It is well known that the liar paradox shows that crisp Peano arithmetic PA cannot be consistently extended by adding a truth predicate Tr(x)satisfying 's iff Tr(s')' for all sentences s, where s' is the goedel number of s. We show that such a consistent extension is possible if Tr is allowed to be many valued with truth values in [0,1]. However such a theory has no standard model, and it becomes inconsistent if Tr is required to commute with propositional connectives.
|Translated title of the contribution||The liar paradox and fuzzy logic|
|Pages (from-to)||339 - 346|
|Number of pages||8|
|Journal||Journal of Symbolic Logic|
|Publication status||Published - Mar 2000|