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Keywords

philosophy, analytic philosophy, history of philosophy

Abstract

This paper is composed of two independent parts. The first is concerned with Russell’s early philosophy of mathematics and his quarrel with Poincaré about the nature of their opposition. I argue that the main divergence between the two philosophers was about the nature of definitions. In the second part, I briefly present Le!niewski’s Ontology and suggest that Le!niewski’s original treatment of definitions in the foundations of mathematics is the natural solution to the problem that divided Russell and Poincaré.

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References

Detlefsen, M. 1992. ‘Poincaré against the logicians’. Synthese 90: 349–378.
http://dx.doi.org/10.1007/BF00500033

Heinzmann, G. 1985. Entre Intuition et analyse. Poincaré et le concept de prédicativité. Paris: Blanchard.

Heinzmann, G. (ed.). 1986. Poincaré, Russell, Zermelo et Peano. Textes de la discussion (1906-1912) sur les fondements des mathématiques: des antinomies à la prédicativité. Paris: Blanchard.

Lesniewski, S. 1992. ‘On Definitions in the So-called Theory of Deduction’. In Surma S. J. et als (eds.) ‘Stanislaw Lesniewski Collected Works’, vol. II, Nijhoff International Philosophy Series, vol. 44. Dordrecht: Reidel.

Poincaré, H. 1905/1906. ‘Les mathématiques et la logique’. Revue de métaphysique et de morale 13: 815–835 / 14: 17–34, 294–317.

Poincaré, H. 1909. ‘La logique de l’infini’. Revue de métaphysique et de morale 17: 461–482.

Poincaré, H. 1968 (1902). La science et l’hypothèse. Paris: Flammarion.

Russell, B. 1905. ‘Review of Science and Hypothesis by H. Poincaré’. Mind 14, no. 55: 412–418.
http://dx.doi.org/10.1093/mind/XIV.3.412

Russell, B. 1906. ‘Les paradoxes de la logique’. Revue de métaphysique et de morale XIV: 627–650. The original English version can be found in Essays in Analysis, pp. 190-214.

Russell, B. 1972 (1903). The Principles of Mathematics. London: George Allen & Unwin.

Russell, B. 1973. Essays in Analysis, ed. Douglas Lackey. George Allen & Unwin.

Simons, P. 1982. ‘On Understanding Lesniewski’. History and Philosophy of Logic 3: 165–191.
http://dx.doi.org/10.1080/01445348208837038

Simons, P. 1987. Parts, A study in Ontology. Oxford: Clarendon Press.

Slupecki, J. 1984. ‘S. Lesniewski’s Calculus of Names’. In Srzednicki et al. 1984, 59–122.

Sobocinski, B. 1984. ‘Lesniewski’s analysis of Russell’s paradox’. In Srzednicki et al. 1984, 11–44.

Srzednicki, Jan T., Rickey, V.F. & Czelakowski, J. (eds.). 1984. Lesniewski’s systems: Ontology and Mereology. La Haye: M. Nijhoff.

Tarski, A. 1983. ‘On the primitive term of logistic’. In J. Corcoran (ed.) ‘Logic, Semantics, and Metamathematics’, 1–23. Hackett Publishing.

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