Mathematics without numbers : towards a modal-structural interpretation
著者
書誌事項
Mathematics without numbers : towards a modal-structural interpretation
Clarendon Press , Oxford University Press, 1989
- :pbk.
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注記
Bibliography: p. [145]-150
Includes index
内容説明・目次
内容説明
This treatise presents an interpretation of mathematics as the investigation of "structural possibilities", as opposed to absolute Platonic objects. After treating the natural numbers and analysis, the approach is extended to set theory, where it is shown how to dispense with a fixed universe of sets. Finally, problems of application to the physical world are addressed.
目次
- Part 1 The natural numbers and analysis: the modal-structural framework - the hypothetical component
- the categorical component - an axiom of infinity and a derivation (inspired by Dedekind with help from Frege)
- justifying the translation scheme
- justification from within
- extensions
- the question of nominalism. Part 2 Set theory: informal principles - many versus one
- the relevant structures
- unbounded sentences - Putnam semantics
- axioms of infinity - looking back
- axioms of infinity - climbing up. Part 3 Mathematics and physical reality: the leading ideas
- carrying the mathematics of modern physics
- global solutions
- metaphysical realist commitments - "synthetic determination" relations
- a role for representation theorems.
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