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Philosophical Approaches to the Foundations of Logic and Mathematics
In Honor of StanisÅaw Krajewski
Series:
Editor:
Eleven papers collected in the volume Philosophical Approaches to the Foundations of Logic and Mathematics address various aspects of the ârootsâ, 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 ârootsâ of logic in a genetic perspective, the primacy of truth or satisfaction, and the âeffectivenessâ of mathematics in terms of categorical semantics.
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 ârootsâ of logic in a genetic perspective, the primacy of truth or satisfaction, and the âeffectivenessâ of mathematics in terms of categorical semantics.
Marcin TrepczyÅski, PhD, philosopher and assistant professor at the University of Warsaw. Author of numerous articles and a monograph on relationships between logic and theology.
Content
Introduction: Philosophy Asking about the Foundations of Logic and Mathematics Marcin TrepczynÌski
1 From Speculative to Practical Foundations of Mathematics: A Communication-Centered Account Vladislav Shaposhnikov
2 Is There an Absolute Mathematical Reality? Zbigniew KroÌl
3 Mathematical Modalities and Mathematical Explanations Krzysztof WoÌjtowicz
4 Apriorism, Aposteriorism and the Genesis of Logic Jan WolenÌski
5 On Some Problems with Truth and Satisfaction Cezary CiesÌlinÌski
6 Inductive Plausibility and Certainty: A Multimodal Paraconsisent and Nonmonotonic Logic Ricardo Silvestre
7 On the Reception of Cantorâs Theory of Infinity (Mathematicians Vs. Theologians) Roman Murawski
8 How Is the World Mathematical? Michael Heller
9 An Analysis of Paradoxes Anna WoÌjtowicz
10 Computation and Visualization Thought Experiments after Lakatosâs Heuristic Guessing Method (Semantics of Thought Experiments â Pt. Mathematical Thought Experiments) C. Peter Hertogh
Closing Words: Are Dogs Logical Animals? Jean-Yves BeÌziau
Index
Introduction: Philosophy Asking about the Foundations of Logic and Mathematics Marcin TrepczynÌski
1 From Speculative to Practical Foundations of Mathematics: A Communication-Centered Account Vladislav Shaposhnikov
2 Is There an Absolute Mathematical Reality? Zbigniew KroÌl
3 Mathematical Modalities and Mathematical Explanations Krzysztof WoÌjtowicz
4 Apriorism, Aposteriorism and the Genesis of Logic Jan WolenÌski
5 On Some Problems with Truth and Satisfaction Cezary CiesÌlinÌski
6 Inductive Plausibility and Certainty: A Multimodal Paraconsisent and Nonmonotonic Logic Ricardo Silvestre
7 On the Reception of Cantorâs Theory of Infinity (Mathematicians Vs. Theologians) Roman Murawski
8 How Is the World Mathematical? Michael Heller
9 An Analysis of Paradoxes Anna WoÌjtowicz
10 Computation and Visualization Thought Experiments after Lakatosâs Heuristic Guessing Method (Semantics of Thought Experiments â Pt. Mathematical Thought Experiments) C. Peter Hertogh
Closing Words: Are Dogs Logical Animals? Jean-Yves BeÌziau
Index
All interested in philosophy of sciences, especially philosophy of logic and philosophy of mathematics.