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

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Abstract
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 physicalsuch a valuation illuminates the KochenSpecker theorem; in part mathematicalthe valuations arise naturally in the theory of presheaves; and in part conceptualthe 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  

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Keywords:  Topos theory, category theory, partial truth, KochenSpecker 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  
Subjects:  Specific Sciences > Mathematics Specific Sciences > Physics > Quantum Mechanics 

Date:  January 2000  
URI:  http://philsciarchive.pitt.edu/id/eprint/192 
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