The course will examine a cluster of interrelated issues concerning probability, determinism, logic, and the foundations of quantum mechanics. First we will consider senses in which classical Newtonian mechanics is (and is not) deterministic. Then we will carefully analyze (versions of) "Bell's theorem". These can be understood to show the impossibility of reconciling determinism with "locality" in microphysics. They can also be taken to show that "quantum probability" is non-standard, i.e., not in conformity with the characterization of probability given by Kolmogorov.  Finally, we will consider certain controversial claims of Hilary Putnam about the connection between probability and logic in quantum mechanics. (It was Putnam's view, at least at one time, that "quantum probability" is standard, but "quantum logic" is not.)

The course will not presuppose any specific course work in physics, but will take for granted familiarity with formal logic (LPS 30 or its equivalent), and basic undergraduate mathematics (at least calculus and linear algebra). More advanced prior training in mathematics and/or physics will certainly be helpful.

Instructor: David Malament, SST 757, 824-7374. I can be reached, most reliably, by e-mail:  dmalamen@uci.edu. Office hours:  Tu 11-12, and by appointment. 

Course requirements: Auditors are welcome. Students who want to take the course for a grade will be asked to submit a small number of problem sets, and either write a short paper (on the order of 10 pages) on an approved topic or take a final (take-home) exam.  The exam/paper will be due on Thursday, December 7th.

Assigned Reading: The course outline that follows lists both published articles and handouts that I have prepared. Some can  be downloaded. Others will available in the tray outside my office for duplication. (Note:  The handouts are rather terse and formal in character. They are intended to supplement course lectures, not to be read on their own.)  

Supplemental Reading:   I have also put together a short list of supplemental readings.   Those looking for paper topics (and others) may find it useful. But it should be understood that  none of the works listed are required and some presuppose a fair bit of technical background. 

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Tentative Course Outline with Assigned Readings 

I.      Overview 

II.    Determinism (and Indeterminism) in Classical Physics 

Hoefer, Carl, "Causal Determinism", The Stanford Encyclopedia of Philosophy (Summer 2008 Edition), Edward N. Zalta (ed.)

Norton, John, "The Dome: A Simple Violation of Determinism in Newtonian Mechanics"    (This is an online excerpt (with animation!)  from  "Causation as Folk Science", The Philosopher's Imprint, volume 3, number 4, November 2003.)

Malament, David, "Norton's Slippery Slope"  (forthcoming in Philosophy of Science)

III.     Bell's Theorem  

Notes on Bell's Theorem

Fine, Arthur, "Do Correlations Need to Be Explained?", in Cushing, James and McMullin, Ernan (eds.), Philosophical Consequences of Quantum Theory: Reflections on Bell's Theorem, University of Notre Dame Press, 1989

IV.  "Quantum Logic" 

Notes on Quantum Logic

Putnam, Hilary, "Is Logic Empirical?", in Wartofsky, Marx and Cohen, Robert (eds.),  Boston Studies in Philosophy of Science 5, Reidel, 1968, 216-241;  also reprinted as "The Logic of Quantum Mechanics", in Putnam's Philosophical Papers I, Cambridge University Press, 1975