No, it is not the case that such questions "have no meaning". The "Liar
paradox", in its many forms and instantiations, convey a meaning. The
problem, IMHO, is in the assumption that the negation is "instantaneous".
For example, when we read the sentence "This sentence is false", we "take it
in" as a whole, it is meaningful as a whole, but we must realize that the
reading of the string of letters is not a process that is instantaneous or
"takes no time" to perform. Every physical process requires some non-zero
This is at the heart of my argument against proposals such as those of
Bruno Marchal. The "duration" required to instantiate a relation, even one
between a priori "existing" numbers can not be assumed to be zero and still
be a meaningful one. You are correct in saying that "the question has no
meaning", but only in the Ideal sense of ignoring the reality of duration,
even within Logic.
----- Original Message -----
From: "Hal Finney" <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>; <[EMAIL PROTECTED]>
Sent: Saturday, October 25, 2003 11:51 AM
Subject: Re: Is reality unknowable?
> It's also possible that the question, although seemingly made up of
> ordinary English language words used in a logical way, is actually
> If I say, proposition P is both true and false, that is a sentence made
> up of English words, but it does not really make sense. I could then
> demand to know whether P is true or false, and whatever answer you give,
> I say that it is the opposite. If you say P is true, I point out that
> we just agreed that P was false, and vice versa.
> This is a trivial example because the paradox is so shallow, but the
> same thing is true for deeper paradoxes. The problem is not a failure
> of our reasoning tools, but rather that the question has no meaning.
> So you can't always take a sequence of words and expect to get an
> unambiguous and valid answer. You must always consider the possibility
> that your question is meaningless. The fact that people can't necessarily
> answer it does not imply that mathematics is unknowable or that there
> is no such thing as mathematical knowledge. There may be other reasons
> to think so, but it does not follow merely because a given sequence of
> words has no consistent analysis.
> Hal Finney