Peter Abelard (1079–1142 ce) was the most wide‐ranging philosopher of the twelfth century. He quickly established himself as a leading teacher of logic in and near Paris shortly after 1100. After his affair with Heloise, and his subsequent castration, Abelard became a monk, but he returned to teaching in the Paris schools until 1140, when his work was condemned by a Church Council at Sens. His logical writings were based around discussion of the “Old Logic”: Porphyry's Isagoge, aristotle'S Categories and (...) On Interpretation and boethius'S textbook on topical inference. They comprise a freestanding Dialectica (“Logic”; probably c.1116), a set of commentaries (known as the Logica [Ingredientibus], c. 1119) and a later (c. 1125) commentary on the Isagoge (Logica Nostrorum Petititoni Sociorum or Glossulae). In a work Abelard called his Theologia, issued in three main versions (between 1120 and c.1134), he attempted a logical analysis of trinitarian relations and explored the philosophical problems surrounding God's claims to omnipotence and omniscience. The Collationes (“Debates,” also known as “Dialogue between a Christian, a Philosopher and a Jew”; probably c.1130) present a rational investigation into the nature of the highest good, in which the Christian and the Philosopher (who seems to be modeled on a philosopher of pagan antiquity) are remarkably in agreement. The unfinished Scito teipsum (“Know thyself,” also known as the “Ethics”; c.1138) analyses moral action. (shrink)

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)