Online research in philosophy

This paper draws its title from the recent symposium of which it was part; it attempts to respond to the question raised by that title, taking current work in set theory into account. To this end the paper contrasts set theory with number theory, examines a severe brand of set-theoretic realism that is suggested by a passage from Godel, and sketches a first-order way of looking at the results about competing extensions of Zermelo-Fraenkel set theory. A formalistic sentiment may be (...) detectable in some portions of the paper. (shrink)

Peirce writes "It is an indubitable result of the theory of probabilities that every gambler, if he continues long enough, must ultimately be ruined... if he plays long enough he will be sure some time to have such a run against him as to exhaust his entire fortune.... The same thing is true of an insurance company. Let the directors take the utmost pains... according to the doctrine of chances, the time must come, at last, when their losses will bring (...) them to a stop." This note shows that under the most plausible interpretation of the quoted passage Peirce is committed to a mathematical untruth. (shrink)