This is Greg Restall’s website, with news, writings, pictures, and links. For background see below.

Arithmetic and Truth in Łukasiewicz’s Infinitely Valued Logic

“Arithmetic and Truth in Łukasiewicz’s Infinitely Valued Logic,” Logique et Analyse, 36 (1993) 25–38 (published in 1995).

Peano arithmetic formulated in Łukasiewicz’s infinitely valued logic collapses into classical Peano arithmetic. However, not all additions to the language need also be classical. The way is open for the addition of a real truth predicate satisfying the T-scheme into the language. However, such an addition is not pleasing. The resulting theory is omega-inconsistent. This paper consists of the proofs and interpretations of these two results.

Details

Author: Greg Restall
Status: Published in 1995

Local file: arithluk.pdf (254KB)

Subjects: contraction mathematics models non-classical logic paradox self-reference truth

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 is for photos, archived on the occasional photos page. The right 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 2008-12-31 at 09:56PM.

Thought

I think part of the appeal of mathematical logic is that the formulas look mysterious — You write backward Es!
— Hilary Putnam The Philosophers’ Magazine, Summer 2001.