Dear Hal, 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 duration. 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.
Kindest regards, Stephen ----- 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 > incoherent. > > 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 > >