
Published online:
01 September 2006
Published in print:
22 June 2006
Online ISBN:
9780191603952
Print ISBN:
9780199278244
Contents
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6.1 THE STATEMENT OF THE PROBLEM 6.1 THE STATEMENT OF THE PROBLEM
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6.2 THE USE OF ‘STANDARD LANGUAGES’ 6.2 THE USE OF ‘STANDARD LANGUAGES’
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6.2.1 The Lack of Identity 6.2.1 The Lack of Identity
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6.3 IDENTITY IN CLASSICAL LOGIC AND MATHEMATICS 6.3 IDENTITY IN CLASSICAL LOGIC AND MATHEMATICS
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6.3.1 Identity in First-Order Classical Logic 6.3.1 Identity in First-Order Classical Logic
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6.3.2 Identity in Higher-Order Logic 6.3.2 Identity in Higher-Order Logic
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6.4 SET THEORY AND INDIVIDUATION 6.4 SET THEORY AND INDIVIDUATION
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6.5 CHARACTERIZING INDISTINGUISHABILITY 6.5 CHARACTERIZING INDISTINGUISHABILITY
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6.5.1 Weyl's Strategy 6.5.1 Weyl's Strategy
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6.5.2 Indiscernibility and Structures 6.5.2 Indiscernibility and Structures
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6.5.3 The Implications for the Philosophy of Quantum Theory 6.5.3 The Implications for the Philosophy of Quantum Theory
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Chapter
6 A Problem for Present-Day Mathematics
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Pages
238–271
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Published:June 2006
Cite
French, Steven, and Décio Krause, 'A Problem for Present-Day Mathematics', Identity in Physics: A Historical, Philosophical, and Formal Analysis (Oxford , 2006; online edn, Oxford Academic, 1 Sept. 2006), https://doi.org/10.1093/0199278245.003.0006, accessed 9 May 2025.
Abstract
This chapter explores Manin’s suggestion that formal axioms for indiscernible objects in physics should be given. Collections of such objects cannot be regarded as sets, since such sets are typically taken to be collections of distinguishable objects. The theory of identity in classical logic and set theory is considered to lay the groundwork for the discussion of the corresponding theory for (truly) indiscernible objects in Chapter 7. The usual ways of accommodating such objects in standard logic and mathematics are critically assessed, with emphasis on the concept of indiscernibility in a structure.
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