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Mathematics and Its Applications

Part of the Synthese Library Book Series (volume 385)

DOI: 10.1007/978-3-319-63073-1

ISBN: 978-3-319-63072-4

Publisher: Springer International Publishing - Springer Journals

Aug 24, 2017

1 - 9 of 9 Chapters

Available

Introduction

da Silva, Jairo José

Pages: 1 –10

[Introduction: where the general outline of the book is presented, together with a criticism of the traditional approaches to the philosophy of mathematics.]
Available

Phenomenology

da Silva, Jairo José

Pages: 11 –65

[Phenomenology: where the phenomenological background of the entire work is presented and discussed.]
Available

Logic

da Silva, Jairo José

Pages: 67 –91

[Where the logical principles of identity, bivalence and non-contradiction are clarified and consequently justified as transcendental principles related to the intentional constitution of the domain of an objective science in general.]
Available

Numbers

da Silva, Jairo José

Pages: 93 –129

[Numbers: where the intentional genesis of number concepts is discussed, together with the problem of “imaginary” numbers, a particular instance of the general problem of “imaginary” entities in mathematics – how things that do not exist can be useful for knowing things that exist?]
Available

Sets

da Silva, Jairo José

Pages: 131 –151

[Sets: where the intentional genesis of the mathematical concept of set is discussed.]
Available

Space

da Silva, Jairo José

Pages: 153 –183

[Space: where the intentional genesis of the many representations of space is discussed. It introduces in a particular context the problem of the use of mathematics as a methodological toll for investigating nature.]
Available

Structures

da Silva, Jairo José

Pages: 185 –215

[Structures: where a particular transcendental-phenomenological brand of structuralism is presented. I discuss, in particular, how structures can be investigated by being interpreted in other structures, which plays a central role in my approach to the problem of the applicability of mathematics....
Available

Science

da Silva, Jairo José

Pages: 217 –249

[Science: where the applicability of mathematics, particularly in empirical science, is discussed and the effectiveness of mathematics in science, including the heuristic effectiveness, explained.]
Available

Final Considerations

da Silva, Jairo José

Pages: 251 –271

[Where certain particular issues, such as Benacerraf’s dilemma, indispensability arguments and Steiner’s challenge to “naturalism” are discussed and criticized from the philosophical perspective of the work.]

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