Filozofia i logika intuicjonizmu

Marlena Fila

Abstrakt


At the end of the 19th century in the fundamentals of mathematics appeared a crisis. It was caused by the paradoxes found in Cantor’s set theory. One of the ideas a resolving the crisis was intuitionism – one of the constructivist trends in the philosophy of mathematics. Its creator was Brouwer, the main representative was Heyting.
In this paper described will be attempt to construct a suitable logic for philosophical intuitionism theses. In second paragraph Heyting system will be present – its axioms and matrices truth-. Later Gödel theorem about the inadequacy of finite dimensional matrices for this system will be explained. At the end this paper an infinite sequence of matrices adequate for Heyting axioms proposed by Jaśkowski will be described.


Słowa kluczowe


intuitionism; axioms; matrices truth-; Heyting system; Gödel theorem about the inadequacy of finite dimensional matrices for Heyting system; infinite sequence of matrices

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Bibliografia


Brouwer L. E. J., Intuitionisme en formalisme, Amsterdam 1912, [w:] Filozofia matematyki. Antologia tekstów klasycznych, R. Murawski, Poznań 1994, s. 263–275.

Murawski R., Filozofia matematyki. Zarys dziejów, Warszawa 1995, s. 67–72, 83–136.

Zawirski Z., Geneza i rozwój logiki intuicjonistycznej, „Kwartalnik Filozoficzny” 16 (1946), s. 165–222.

Zinowiew A., Filozoficzne problemy logiki wielowartościowej, Warszawa 1963.




Copyright (c) 2015 Marlena Fila