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SOURCE:	Historical, Philosophical, Political and Law Sciences, Culturology and Study of Art. Issues of Theory and Practice. Tambov: Gramota, 2015. № 11. Part 3. P. 111-113.
SCIENTIFIC AREA:	Philosophical Sciences
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CONCEPTIONS ABOUT NUMBERS IN FREGE’S LOGICISM AND WRIGHT’S AND HEIL’S NEO-LOGICISM

Oleinik Polina Ivanovna
National Research Tomsk State University

Abstract. The article gives a review of the main ideas of the philosophy of mathematics by K. Wright and B. Heil. The purpose of the paper is to characterize one of the problems of this trend - the problem of the connection of the notions of the first level with the notions of the second level in the programme of mathematics formation. The central idea of Wright and Heil that the fundamental laws of arithmetic may be received in the system of second-order logic supplemented by abstraction principle (Hume’s principle) is analyzed.

Key words and phrases: логицизм, нео-логицизм, понятия первого уровня, понятия второго уровня, Аксиома V Фреге, принцип Юма, логика второго порядка, logicism, neo-logicism, notions of the first level, notions of the second level, Frege’s Axiom V, Hume’s principle, second-order logic

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References:

Pashchenko T. V. O vidakh neologitsizma // Filosofiya. Yazyk. Kul'tura: sb. materialov nauchnoi konferentsii studentov, aspirantov i molodykh uchenykh (g. Moskva, 10 marta 2010 g.) / GU-VShE; sost. V. V. Gorbatov. M., 2010. C. 53-64.
Frege G. Logiko-filosofskie trudy / per. s angl., nem., frants. V. A. Surovtseva. Novosibirsk: Sib. univ. izd-vo, 2008. 283 s.
Bays T. The Fruits of Logicism // Notre Dame Journal of Formal Logic. 2000. Vol. 41. P. 415-421.
New Waves in Philosophy of Mathematics / ed. by O. Bueno, O. Linnebo. Hampshire: Palgrave MacMillan, 2009. 320 p.
Wright C. Frege’s Conception of Numbers as Objects. Aberdeen University Press, 1983. 194 p.

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