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:  by appointment. 

Course requirement: Graduate students will be asked to write a paper on some topic related to the course. Undergraduates have the option to either write a paper or take a (take-home) final exam. The paper/exam will be due on the thursday of finals week.   Paper topics must be approved in advance, and students are strongly urged to submit a preliminary draft or detailed outline for comments in advance of final submission.  

Assigned Reading: The course outline that follows lists both published articles and handouts that I have prepared.  (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.      Introduction

II.    Determinism (and Indeterminism) in Classical Physics

Norton, John, "The Dome:  An Unexpectedly Simple Failure of Determinism",  Philosophy of Science, vol. 75, no. 5, 2008, 786-798

Malament, David, "Norton's Slippery Slope", Philosophy of Science, vol. 75, no. 5, 2008, 799-816.

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