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The Continuum Problem may be formulated thus: how many points are there on a straight line? The attempt to provide a mathematically precise answer to this apparently straightforward question gave rise to two great achievements of 20th century logic: the proofs of the consistency and independence of the axiom of choice and the continuum hypothesis from rest of set theory. These results, in turn, raise deep conceptual and philosophical questions about the notion of set: What are sets? In what sense, i f any, do sets exist? How do we attain knowledge of these entities? Since set theory is the common language of modern mathematics, these questions cannot be ignored by any adequate philosophical account of mathematics. The primary goal of this seminar is to study the consistency and independence proofs in some detail, so as to be able to broach some foundational issues in the philosophy of mathematics.
Unless preregistered students attend the first class meeting or communicate directly with the instructor prior to the first class, they will be dropped from the class list. NOTE: Students must still submit a completed Drop/Add form to the Registrar's Office.
COURSE FORMAT: Seminar
Level: UGRD Credit: 1 Gen Ed Area Dept: SBS PHIL Grading Mode: Student Option
Prerequisites: MATH241 AND MATH243 AND PHIL232 Links to Web Resources For This Course.
Last Updated on MAR-26-2001
Copyright Wesleyan University, Middletown, Connecticut, 06459