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Mathematics without numbers : towards a modal-structural interpretation /
Modal logic is combined with notions of part/whole (mereology) enabling a systematic interpretation of ordinary mathematical statements as asserting what would be the case in any (suitable) structure there (logically) might be, e.g. for number theory, functional analysis, algebra, pure geometry, etc...
| Call Number: | Libro Electrónico |
|---|---|
| Main Author: | |
| Format: | Electronic eBook |
| Language: | Inglés |
| Published: |
Oxford : New York :
Clarendon Press ; Oxford Univ. Press,
©1989.
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| Series: | Clarendon Paperbacks Ser.
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| Subjects: | |
| Online Access: | Texto completo |
Table of Contents:
- Introduction
- 1. The Natural Numbers and Analysis
- 0. Introduction
- 1. The Modal-Structuralist Framework: The Hypothetical Component
- 2. The Categorical Component: An Axiom of Infinity and a Derivation (inspired by Dedekind, with help from Frege)
- 3. Justifying the Translation Scheme
- 4. Justification from within
- 5. Extensions
- 6. The Question of Nominalism
- 2. Set Theory
- 0. Introduction
- 1. Informal Principles: Many vs. One
- 2. The Relevant Structures
- 3. Unbounded Sentences: Putnam Semantics
- 4. Axioms of Infinity: Looking back.
- 5. Axioms of Infinity: Climbing up
- Appendix
- 3. Mathematics and Physical Reality
- 0. Introduction
- 1. The Leading Ideas
- 2. Carrying the Mathematics of Modern Physics: RA(2) as a Framework
- 3. Global Solutions
- 4. "Metaphysical Realist" Commitments? "Synthetic Determination" Relations
- 5. A Role for Representation Theorems?
- Bibliography
- Index
- A
- B
- C
- D
- E
- F
- G
- H
- I
- J
- K
- L
- M
- N
- O
- P
- Q
- R
- S
- T
- V
- W
- Z.