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  • Author or Editor: Marcin Trepczyński x
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Abstract

In this introduction to the volume Philosophical Approaches to the Foundations of Logic and Mathematics dedicated to Professor Stanisław Krajewski, I argue that it is worth asking about such foundations and putting together logic and mathematics when we conduct such considerations. There are various problems and questions which apply to both of them. But what is more important, putting them together allows us to make new observations, as in the case of the phenomenon of emergence in mathematics described by Stanisław Krajewski. I also show that asking about the foundations is constitutive for logic and mathematics, and essential for philosophy as such; furthermore, it also plays a significant role for the humanities.

In: Philosophical Approaches to the Foundations of Logic and Mathematics
Eleven papers collected in the volume Philosophical Approaches to the Foundations of Logic and Mathematics address various aspects of the “roots”, basic concepts and the nature of logic and mathematics. Taken together, these papers reveal how many serious philosophical problems lie at the foundations of logic and mathematics.

The topics discussed in this volume include: transcending anti-foundationalism and two concurrent trends of "anthropological" and "practical" understanding of the foundations of mathematics, new approaches to mathematical realism, the “roots” of logic in a genetic perspective, the primacy of truth or satisfaction, and the “effectiveness” of mathematics in terms of categorical semantics.