Infinity and Truth

Chitat Chong, Qi Feng, Theodore A Slaman e W Hugh Woodin 

World Scientific Publishing Company | 2014 | páginas | rar - pdf | 1,6 Mb

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This volume is based on the talks given at the Workshop on Infinity and Truth held at the Institute for Mathematical Sciences, National University of Singapore, from 25 to 29 July 2011. The chapters are by leading experts in mathematical and philosophical logic that examine various aspects of the foundations of mathematics. The theme of the volume focuses on two basic foundational questions: (i) What is the nature of mathematical truth and how does one resolve questions that are formally unsolvable within the Zermelo Fraenkel Set Theory with the Axiom of Choice, and (ii) Do the discoveries in mathematics provide evidence favoring one philosophical view over others? These issues are discussed from the vantage point of recent progresses in foundational studies.

The final chapter features questions proposed by the participants of the Workshop that will drive foundational research. The wide range of topics covered here will be of benefit to students, researchers and mathematicians interested in the foundations of mathematics.

Readership: Mathematicians, philosophers, scientists, graduate students, academic institutions, and research organizations interested in logic and the philosophy of mathematics.

CONTENTS

Foreword vii

Preface ix

Section I. Invited Lectures

Absoluteness, Truth, and Quotients 1

Ilijas Farah

A Multiverse Perspective on the Axiom of Constructibility 25

Joel David Hamkins

Hilbert, Bourbaki and the Scorning of Logic 47

A. R. D. Mathias

Toward Objectivity in Mathematics 157

Stephen G. Simpson

Sort Logic and Foundations of Mathematics 171

Jouko Vaananen

Reasoning about Constructive Concepts 187

Nik Weaver

Perfect Infinities and Finite Approximation 199

Boris Zilber

Section II. Special Session

An Objective Justification for Actual Infinity? 225

Stephen G. Simpson

Oracle Questions 229

Theodore Slaman and W. Hugh Woodin