How to be Really Contraction Free

March 1993

“How to be Really Contraction Free” Studia Logica 52 (1993) 381–391.

I show that any finitely valued logic of a simple kind fails to support naïve comprehension, if it has a conditional. I then go on to show how some infinitely valued logics also fail to be robustly contraction free. Then I make a bold conjecture that robust contraction freedom is sufficient to support naïve set theory. This conjecture was later proved to be wrong by two graduate students from Monash, Sam Buchart and Su Rogerson, in some delightful work in 1997, which has since also been published in Studia Logica.

 download pdf

You are welcome to download and read this document. I welcome feedback on it. Please check the final published version if you wish to cite it. Thanks.


I’m Greg Restall, and this is my personal website. I am the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews, and the Director of the Arché Philosophical Research Centre for Logic, Language, Metaphysics and Epistemology I like thinking about – and helping other people think about – logic and philosophy and the many different ways they can inform each other.


To receive updates from this site, subscribe to the RSS feed in your feed reader. Alternatively, follow me at, where most updates are posted.


This site is powered by Netlify, GitHub, Hugo, Bootstrap, and coffee.   ¶   © 1992– Greg Restall.