Systemy dedukcyjne Leśniewskiego - podstawy filozofii i matematyki

Abstrakt

The systems built by Leśniewski have a twofold function: mathematical and philosophical. The author explains with the help of examples in what this function consists. It turns out that in Leśniewski's approach the new account of the basis of traditional philosophy is of primary importance, for it is on this account that the new account of the foundations of mathematics is based. In this way we come closer to the realisation of the idea of the unity of the Aristotelian "theoretical philosophy", whose basis and starting point is the "first philosophy" (metaphysics) and whose final stage of development is mathematics. Leśniewski's deductive systems are entirely adequate as methodological tools (organon) of the final grounding of both philosophy (in its main theoretical branches: i.e. in ontology and epistemology) and mathematics (in its main theoretical branches: i.e. in arithmetic and geometry). However, to this aim the relevant elements of these deductive systems should be fully developed; they should be much more precise and complex than the initial assumptions in this range.