Philosophical Approaches to the Foundations of Logic and Mathematics

In Honor of Stanisław Krajewski


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.

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Marcin Trepczyński, PhD, philosopher and assistant professor at the University of Warsaw. Author of numerous articles and a monograph on relationships between logic and theology.
Introduction: Philosophy Asking about the Foundations of Logic and Mathematics Marcin Trepczyński
1 From Speculative to Practical Foundations of Mathematics: A Communication-Centered Account Vladislav Shaposhnikov
2 Is There an Absolute Mathematical Reality? Zbigniew Król
3 Mathematical Modalities and Mathematical Explanations Krzysztof Wójtowicz
4 Apriorism, Aposteriorism and the Genesis of Logic Jan Woleński
5 On Some Problems with Truth and Satisfaction Cezary Cieśliński
6 Inductive Plausibility and Certainty: A Multimodal Paraconsisent and Nonmonotonic Logic Ricardo Silvestre
7 On the Reception of Cantor’s Theory of Infinity (Mathematicians Vs. Theologians) Roman Murawski
8 How Is the World Mathematical? Michael Heller
9 An Analysis of Paradoxes Anna Wójtowicz
10 Computation and Visualization Thought Experiments after Lakatos’s Heuristic Guessing Method (Semantics of Thought Experiments – Pt. Mathematical Thought Experiments) C. Peter Hertogh
Closing Words: Are Dogs Logical Animals? Jean-Yves Béziau
All interested in philosophy of sciences, especially philosophy of logic and philosophy of mathematics.