Epistemology versus Ontology

Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf

Nonfiction, Science & Nature, Mathematics, Logic, Religion & Spirituality, Philosophy
Cover of the book Epistemology versus Ontology by , Springer Netherlands
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: ISBN: 9789400744356
Publisher: Springer Netherlands Publication: July 10, 2012
Imprint: Springer Language: English
Author:
ISBN: 9789400744356
Publisher: Springer Netherlands
Publication: July 10, 2012
Imprint: Springer
Language: English

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?

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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?

More books from Springer Netherlands

Cover of the book Time and Ethics by
Cover of the book The Capability Approach, Technology and Design by
Cover of the book Mechanisms of Polymer Degradation and Stabilisation by
Cover of the book Handbook of Synthetic Substrates by
Cover of the book On the Teaching of Linear Algebra by
Cover of the book Nanoscience Advances in CBRN Agents Detection, Information and Energy Security by
Cover of the book Children’s Rights and the Capability Approach by
Cover of the book The Commentary of Conrad of Prussia on the De Ente et Essentia of St. Thomas Aquinas by
Cover of the book Greatness and Philosophy by
Cover of the book The Demographic Transition and Development in Africa by
Cover of the book Einstein and Aquinas: A Rapprochement by
Cover of the book Genomics, Obesity and the Struggle over Responsibilities by
Cover of the book Sulphur in Plants by
Cover of the book Microwave-Induced Synthesis of Aromatic Heterocycles by
Cover of the book Climate Change and Sustainable Urban Development in Africa and Asia by
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy