Book contents
- Frontmatter
- Dedication
- Contents
- Figures
- Preface
- Acknowledgements
- Symbols and Abbreviations
- 1 Introduction
- 2 Metaphysics of Mathematics
- 3 Arbitrary Objects
- 4 Mathematical Objects as Arbitrary Objects
- 5 Structure in Mathematics
- 6 Mathematical Structures
- 7 Kit Fine
- 8 Generic Systems and Mathematical Structuralism
- 9 Reasoning about Generic ω-Sequences
- 10 Probability and Random Variables
- 11 Directions for Future Research
- Bibliography
- Index
9 - Reasoning about Generic ω-Sequences
Published online by Cambridge University Press: 24 May 2019
- Frontmatter
- Dedication
- Contents
- Figures
- Preface
- Acknowledgements
- Symbols and Abbreviations
- 1 Introduction
- 2 Metaphysics of Mathematics
- 3 Arbitrary Objects
- 4 Mathematical Objects as Arbitrary Objects
- 5 Structure in Mathematics
- 6 Mathematical Structures
- 7 Kit Fine
- 8 Generic Systems and Mathematical Structuralism
- 9 Reasoning about Generic ω-Sequences
- 10 Probability and Random Variables
- 11 Directions for Future Research
- Bibliography
- Index
Summary
This chapter is logical in character. The focus is on the logical properties of one particular generic structure: the generic omega-sequence. I take the perspective that is internal to arithmetic, from which arithmetic investigates \emph{one} structure.
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- The Metaphysics and Mathematics of Arbitrary Objects , pp. 162 - 188Publisher: Cambridge University PressPrint publication year: 2019