## Journal of Symbolic Logic

### The Liar Paradox and Fuzzy Logic

#### Abstract

Can one extend crisp Peano arithmetic PA by a possibly many-valued predicate Tr(x) saying "x is true" and satisfying the "dequotation schema" $\varphi \equiv \text{Tr}(\bar{\varphi})$ for all sentences $\varphi$? This problem is investigated in the frame of Lukasiewicz infinitely valued logic.

#### Article information

Source
J. Symbolic Logic, Volume 65, Issue 1 (2000), 339-346.

Dates
First available in Project Euclid: 6 July 2007

https://projecteuclid.org/euclid.jsl/1183746025

Mathematical Reviews number (MathSciNet)
MR1782124

Zentralblatt MATH identifier
0945.03031

JSTOR