“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.
I’m Greg Restall, and this is my personal website. I teach philosophy and logic as Professor of Philosophy at the University of Melbourne. ¶ From August 2021, I will be the Shelby Cullom Davis Professor of Philosophy at the University of St Andrews. ¶ Start at the home page of this site—a compendium of recent additions around here—and go from there to learn more about who I am and what I do. ¶ This is my personal site on the web. Nothing here is in any way endorsed by the University of Melbourne.