FOM: Re: FoM: Quantum Logic

[A.P. Hazen]

Todd Wilson asks for references on "Quantum Logic".  Level unspecified;
THIS reply assumes (except at the bottom) that he wants the references to
give to a curious undergraduate.
  There is a textbook by Peter Gibbins (sp? maybe Gribbins), "Particles and
Paradoxes": this is largely philosophy of science, but presents a natural
deduction formulation (in the style of Lemmon's textbook) of orthomodular
logic.
   For philosophical propaganda in favor of q.l., various papers by Hilary
Putnam reprinted in his "Matter, Mathematics and Method" (I may have the
order of words in the title wrong; it is vol. I of his "Philosophical
Papers").
   Note that "Quantum Logic" is not a uniquely referring expression:
orthomodular logic is the most studied, but Reichenbach's book argued for a
certain 3-valued logic, and there are proposals based on partial Boolean
algebras: there is a logical calculus based on this last idea by Yannis
Delmas-Rigoutsos in "Journal of Philosophical Logic," vol. 26 (1997), pp.
57-67.  I found B.C. Van Frassen's discussion in "The Labyrinth of Quantum
Logics" (in Robert S. Cohen, ed.,"Logical and epistemological Studies in
Contemporary Physics," Reidel 1974, pp. 224-254) useful in giving a
philosophical framework in which to understand the relations between these
"logics." (I didn't find it a particularly easy read, but an undergraduate
with a reasonable math background could get a lot out of it.
----
    Wilson asks in particular for references about the relevance of q.l. to
f.o.m.  There is an easy negative result due to Mike Dunn, showing that a
set theoretic extensionality principle collapses higher-order orthomodular
logic into classical logic: his paper is in a volume called "Analytic
Philosophy: a defense by example," edd. by (?firstname forgotten?) Austin.
     I am not familiar with the last of Enderton's references in his
posting, but the Dalla Chiara and Beltrametti &c references are both good:
Dalla Chiara probably being the more introductory.
----
Allen Hazen
Philosophy Department
University of Melbourne