[Vision2020] Logical paradoxes

[Ted Moffett]

Ordinary language allows the statement of logically absurd propositions that
are grammatically and syntactically correct.  Ralph references the famous
"Epimenides paradox," that was in part the inspiration for mathematician and
logician Bertrand Russell to develop his theory of types to construct a
"language" that would avoid the logical absurdities of ordinary language.
Some philosophers and logicians regard ordinary language as so flawed that
is it has questionable value for technical philosophy.  For example, a self
referential statement such as "This sentence is false." is logically
absurd.  If the sentence is true, it must be false.  If it is false, then it
is true.  Russell's theory of types addressed these sorts of self
referential statements:

http://en.wikipedia.org/wiki/Epimenides_paradox

Paradoxical versions of the Epimenides problem are closely related to a
class of more difficult logical problems, including the liar
paradox<http://en.wikipedia.org/wiki/Liar_paradox>,
Russell's paradox <http://en.wikipedia.org/wiki/Russell%27s_paradox>, and
the Burali-Forti paradox <http://en.wikipedia.org/wiki/Burali-Forti_paradox>,
all of which have self-reference in common with Epimenides. Indeed, the
Epimenides paradox is usually classified as a variation on the liar paradox,
and sometimes the two are not distinguished. The study of self-reference led
to important developments in logic and mathematics in the twentieth century.
------------------------

The Epimenides paradox appears explicitly in "Mathematical Logic as Based on
the Theory of Types", by Bertrand
Russell<http://en.wikipedia.org/wiki/Bertrand_Russell>,
in the *American Journal of Mathematics*, volume 30, number 3 (July, 1908),
pages 222-262, which opens with the following:
 *The oldest contradiction of the kind in question is the Epimenides.
Epimenides the Cretan said that all Cretans were liars, and all other
statements made by Cretans were certainly lies. Was this a lie?*

In that article, Russell uses the Epimenides paradox as the point of
departure for discussions of other problems, including the Burali-Forti
paradox <http://en.wikipedia.org/wiki/Burali-Forti_paradox> and the paradox
now called Russell's paradox<http://en.wikipedia.org/wiki/Russell%27s_paradox>.
Since Russell, the Epimenides paradox has been referenced repeatedly in
logic. Typical of these references is *Gödel, Escher,
Bach<http://en.wikipedia.org/wiki/G%C3%B6del,_Escher,_Bach>
* by Douglas Hofstadter <http://en.wikipedia.org/wiki/Douglas_Hofstadter>,
which accords the paradox a prominent place in a discussion of
self-reference.
------------------------------------------
Vision2020 Post: Ted Moffett

On 4/26/09, Ralph Nielsen <nielsen at uidaho.edu> wrote:
>
> I just happened to run across this little tidbit from something that
> proclaims itself as MOSCOW EDUCATION (IDAHO); EDUCATIONAL RESEARCH,
> STATISTICS, REPORTS, AND COMMENTARY FROM MOSCOW, IDAHO, by some-one who
> calls himself Right-Mind.
>
> In the Moscow Pullman Daily News:
>
> There is only one absolute truth: "There is no 'absolute truth.' " Lovers
> of wisdom have known this for centuries.
>
> —*Ralph Nielsen, Moscow*
>
> Maybe that statement is embraced by Nielsen; but he would fail 8th grade
> logic for making such an illogical statement.
>
>
> *****************************************************************************
>
> It would seem that Mr. Right-Mind has never heard of a logical paradox. As
> a matter of fact, I heard this from a graduate of Gonzaga University, who
> said he has never forgotten this humbling fact that was taught by his
> philosophy professor at Gonzaga.
>
> We can even find a logical paradox in the Bible, "It was one of them, their
> very own prophet, who said, "Cretans are always liars..." That testimony is
> true" (Titus 1:12). As Right-Mind would say, "Maybe that statement is
> embraced by Paul, in his letter to Titus; but he would fail 8th grade
> logic for making such an illogical statement."
>
> Ralph Nielsen
>
>
>
>
>
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