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Rola aksjomatu w matematyce współczesnej oraz w perspektywie dociekań nad aksjomatem wyboru

100%
Lewandowska K.
Zagadnienia Filozoficzne w Nauce
|
2011
|
issue 48
148-165
PL
We show how philosophy effected the shape of mathematics when the proof of Well-Ordering Principle was formulated by Ernst Zermelo. We also consider the significance of philosophy of mathematics today. We concentrate on Solomon Feferman and Penelope Maddy attitude in the recent debate on the need of new axioms in mathematics.
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Filozofia i logika intuicjonizmu

71%
Fila M.
Semina Scientiarum
|
2015
|
vol. 14
EN
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.
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