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Identity, individuality and indistinguishability in physics and mathematics
1Laboratoire SPHERE (UMR 7219), Université Paris Cité - CNRS, 8 Rue Albert Einstein, Bâtiment Olympe de Gouge, 75013 Paris, France.
Summary
This survey explores identity, individuality, and indistinguishability in physics and mathematics. Indistinguishability is a key structural feature, not a problem to be solved.
Area of Science:
- Explores foundational concepts in theoretical physics and mathematics.
- Focuses on the philosophical and scientific underpinnings of identity and individuality.
Background:
- Discusses longstanding scientific and philosophical debates surrounding identity, individuality, and indistinguishability.
- Highlights the relevance of these concepts across various scientific disciplines.
Purpose of the Study:
- To critically analyze different viewpoints on the existence of indistinguishable objects in scientific theories.
- To underscore the formal significance of indistinguishability in physics and mathematics.
Main Methods:
- Conducts a survey of existing literature and theories.
- Critically analyzes positions on indistinguishable objects within quantum mechanics, gauge theories, and homotopy type theory.
Main Results:
- Identifies various forms of indistinguishability across different scientific domains.
- Argues that indistinguishability is a fundamental structural element rather than a problem.
Conclusions:
- Indistinguishability is a rich formal structure integral to theories in physics and mathematics.
- Emphasizes the need for a deeper understanding of indistinguishability's role.
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