David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Symbolic Logic 59 (2):501-515 (1994)
With a certain graphic interpretation in mind, we say that a function whose value at every point in its domain is a nonempty set of real numbers is an Abacus. It is shown that to every collection C of abaci there corresponds a logic, called an abacus logic, i.e., a certain set of propositions partially ordered by generalized implication. It is also shown that to every collection C of abaci there corresponds a theory JC in a classical propositional calculus such that the abacus logic determined by C is isomorphic to the poset of JC. Two examples are given. In both examples abacus logic is a lattice in which there happens to be an operation of orthocomplementation. In the first example abacus logic turns out to be the Lindenbaum algebra of JC. In the second example abacus logic is a lattice isomorphic to the ortholattice of subspaces of a Hilbert space. Thus quantum logic can be regarded as an abacus logic. Without suggesting "hidden variables" it is finally shown that the Lindenbaum algebra of the theory in the second example is a subalgebra of the abacus logic B of the kind studied in example 1. It turns out that the "classical observables" associated with B and the "quantum observables" associated with quantum logic are not unrelated. The value of a classical observable contains, in coded form, information about the "uncertainty" of a quantum observable. This information is retrieved by decoding the value of the corresponding classical observable
|Keywords||No keywords specified (fix it)|
|Categories||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
No citations found.
Similar books and articles
Othman Qasim Malhas (1987). Quantum Logic and the Classical Propositional Calculus. Journal of Symbolic Logic 52 (3):834-841.
P. Mittelstaedt & E. -W. Stachow (1978). The Principle of Excluded Middle in Quantum Logic. Journal of Philosophical Logic 7 (1):181 - 208.
E. -W. Stachow (1976). Completeness of Quantum Logic. Journal of Philosophical Logic 5 (2):237 - 280.
Bob Coecke (2002). Disjunctive Quantum Logic in Dynamic Perspective. Studia Logica 71 (1):47 - 56.
Michael R. Gardner (1971). Is Quantum Logic Really Logic? Philosophy of Science 38 (4):508-529.
Martijn Caspers, Chris Heunen, Nicolaas P. Landsman & Bas Spitters (2009). Intuitionistic Quantum Logic of an N-Level System. Foundations of Physics 39 (7):731-759.
Peter Mittelstaedt (1978). The Metalogic of Quantum Logic. PSA: Proceedings of the Biennial Meeting of the Philosophy of Science Association 1978:249 - 256.
Peter Gibbins (1987). Particles and Paradoxes: The Limits of Quantum Logic. Cambridge University Press.
E. -W. Stachow (1978). Quantum Logical Calculi and Lattice Structures. Journal of Philosophical Logic 7 (1):347 - 386.
Added to index2009-01-28
Total downloads23 ( #126,447 of 1,725,443 )
Recent downloads (6 months)1 ( #349,420 of 1,725,443 )
How can I increase my downloads?