|Abstract||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)|
|Categories||No categories specified (fix it)|
|Through your library||Only published papers are available at libraries|
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 downloads14 ( #83,218 of 549,753 )
Recent downloads (6 months)1 ( #63,425 of 549,753 )
How can I increase my downloads?