Topos theory as a framework for partial truth
|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 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.|
|Keywords||No keywords specified (fix it)|
No categories specified
(categorize this paper)
|External links||This entry has no external links. Add one.|
|Through your library||Only published papers are available at libraries|
Similar books and articles
Volker Halbach, Axiomatic Theories of Truth. Stanford Encyclopedia of Philosophy.
William M. Farmer (1990). A Partial Functions Version of Church's Simple Theory of Types. Journal of Symbolic Logic 55 (3):1269-1291.
Otávio Bueno (2000). Quasi-Truth in Quasi-Set Theory. Synthese 125 (1-2):33-53.
John Hamilton, Chris Isham & Jeremy Butterfield, A Topos Perspective on the Kochen-Specker Theorem: III. Von Neumann Algebras as the Base Category.
Chris Isham & Jeremy Butterfield, A Topos Perspective on the Kochen-Specker Theorem: I. Quantum States as Generalised Valuations.
Jeremy Butterfield & Chris Isham, A Topos Perspective on the Kochen-Specker Theorem: IV. Interval Valuations.
Added to index2009-01-28
Total downloads9 ( #122,328 of 722,722 )
Recent downloads (6 months)0
How can I increase my downloads?