Book Epistemology Versus Ontology: Essays on the Philosophy and Foundations of Mathematics in Honour of p lindstr m., sten

portada Epistemology Versus Ontology: Essays on the Philosophy and Foundations of Mathematics in Honour of per Martin-Lof (Logic, Epistemology, and the Unity of Science)

Type

Physical Book

Publisher

Springer

Author

lindstr m., sten

Year

2012

Language

English

Pages

385

Format

Hardcover

ISBN

940074434x

ISBN13

9789400744349

Edition No.

2012

Synopsis "Epistemology Versus Ontology: Essays on the Philosophy and Foundations of Mathematics in Honour of per Martin-Lof (Logic, Epistemology, and the Unity of Science)"

This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice (ZFC). This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively pursued today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics?

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Epistemology Versus Ontology: Essays on the Philosophy and Foundations of Mathematics in Honour of per Martin-Lof (Logic, Epistemology, and the Unity of Science) - lindstr m., sten

Synopsis "Epistemology Versus Ontology: Essays on the Philosophy and Foundations of Mathematics in Honour of per Martin-Lof (Logic, Epistemology, and the Unity of Science)"

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