[FOM] Theories of truth

[Harvey Friedman]

I am at least aware of an enormous literature on the liar's paradox 
by philosophers, before, but particularly after Saul Kripke's "theory 
of truth". The idea is to make interesting/natural definitions by 
transfinite induction that determine the truth and falsity of many 
self referential assertions, but leave some undecided as to truth 
value. For instance, "this sentence is true" would be decided as 
true, but "this sentence is false" would have an undetermined truth 
value. This is normally done in for the language L of Peano 
arithmetic with a unary predicate symbol T(n) added. Syntactically, 
there are no issues with regard to L. The question is: which 
sentences of L are to be true, which are to be false, and which 
undetermined? The interpretation of T(n) is to be "n is the Godel 
number of a sentence of L that is true".

Many people on this list know this literature better than I do and 
could provide a nice set of references.