Monads and Sets: on Gödel and Leibniz

old_uid899
titleMonads and Sets: on Gödel and Leibniz
start_date2006/03/20
schedule11h-13h
onlineno
summaryGödel subscribed to a Leibnizian monadology as the true metaphysics. At the same time, he believed that Cantorian set theory was a true theory. Leibniz, however, argued that in mathematics there can be no infinite wholes, which would preclude an embedding of Cantorian set theory in a Leibnizian metaphysics. I will first try to show that Leibniz' argument is invalid even by his own standards. Then I turn to an attempt of Gödel's to justify, by drawing an analogy to the monadology, the Reflection Principle in set theory. Of this attempt I will argue that it fails. More generally, I will argue that while a Leibnizian metaphysics may well be compatible with Cantorian set theory, by itself it provides no clues that can be used to justify set-theoretical principles.
responsiblesBarberousse, Tessier Cardon