NetNews Usenet Archive 1992 #30/NN_1992_30.iso/spool/sci/logic/2470

Internet Message Format | 1992-12-21 | 1.6 KB

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From: [e-mail] (Michael Hand)
Newsgroups: sci.logic
Subject: Re: Liar paradox
Date: 18 Dec 1992 12:40:15 -0600
Organization: Texas A&M University, College Station, TX
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Titus 1:12.
    One of themselves, a prophet of their own, said, "Cretans are
    always liars, evil beasts, lazy gluttons."

So far, Paul hasn't himself uttered anything paradoxical, he's
only reported a potentially paradoxical utterance.  The Cretan's
own claim is ambiguous (at least in this translation).  The
"always" could be the one used by Russell in "On Denoting", not
a quantifier over times, as is usual, but over individuals.  As
Russell says

    C(everything) means "C(x) is always true"

Paul may merely mean to ensure that "Cretans" is read as a universal.
On the other hand, he may indeed mean "always" to quantify over times,
leaving it understood that he means *all* Cretans (as opposed to
*typical* Cretans, as when we say that dogs have four legs).
This reading is paradoxical, given the added assumption that if
someone is *always* a liar then s/he *never* tells the truth.  On
the third hand, if one lie makes the speaker a liar forever, then
there again is no paradox.
B-o} Michael
--
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Michael Hand                     phone [phone], fax [phone]
Dept of Philosophy, Texas A&M Univ, College Station TX 77843-4237 U.S.A.