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Topos Theory as a Framework for Partial Truth

Butterfield, Jeremy (2000) Topos Theory as a Framework for Partial Truth. [Preprint]


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This paper develops some ideas from previous work (coauthored, mostly with C.J.Isham). In that work, the main proposal is to assign as the value of a physical quantity in quantum theory (or classical physics), not a real number, but a certain kind of set (a sieve) of quantities that are functions of the given quantity. The motivation was in part physical---such a valuation illuminates the Kochen-Specker theorem; in part mathematical---the valuations arise naturally in the theory of presheaves; and in part conceptual---the valuations arise from applying to propositions about the values of physical quantities some general axioms governing partial truth for any kind of proposition. In this paper, I give another conceptual motivation for the proposal. I develop (in Sections 2 and 3) the notion of a topos (of which presheaves give just one kind of example); and explain how this notion gives a satisfactory general framework for making sense of the idea of partial truth. Then I review (in Section 4) how our proposal applies this framework to the case of physical theories.

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Item Type: Preprint
Butterfield, Jeremy
Keywords: Topos theory, category theory, partial truth, Kochen-Specker theorem, intuitionistic logic
Subjects: Specific Sciences > Mathematics
Specific Sciences > Physics > Quantum Mechanics
Depositing User: Jeremy Butterfield
Date Deposited: 09 Mar 2001
Last Modified: 07 Oct 2010 15:10
Item ID: 192

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