amsterdam: North Holland / Warszawa: PWN. 250–277 (1970).
Miéville D.: Introduction à l’œuvre logique de S. Leśniewski. I. La Protothétique, II. L’Ontologie. Travaux de logique. Neuchâtel: Université (2001–2004).
Pascal B.: De l’esprit géométrique et de l’art de persuader. (1658).
Russell B.: The Principles of Mathematics. Cambridge University Press (1903).
Tarski A.: On the Primitive Term of Logistic. In Logic, Semantics, Metamathematics: Papers from 1923 to 1944. Oxford: Clarendon. 1–23 (1923).
Whitehead A. N., Russell B.: Principia Mathematica. 2nd ed. Cambridge Univ. Press. (1927).
Joray P.: Un systeme de deduction naturelle pour la Protothetique de Leśniewski. Argumentum. Journal of the Seminar of Discursive Logic, Argumentation Theory and Rhetoric 18(1). 45–65 (2020).
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Joray, P. (2022). Definition and Inference in Leśniewski’s Logic. In: Béziau, JY., Desclés, JP., Moktefi, A., Pascu, A.C. (eds) Logic in Question. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-94452-0_13
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