Lolli, Gabriele, Panza, Marco, Venturi, Giorgio (Eds.)
2015, XIX, 336 p. 27 illus., 10 illus. in color.
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Allows young (untenured) scholars meet philosophy in their (non philosophical) work
Revisits traditional questions and explores new realities
Demonstrates the limits of formalization
This book brings together young researchers from a variety of fields within mathematics, philosophy and logic. It discusses questions that arise in their work, as well as themes and reactions that appear to be similar in different contexts. The book shows that a fairly intensive activity in the philosophy of mathematics is underway, due on the one hand to the disillusionment with respect to traditional answers, on the other to exciting new features of present day mathematics. The book explains how the problem of applicability once again plays a central role in the development of mathematics. It examines how new languages different from the logical ones (mostly figural), are recognized as valid and experimented with and how unifying concepts (structure, category, set) are in competition for those who look at this form of unification. It further shows that traditional philosophies, such as constructivism, while still lively, are no longer only philosophies, but guidelines for research. Finally, the book demonstrates that the search for and validation of new axioms is analyzed with a blend of mathematical historical, philosophical, psychological considerations.
Content Level »Research
Keywords »Axioms of Set Theory - Church’s Thesis and Naturalness of Axioms - Constructibility, Naturalism, Axiomatics - Constructive Approach to the Infinitesimal Analysis - Dynamics of Diagrams in Knot Theory - Fundamental Theorem of Algebra - Gottlob Frege’s Grundgesetze - Husserl Raumbuch - Intuitionism and Cognitive Sciences - Languages and the Extension of Knowledge - Mathematics is a Science of Structures - Parametric Polymorphism - Philosophy of Mathematics - Structuralism, Categorical and Set Theoretical Foundations