FOM: Truth for sentence tokens

[Harvey Friedman]

I would like to make a general remark concerning research on the 
"Liar Paradox".

When I see this Paradox discussed, I always want to know what some 
criteria are for a "solution". I wish scholars would pay more 
attention to this issue.

There seem to be very few cases where paradoxes are given generally 
recognized "solutions" that have proved to be of great lasting value 
by any reasonable criteria. I.e., where the "solutions" are so 
clarifying and natural that they form the basis for further major and 
extensive developments.

One is the Zeno paradox, with its "solution" being the whole setup 
surrounding the natural number and real number systems, and their 
connections with counting, space, and time.

A second is the Russell paradox for sets, with its "solution" being 
set theory, formal and informal.

It would be very interesting to do something of this order of 
importance for the Liar Paradox. Of course, pondering the Liar 
Paradox has already spawned the technical development called "self 
reference in formal systems" that Godel set up to prove his famous 
incompleteness theorem(s). That is a very big deal, but is not the 
same as a "solution" to the Liar Paradox in the sense we are talking 
about.