🚀 go-pugleaf

In article <BzEM6u.2C1@watdragon.uwaterloo.ca> pasward@maytag.uwaterloo.ca (Paul A.S. Ward) writes:
>In article <GUTTMAN.92Dec16164336@circe.mitre.org> guttman@circe.mitre.org (Joshua D. Guttman) writes:
>
>>Kripke, who's always entertaining, says that the statement is quoted by St.
>>Paul in one of the Epistles, who writes that Epimenides, even one of their own,
>>states that all Cretans are liars.  St Paul adds, "This testimony is true."
>>Paul seems to have missed the logical subtlety here.
>
>Not necessarily.  Since Paul is not Cretan, he can agree with the statement
>"All Cretans are liars" without causing a paradox.  The essence is the 
>difference between the paradoxical "I always lie" and the non-paradoxical
>"You always lie" statements.
>
>Just sign me "One Paul defending another"
>
>Paul.

Epimenedes the Cretan himself can assert that all Cretans are liars
without danger of paradox, under most circumstances.  The precise
conditions under which this is possible depend on the definition of
"liar".  If a liar is a person who _always_ lies, then Epimenedes can
assert "All Cretans are liars" and be (in this instance) lying, as
long as some Cretan somewhere at some time made a true statement.
Paradox only ensues if every other proposition ever made by a Cretan
was just plain false.  If "liar" means a person who sometimes or even
usually lies but may occasionally tell the truth, then there is no
danger of paradox at all; Epimenedes may either be lying (there are
Cretans who always or habitually tell the truth) or he may be telling
the truth, in a momentary lapse into veracity.

But it is disturbing that the meaningful character of the assertion
depends on the extraneous fact of some other Cretan telling the truth
some time or other, in the first, interesting case.
-- 
The opinions expressed		|     --Sincerely,
above are not the "official"	|     M. Randall Holmes
opinions of any person		|     Math. Dept., Boise State Univ.
or institution.			|     holmes@opal.idbsu.edu