Skolem's Paradox

In Edward N. Zalta (ed.), Stanford Encyclopedia of Philosophy (2009)


Skolem's Paradox involves a seeming conflict between two theorems from classical logic. The Löwenheim Skolem theorem says that if a first order theory has infinite models, then it has models whose domains are only countable. Cantor's theorem says that some sets are uncountable. Skolem's Paradox arises when we notice that the basic principles of Cantorian set theory—i.e., the very principles used to prove Cantor's theorem on the existence of uncountable sets—can themselves be formulated as a collection of first order sentences. How can the very principles which prove the existence of uncountable sets be satisfied by a model which is itself only countable? How can a countable model satisfy the first order sentence which says that there are uncountably many mathematical objects—e.g., uncountably many real numbers?

Download options


    Upload a copy of this work     Papers currently archived: 72,660

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library


Added to PP

54 (#213,930)

6 months
2 (#259,525)

Historical graph of downloads
How can I increase my downloads?

Similar books and articles

Author's Profile

Timothy Bays
University of Notre Dame

References found in this work

No references found.

Add more references