Path: utzoo!attcan!uunet!mcvax!ukc!cs.tcd.ie!vax1!rwallace
From: rwallace@vax1.tcd.ie
Newsgroups: comp.ai
Subject: Re: Fun with the semantics of paradox
Message-ID: <30987@vax1.tcd.ie>
Date: 20 Jan 89 18:17:47 GMT
References: <1883@buengc.BU.EDU> <2996@uhccux.uhcc.hawaii.edu> <905@ubu.warwick.UUCP> <7282@venera.isi.edu>
Organization: Computer Laboratory, Trinity College Dublin
Lines: 21

In article <7282@venera.isi.edu>, smoliar@vaxa.isi.edu (Stephen Smoliar) writes:
>>To clarify what I mean above by my understanding of the terms
>>ambiguous and undecidable, I suspect that the sentence "This sentence
>>is true" is ambiguous, since it can consistently be either true or
>>false, and "This sentence is false" is undecidable, since it cannot be
>>either.  Both sentences seem to me to be meaningless.
>>
> This has been giving me trouble, too.  Another possible interpretation is that
> "meaningless" refers to sentences that are not well-formed;  but then, of
> course, they are not really sentences, in which case it does not make sense
> to talk of their having truth values.

I don't really see what the problem is about paradoxes like "This statement is
false". Many formal systems contain expressions which cannot be evaluated
within that system. Mathematics contains things like 1/0. Logic contains
things like "This statement is false". Although a logical statement, it has
no logical solution. So what? Why get worried about it?

"To summarize the summary of the summary: people are a problem"
Russell Wallace, Trinity College, Dublin
rwallace@vax1.tcd.ie