FOM: Truth for sentence tokens
Harvey Friedman
friedman at math.ohio-state.edu
Fri Aug 30 10:03:45 EDT 2002
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.
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