Wójtowicz Krzysztof
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47(2011)4 - Science versus Utopia. Limits of Scientific Cognition

Krzysztof Wójtowicz

On (some) presuppositions in mathematics

  • language: English


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.

 

 
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45(2009)1 - In honour of Professor Edward Nieznański

Krzysztof Wójtowicz

Quantum computation theory and the aprioricity of mathematics

  • language: Polish


Summary

The problem of the nature of mathematical knowledge is discussed in the context of quantum computation theory. The main question is if the theoretical results concerning quantum algorithms shed new light on this discussion. The “received view” concerning mathematical knowledge (in the tradition of Descartes or Gödel) is shortly presented, the main ideas of quantum computation theory pointed out and the problem formulated.