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How to be Really Contraction Free

“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.

Details

Author: Greg Restall
Status: Published in 1993

Local file: reallycf.pdf (6MB)

Subjects: algebras contraction models non-classical logic paradox

About

I’m Greg Restall, and this is my website. I work in Philosophy at the University of Melbourne. Email: greg at consequently.org; Post: School of of Philosophy, Anthropology and Social Inquiry, University of Melbourne, Parkville 3010, Australia.

Start at the home page—a summary of the site. The left column is news, archived on the news archive page. The central column contains recent items from the writing page, which lists my publications. These are also categorised by topic. You can follow my links at my account on delicious and occasional short snarky remarks at @consequently on twitter.

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This site is handcoded: I write text in Textmate, and Webby files things in the right place and uploads them to the server. This page was last modified on 2008-12-30 at 01:00AM.

Thought

Be kind, for everyone you meet is fighting a great battle.
— Philo of Alexandria