|
Monads and Sets: on Gödel and Leibniz| old_uid | 899 |
|---|
| title | Monads and Sets: on Gödel and Leibniz |
|---|
| start_date | 2006/03/20 |
|---|
| schedule | 11h-13h |
|---|
| online | no |
|---|
| summary | Gödel 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. |
|---|
| responsibles | Barberousse, Tessier Cardon |
|---|
| |
|