Mathematics and Its Applications

1. Front Matter

   Pages i-vii

   PDF

2. Introduction

   • Jairo José da Silva

   Pages 1-10

3. Phenomenology

   • Jairo José da Silva

   Pages 11-65

4. Logic

   • Jairo José da Silva

   Pages 67-91

5. Numbers

   • Jairo José da Silva

   Pages 93-129

6. Sets

   • Jairo José da Silva

   Pages 131-151

7. Space

   • Jairo José da Silva

   Pages 153-183

8. Structures

   • Jairo José da Silva

   Pages 185-215

9. Science

   • Jairo José da Silva

   Pages 217-249

10. Final Considerations

    • Jairo José da Silva

    Pages 251-271

11. Back Matter

    Pages 273-275

    PDF

This monograph offers a fresh perspective on the applicability of mathematics in science. It explores what mathematics must be so that its applications to the empirical world do not constitute a mystery. In the process, readers are presented with a new version of mathematical structuralism.


The author details a philosophy of mathematics in which the problem of its applicability, particularly in physics, in all its forms can be explained and justified. Chapters cover: mathematics as a formal science, mathematical ontology: what does it mean to exist, mathematical structures: what are they and how do we know them, how different layers of mathematical structuring relate to each other and to perceptual structures, and how to use mathematics to find out how the world is.


The book simultaneously develops along two lines, both inspired and enlightened by Edmund Husserl’s phenomenological philosophy. One line leads to the establishmentof a particular version of mathematical structuralism, free of “naturalist” and empiricist bias. The other leads to a logical-epistemological explanation and justification of the applicability of mathematics carried out within a unique structuralist perspective. This second line points to the “unreasonable” effectiveness of mathematics in physics as a means of representation, a tool, and a source of not always logically justified but useful and effective heuristic strategies.

• Philosophy of Mathematics
• Structuralism
• applicability of mathematics in science
• Mathematics as a formal science
• Mathematical ontology
• Mathematical structures
• How to use mathematics to find out how the world is
• On Husserl’s Philosophy of Logic and Mathematics

• Researcher - CNPq, Ministry of Science, Technology, Innovation and Communication - Brazil, Brasilia, DF, Brazil

  Jairo José da Silva

Professor of Mathematics (retired) – State University of São Paulo, my main interests are the philosophy of formal and empirical sciences, phenomenology and the foundations of mathematics, fields which concentrate my publications. I am the co-author, together with Claire Ortiz Hill, of the book The Road Not Taken – On Husserl’s Philosophy of Logic and Mathematics (London: College Publications, 2013). I am a member of the Centre of Philosophy of the University of Lisbon and a researcher at the National Council of Scientific and Technological Development (CNPq) of the Brazilian Ministry of Science and Technology.

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