Quantum Logic and Possibility Structures

Dissertation, University of Maryland, College Park (1992)

Abstract
Quantum mechanics is difficult to understand not because it is irreducibly probabilistic. It is difficult to understand because the probabilities themselves seem to defy reasonable interpretation. I propose that quantum logic, realistically construed as telling us something about the physical world, is one part of such a reasonable interpretation. ;The main idea behind a realist quantum logic is that a logic generates a possibility structure, and that quantum logic generates the possibility structure of quantum mechanical systems. Most work on quantum logic has involved a description of this possibility structure, and arguments for why the differences between the classical and quantum possibility structures account for the differences between classical and quantum mechanical systems. Less attention has been paid to the physical meaning of the quantum possibility structure. This is primarily the issue I will address. In doing so it will be necessary to consider a variety of issues including: what a possibility structure is, how, in general, possibility structures are given physical meaning, and how the possibility structure generated by quantum logic is related to other modalities occurring in quantum mechanics. ;The dissertation is divided into five chapters. The first is an argument that, despite first appearances, classical logic and probability are not disconfirmed by the experimental violations of Bell's inequalities. Thus, one cannot argue for quantum logic on empirical grounds. The second chapter is a consideration of Pitowsky's quantum logic, and an argument against his claim that all realist quantum logics are non-local hidden-variables theories. In the third chapter, I present an account of physical modality based upon logical modality and physical theory. Chapter four is an argument that there are two levels of modality in quantum mechanics: one corresponding to the possibility structure given by quantum logic, and the other corresponding to the theory's probabilistic character. In the last chapter, I present a version of quantum logic and show how it characterizes the possibility structure of quantum mechanics
Keywords No keywords specified (fix it)
Categories (categorize this paper)
Options
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 44,474
External links

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.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Are the Laws of Quantum Logic Laws of Nature?Peter Mittelstaedt - 2012 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 43 (2):215-222.
Quantum Logic, Realism, and Value Definiteness.Allen Stairs - 1983 - Philosophy of Science 50 (4):578-602.
Quantum Logic and Quantum Reconstruction.Allen Stairs - 2015 - Foundations of Physics 45 (10):1351-1361.
Correlations, Contextuality and Quantum Logic.Allen Stairs & Jeffrey Bub - 2013 - Journal of Philosophical Logic 42 (3):483-499.
Von Neumann’s Concept of Quantum Logic and Quantum Probability.Miklós Rédei - 2001 - Vienna Circle Institute Yearbook 8:153-172.
Logic, Quantum Logic and Empiricism.John Bell & Michael Hallett - 1982 - Philosophy of Science 49 (3):355-379.
Systems of Quantum Logic.Satoko Titani, Heiji Kodera & Hiroshi Aoyama - 2013 - Studia Logica 101 (1):193-217.
Only If Quanta Had Logic.James H. McGrath - 1978 - PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978:268 - 275.

Analytics

Added to PP index
2015-02-02

Total views
0

Recent downloads (6 months)
0

How can I increase my downloads?

Downloads

Sorry, there are not enough data points to plot this chart.

My notes

Sign in to use this feature