Epistemology versus Ontology:Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf

图书简介

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?

Introduction by the editors.- Part I. Philosophy of Logic and Mathematics.- Kant and Real Numbers: Mark van Atten.- Wittgenstein’s Diagonal Argument: A Variation on Cantor and Turing: Juliet Floyd.- Aristotle’s Deductive Logic: A Proof-Theoretical Study: Jan von Plato.- Truth and Proof: Ontological or Epistemic concepts?: Dag Prawitz.- In the Shadow of Incompleteness: Hilbert and Gentzen: Wilfried Sieg.- Causality, biological evolution, and the rules of logic: Jan Smith.- The “Middle Wittgenstein” and Modern Mathematics: Sören Stenlund.- Part II. Foundations.- Type theory and homotopy: Steve Awodey.- A Computational Interpretation of Forcing in Type Theory: Thierry Coquand; Guilhem Jaber.- Program Testing and Constructive Validity: Peter Dybjer.- Normativity in Logic: Jean-Yves Girard.- Constructivist and Structuralist Foundations: Bishop’s and Lawvere’s Theories of Sets: Erik Palmgren.- Machine Translation and Type Theory: Aarne Ranta.- Constructive Zermelo-Fraenkel Set Theory and Powerset: Michael Rathjen.- Real and Ideal Entities in a Minimalist Constructive Foundation (in progress): Giovanni Sambin.- Primitive Recursive Arithmetic: Its Role in the Foundations of Mathematics: William Tait.- Second Order Logic, Set Theory and Foundations of Mathematics: Jouko Väänänen.-

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Epistemology versus Ontology:Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf（Logic, Epistemology, and the Unity of Science） 认识论与本体论：哲学与数学基础文集,纪念Per Martin-Lf 马克思主义哲学

Epistemology versus Ontology:Essays on the Philosophy and Foundations of Mathematics in Honour of Per Martin-Löf（Logic, Epistemology, and the Unity of Science）

认识论与本体论：哲学与数学基础文集,纪念Per Martin-Lf
马克思主义哲学