From Mathematics to Philosophy Routledge Revivals 1st Edition by Hao Wang ISBN 1138687731  978-1138687738

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ISBN 10: 1138687731
ISBN 13: 978-1138687738
Author: Hao Wang

First published in 1974. Despite the tendency of contemporary analytic philosophy to put logic and mathematics at a central position, the author argues it failed to appreciate or account for their rich content. Through discussions of such mathematical concepts as number, the continuum, set, proof and mechanical procedure, the author provides an introduction to the philosophy of mathematics and an internal criticism of the then current academic philosophy. The material presented is also an illustration of a new, more general method of approach called substantial factualism which the author asserts allows for the development of a more comprehensive philosophical position by not trivialising or distorting substantial facts of human knowledge.

From Mathematics to Philosophy Routledge Revivals 1st Table of contents:

1. Introduction

   • Overview of Mathematics and Philosophy
   • The Interdisciplinary Relationship Between the Two Fields
   • A Historical Perspective

2. Philosophical Foundations of Mathematics

   • The Nature of Mathematical Truth
   • Realism vs. Anti-Realism in Mathematics
   • The Problem of Mathematical Objects

3. Logic and Philosophy

   • The Role of Logic in Mathematical Thought
   • Formal Systems and Philosophical Implications
   • Logical Positivism and Its Criticisms

4. Set Theory and the Foundations of Mathematics

   • Zermelo-Fraenkel Set Theory and Philosophical Questions
   • Paradoxes in Set Theory and Their Philosophical Impact
   • The Continuum Hypothesis and Its Philosophical Significance

5. Proof and Mathematical Justification

   • The Philosophy of Mathematical Proof
   • Constructivism and Intuitionism
   • Formalism vs. Platonism in Mathematical Practice

6. Mathematics and the Philosophy of Language

   • The Linguistic Turn and Its Impact on Mathematical Philosophy
   • Mathematical Language and Its Interpretation
   • The Philosophy of Mathematical Expression

7. The Influence of Mathematics on Other Branches of Philosophy

   • Epistemology and the Role of Mathematics
   • Ethics, Metaphysics, and the Mathematical Perspective
   • The Impact of Mathematical Methods on Philosophical Inquiry

8. The Philosophy of Infinity

   • Mathematical Conceptions of Infinity
   • The Infinite in Metaphysical and Ontological Discussions
   • The Role of Infinity in Modern Philosophy

9. Mathematics and Logic in the 20th Century

   • Developments in Mathematical Logic
   • The Impact of Gödel’s Incompleteness Theorems
   • The Rise of Computer Science and Its Philosophical Implications

10. The Future of Mathematics and Philosophy

    • The Ongoing Dialogue Between Mathematics and Philosophy
    • Emerging Trends and Philosophical Questions in Mathematics
    • The Role of Technology and Artificial Intelligence in Shaping the Future of Both Fields

11. Conclusion

    • Summary of Key Ideas and Arguments
    • The Continuing Relevance of Mathematical Philosophy
    • Final Thoughts on the Interdependence of Mathematics and Philosophy

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