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License Agreement on scientific materials use.
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CONCEPTIONS ABOUT NUMBERS IN FREGE’S LOGICISM AND WRIGHT’S AND HEIL’S NEO-LOGICISM
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Polina Ivanovna Oleinik
National Research Tomsk State University
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Submitted:
November 1, 2015
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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.
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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:
- Пащенко Т. В. О видах неологицизма // Философия. Язык. Культура: сб. материалов научной конференции студентов, аспирантов и молодых ученых (г. Москва, 10 марта 2010 г.) / ГУ-ВШЭ; сост. В. В. Горбатов. М., 2010. C. 53-64.
- Фреге Г. Логико-философские труды / пер. с англ., нем., франц. В. А. Суровцева. Новосибирск: Сиб. унив. изд-во, 2008. 283 с.
- 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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