How to make paradoxes in set theory
by
Boris Čulina
Faculty of mechanical engineering and naval architecture, University of Zagreb

Frege's naive set theory is based on an assumption that for every property there is a set of all objects with the property. But for some properties it leads to contradiction. Modern set theory resolved the problem in a pragmatic way, by postulating enough sets for mathematical purposes but, it is beleived, not too much, to avoid contradictions. So there is no contradiction, but the paradox remains - why there are no some sets.

Sentence which claims that some property P doesn't have the associated set can be reformulated in a logically equivalent sentence which gives some logical understanding why is it so. It says that the property has a creative choice on it. It means that for every set of objects with property P there is an object with property P outside the set. Among other things it gives instructions how to make paradoxes - by investigating set operations we are looking for properties with a creative choice on them. Old paradoxes are investigated in this way, some new are made, and some general results are exhibited.

Date received: March 15, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caex-16.