“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.
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.