Journal of Philosophical Logic 36 (4):449 - 472 (2007)
|Abstract||A non-monotonic theory of probability is put forward and shown to have applicability in the quantum domain. It is obtained simply by replacing Kolmogorov’s positivity axiom, which places the lower bound for probabilities at zero, with an axiom that reduces that lower bound to minus one. Kolmogorov’s theory of probability is monotonic, meaning that the probability of A is less then or equal to that of B whenever A entails B. The new theory violates monotonicity, as its name suggests; yet, many standard theorems are also theorems of the new theory since Kolmogorov’s other axioms are retained. What is of particular interest is that the new theory can accommodate quantum phenomena (photon polarization experiments) while preserving Boolean operations, unlike Kolmogorov’s theory. Although non-standard notions of probability have been discussed extensively in the physics literature, they have received very little attention in the philosophical literature. One likely explanation for that difference is that their applicability is typically demonstrated in esoteric settings that involve technical complications. That barrier is effectively removed for non-monotonic probability theory by providing it with a homely setting in the quantum domain. Although the initial steps taken in this paper are quite substantial, there is much else to be done, such as demonstrating the applicability of non-monotonic probability theory to other quantum systems and elaborating the interpretive framework that is provisionally put forward here. Such matters will be developed in other works.|
|Keywords||No keywords specified (fix it)|
|Through your library||Configure|
Similar books and articles
L. Hardy (2003). Probability Theories in General and Quantum Theory in Particular. Studies in History and Philosophy of Science Part B 34 (3):381-393.
David Atkinson & Jeanne Peijnenburg (1999). Probability as a Theory Dependent Concept. Synthese 118 (3):307-328.
Hugues Leblanc (1989). The Autonomy of Probability Theory (Notes on Kolmogorov, Rényi, and Popper). British Journal for the Philosophy of Science 40 (2):167-181.
Meir Hemmo (2007). Quantum Probability and Many Worlds. Studies in History and Philosophy of Science Part B 38 (2):333-350.
Fred Kronz (2008). Non-Monotonic Probability Theory for N-State Quantum Systems. Studies in History and Philosophy of Science Part B 39 (2):259-272.
D. Atkinson (1998). The Light of Quantum Mechanics. Dialectica 52 (2):103–126.
Richard Bradley (2006). Adams Conditionals and Non-Monotonic Probabilities. Journal of Logic, Language and Information 15 (1-2).
Vieri Benci, Leon Horsten & Sylvia Wenmackers (forthcoming). Non-Archimedean Probability. Milan Journal of Mathematics.
James Hawthorne (1988). A Semantic Approach to Non-Monotonic Conditionals. In J. F. Lemmer & L. N. Kanal (eds.), Uncertainty in Artificial Intelligence 2. Elsevier.
Added to index2009-01-28
Total downloads7 ( #133,420 of 549,068 )
Recent downloads (6 months)1 ( #63,185 of 549,068 )
How can I increase my downloads?