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In article <1476@eouk13.eoe.co.uk> pwestlak@eoe.co.uk (Peter Westlake) writes:

   Please forgive me if this is a naive question (or even completely stupid :-)

   The way I have heard the original Cretan liar paradox expressed is that
   Epiminedes, a Cretan, said "All Cretans are liars". The reasoning goes that
   as Epiminedes is known to be from Crete, he therefore claims to be a liar, 
   and therefore claims not to be, which is a paradox.  But it seems to me
   (in my ignorance) that this statement permits a consistent interpretation,
   namely that SOME Cretans are liars, and that Epiminedes is one of them.
   By supposing the existence of other Cretans, we avoid a paradox.

   So a) I have the original statement wrong
   or b) it never was a paradox really
   or c) I have missed something obvious and everything I say is false.
   Break it to me gently, especially if I have misspelled "Epi.*".


I think you misspelled Epimenides, but you're right about it's not being
paradoxical, as stated.  I think that his statement was enough to make people
realize, though, that something very similar was going to be really paradoxical
("This very sentence is false").

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.

	Joshua Guttman 

In article <GUTTMAN.92Dec16164336@circe.mitre.org> guttman@circe.mitre.org (Joshua D. Guttman) writes:
>In article <1476@eouk13.eoe.co.uk> pwestlak@eoe.co.uk (Peter Westlake) writes:
>
>   Please forgive me if this is a naive question (or even completely stupid :-)
>
>   The way I have heard the original Cretan liar paradox expressed is that
>   Epiminedes, a Cretan, said "All Cretans are liars". The reasoning goes that
>   as Epiminedes is known to be from Crete, he therefore claims to be a liar, 
>   and therefore claims not to be, which is a paradox.  But it seems to me
>   (in my ignorance) that this statement permits a consistent interpretation,
>   namely that SOME Cretans are liars, and that Epiminedes is one of them.
>   By supposing the existence of other Cretans, we avoid a paradox.
>
>   So a) I have the original statement wrong
>   or b) it never was a paradox really
>   or c) I have missed something obvious and everything I say is false.
>   Break it to me gently, especially if I have misspelled "Epi.*".
>
>
>I think you misspelled Epimenides, but you're right about it's not being
>paradoxical, as stated.  I think that his statement was enough to make people
>realize, though, that something very similar was going to be really paradoxical
>("This very sentence is false").
>
>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.
>
>	Joshua Guttman 

There is a collection of essays by Quine called `Paradoxes and Other
Essays' which deals with the above paradox (nonparadox), with a quote
by St. Paul followed by a blurb by Quine.  The first essay deals with
antimonies in clear expository manner.

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.

In article <GUTTMAN.92Dec16164336@circe.mitre.org>, guttman@circe.mitre.org (Joshua D. Guttman) writes:
|> In article <1476@eouk13.eoe.co.uk> pwestlak@eoe.co.uk (Peter Westlake) writes:
|> 
|>    Please forgive me if this is a naive question (or even completely stupid :-)
|> 
|>    The way I have heard the original Cretan liar paradox expressed is that
|>    Epiminedes, a Cretan, said "All Cretans are liars". The reasoning goes that
|>    as Epiminedes is known to be from Crete, he therefore claims to be a liar, 
|>    and therefore claims not to be, which is a paradox.  But it seems to me
|>    (in my ignorance) that this statement permits a consistent interpretation,
|>    namely that SOME Cretans are liars, and that Epiminedes is one of them.
|>    By supposing the existence of other Cretans, we avoid a paradox.
|> 
|>    So a) I have the original statement wrong
|>    or b) it never was a paradox really
|>    or c) I have missed something obvious and everything I say is false.
|>    Break it to me gently, especially if I have misspelled "Epi.*".
|> 
|> 
|> I think you misspelled Epimenides, but you're right about it's not being
|> paradoxical, as stated.  I think that his statement was enough to make people
|> realize, though, that something very similar was going to be really paradoxical
|> ("This very sentence is false").
|> 
|> 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.
|> 
|> 	Joshua Guttman 

Or we have missed the subtlety of St. Paul ... possibly his sense of
humor?
-- 
Gary H. Merrill  [Principal Systems Developer, C Compiler Development]
SAS Institute Inc. / SAS Campus Dr. / Cary, NC  27513 / (919) 677-8000
sasghm@theseus.unx.sas.com ... !mcnc!sas!sasghm

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

In article <1992Dec16.191006.16896@jarvis.csri.toronto.edu> leemike@eecg.toronto.edu (Michael Lee) writes:
>There is a collection of essays by Quine called `Paradoxes and Other
>Essays' which deals with the above paradox (nonparadox), with a quote
>by St. Paul followed by a blurb by Quine.  The first essay deals with
>antimonies in clear expository manner.

The collection by Quine is titled "The Ways of Paradox"; the essay in
question is eponymous.  The title is a reference to Gilbert and Sullivan's
"Pirates of Penzance":  "How quaint the ways of paradox/ At common sense
they gaily mock".

Warren Goldfarb
Department of Philosophy
Harvard University