Krzysztof Wójtowicz
On (some) presuppositions in mathematics
Summary
The paper considers the problem of presuppositions in mathematics and in philosophy of mathematics. Both mathematicians and philosophers of mathematics make certain assumptions about mathematics, e.g. that it is formalizable, that there are unsolvable problems in mathematics (or – on the contrary – that all such problems can be solved), or that mathematical proofs have no empirical content. In this context, three groups of problems are discussed, which seem particularly interesting: 1. The relation between the formal and the informal discourse in mathematics, 2. The question of “ignorabimus” in mathematics, 3. The a priori status of mathematics.
