This article is dedicated to Professor Burton Dreben on his coming of age. I owe him particular thanks for his careful reading and numerous suggestions for improvement. My thanks go also to Jose Ruiz and the referee for their helpful comments. Parts of this account were given at the 1995 summer meeting of the Association for Symbolic Logic at Haifa, in the Massachusetts Institute of Technology logic seminar, and to the Paris Logic Group. The author would like to express his thanks to the various organizers, as well as his gratitude to the Hebrew University of Jerusalem for its hospitality during the preparation of this article in the autumn of 1995.

this paper, the seminal results of set theory are woven together in terms of a unifying mathematical motif, one whose transmutations serve to illuminate the historical development of the subject. The motif is foreshadowed in Cantor's diagonal proof, and emerges in the interstices of the inclusion vs. membership distinction, a distinction only clarified at the turn of this century, remarkable though this may seem. Russell runs with this distinction, but is quickly caught on the horns of his well-known paradox, an early expression of our motif. The motif becomes fully manifest through the study of functions f :

statement of his theory of logical types.This simple version of the theory is designed to block the reasoning that leads to the paradox of the Russell class. But Russell notes immediately that new problems arise.The problems culminate in the paradox of propositions.This is a problem that seems to run in exact parallel to the paradox of the Russell class.It seemed therefore desirable to Russell that a single solution to both paradoxes be found.Since the simple theory of types (ST) does not offer such a solution it is commonly believed that the paradox of propositions was Russell’s principal motive— at least at the time when he had just finished writing the Principles—for searching for and eventually formulating a ramified theory of types (RT). In the next section I shall present the very first version of ST as it occurs in the Principles.I shall explain in which direction Russell was seeking for a solution to the paradox of propositions which would run in parallel to his solution to the class paradox. Next I turn to the Russell-Frege correspondence of 1902 and 1903.Apart