David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory. In those papers, the main idea was to assign a sieve as a partial and contextual truth-value to a proposition that the value of a quantity lies in a certain set D of real numbers. Here we relate such sieve-valued valuations to valuations that assign to quantities subsets, rather than single elements, of their spectrum (we call these interval valuations). There are two main results. First, there is a natural correspondence between these two kinds of valuation, which uses the notion of a state's support for a quantity (Section 3). Second, if one starts with a more general notion of interval valuation, one sees that our interval valuations based on the notion of support (and correspondingly, our sieve-valued valuations) are a simple way to secure certain natural properties of valuations, such as monotonicity (Section 4)
|Keywords||No keywords specified (fix it)|
No categories specified
(categorize this paper)
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
Goro Kato & Tsunefumi Tanaka (2006). Double-Slit Interference and Temporal Topos. Foundations of Physics 36 (11):1681-1700.
Similar books and articles
Ehud Hrushovski & Itamar Pitowsky (2004). Generalizations of Kochen and Specker's Theorem and the Effectiveness of Gleason's Theorem. Studies in History and Philosophy of Science Part B 35 (2):177-194.
Alexandra Shlapentokh (2003). Existential Definability with Bounds on Archimedean Valuations. Journal of Symbolic Logic 68 (3):860-878.
Gary M. Hardegree (2005). Completeness and Super-Valuations. Journal of Philosophical Logic 34 (1):81 - 95.
Alexander Bochman (1990). Concerted Instant-Interval Temporal Semantics. II. Temporal Valuations and Logics of Change. Notre Dame Journal of Formal Logic 31 (4):580-601.
Steven E. Edwards (1987). In Defense of Environmental Economics. Environmental Ethics 9 (1):73-85.
Bo Petersson (2011). Axel Hägerström and His Early Version of Error Theory. Theoria 77 (1):55-70.
Chris Isham & Jeremy Butterfield, A Topos Perspective on the Kochen-Specker Theorem: I. Quantum States as Generalised Valuations.
John Hamilton, Chris Isham & Jeremy Butterfield, A Topos Perspective on the Kochen-Specker Theorem: III. Von Neumann Algebras as the Base Category.
Added to index2009-01-28
Total downloads29 ( #130,329 of 1,790,229 )
Recent downloads (6 months)9 ( #93,905 of 1,790,229 )
How can I increase my downloads?