Abstract
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 |
|---|---|
| Original language | English |
| Pages (from-to) | 339 - 346 |
| Number of pages | 8 |
| Journal | Journal of Symbolic Logic |
| Volume | 65 |
| Publication status | Published - Mar 2000 |