Логіцизм Бертрана Расела проти антиномій розуму Імануеля Канта

Viktor Kozlovskyi

doi:10.31649/sent45.02.026

Authors

Viktor Kozlovskyi National University of Kyiv-Mohyla Academy https://orcid.org/0000-0001-8302-3977

DOI:

https://doi.org/10.31649/sent45.02.026

Keywords:

Frege, Peano, Russell’s paradoxes, theory of types, transcendentalism

Abstract

The article argues that the logicism through which Russell approached Kant’s antinomies possessed a distinct character, determined by: a) discovery of paradoxes, and b) theory of types as finding ways to solve them. The paper demonstrates both the strengths and weaknesses of Russell’s logicism regarding his approach to Kant’s mathematical antinomies, which concern the concepts of the world as a totality of phenomena and nature as a dynamic whole. The strengths of this logicism lie in the precise definitions of infinity and continuity as concepts of «pure arithmetic». Conversely, its weakness is the disregard for Kantian transcendentalism, the very framework within which the antinomies retain their meaning. It is transcendentalism as presupposing the subjective forms of intuition, space and time that renders the antinomies possible as productive ideas of reason. Rejecting these forms eliminates the «semantic field» within which the antinomies maintain their epistemological value.

Author Biography

Viktor Kozlovskyi, National University of Kyiv-Mohyla Academy

PhD, Associate Professor, Department of Philosophy and Religious Studies

References

Church, А. (1976). Comparison of Russell's Resolution of the Semantical Antinomies with That of Tarski. The Journal of Symbolic Logic, 41(4), 747-760. https://doi.org/10.2307/2272393

Coffa, A. (1981). Russell and Kant. Synthese, 46(2), 247-263. https://doi.org/10.1007/BF01064390

Floyd, J., & Kanamori, A. (2016). Gödel vis-à-vis Russell: Logic and Set Theory to Philosophy. In G. Crocco & E.-M. Engelen (Eds.), Kurt Gödel Philosopher-Scientist (pp. 243-326). Marseille: Presses universitaires de Provence. https://doi.org/10.4000/books.pup.53640

Frege, G. (1879). Begriffsschrift, eine der Arithmetischen Nachgebildete: Formelsprache des reinen Denkens. Halle: Verlag von Louis Nebert.

Gödel, K. (1931). Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I. Monatshefte für Mathematik und Physik. Akademische Verlagsgesellschaft, 38, 173-198. https://doi.org/10.1007/BF01700692

Halmos, P. R. (2019). Naive Set Theory. Los Angeles: BowWow Press.

Hegel, G. W. F. (1968 sqq.). Gesammelte Werke. 31 Bde. (Rheinisch-Westfälischen Akademie der Wissenschaften, Hrsg.). Hamburg: Meiner.

Irvine, A. (2009). Bertrand Russell's Logic. In D. M. Gabbay & J. Woods (Eds.), Handbook of the History of Logic. Vol. 5. Logic from Russell to Church (pp.1-28). Amsterdam: Elsevier. https://doi.org/10.1016/S1874-5857(09)70020-2

Kant, I. (1900 sqq.). Gesammelte Schriften: Hrsg. von der Preußische Akademie der Wissenschaf-ten; Deutsche Akademie der Wissenschaften zu Berlin; Akademie der Wissenschaften zu Göttingen (Akademie-Ausgabe, XXIX Bde). Berlin: Reimer & De Gruyter.

Kozlovskyi, V. (2024). Russell’s doctrine of space and time in connection with Kant’s transcendental aesthetics. [In Ukrainian]. Sententiae, 43(2), 6-32. https://doi.org/10.31649/sent43.02.006

Kozlovskyi, V. (2025). Mathematics in the Light of Transcendental Aesthetics: Did Kant Create a ‘Philosophy of Mathematics’? [In Ukrainian]. Sententiae, 44(2), 58-86. https://doi.org/10.31649/sent44.02.058

Onof, C. (2013). The Cost of Discarding Intuition - Russell’s Paradox as Kantian Antinomy. In S. Bacin, A. Ferrarin, C. La Rocca & M. Ruffing (Eds.), Kant und die Philosophie in weltbürgerlicher Absicht: Akten des XI. Kant-Kongresses 2010 (pp. 171-184). Berlin: De Gruyter. https://doi.org/10.1515/9783110246490.4031

Peano, G. (1973). The Principles of Arithmetic, Presented by a New Method. In H. Kennedy (Ed.), Selected works of Giuseppe Peano (pp.101-134). Toronto: University of Toronto Press.

Russell, B. (1945). A History of Western Philosophy and Its Connection with Political and Social Circumstances from the Earliest Times to the Present Day. New York: Simon and Schuster.

Russell, B. (1959). Wisdom of the West: A Historical Survey of Western Philosophy in Its Social and Political Setting. London: Macdonald.

Russell, B. (2010). The Principles of Mathematics. London: Routledge.

Russell, B. (2017). Mathematical Logic as based on the Theory of Types. In B. Russell, Logic and Knowledge. Essays.1901-1950 (pp. 59-102). London: Allen & Unwin.

Russell, B. (2022). The Analysis of Mind. London: Routledge. https://doi.org/10.4324/9781003308935

Urquhart, А. (2008). Logic and denotation. In N. Griﬃn & D. Jacquette (Еds.), Russell vs. Meinong: The Legacy of “On Denoting” (рр.1-16). London: Routledge.

Whitehead, A. N., & Russell, B. (1963). Principia Mathematica (Vоl. 1). Cambridge: Cambridge UP.