Re: Godel on BBC 4

On Sat, 25 Oct 2008 04:01:25 +0100, John Jones <jonescardiff@xxxxxxx> said:
Chris Menzel wrote:
On Mon, 13 Oct 2008 22:27:44 +0100, John Jones <jonescardiff@xxxxxxx> said:
Chris Menzel wrote:
On Thu, 09 Oct 2008 19:03:08 +0100, John Jones <jonescardiff@xxxxxxx>
said:
...
It wasn't the inaccuracies or accuracies that staggered me. It was
the fact that no-one challenged the Godellian project at all.
Perhaps because the idea of "challenging the Godellian project" is
about as silly as, say, "challenging the Euclidean project" of
classical geometry or "challenging the Leibnizian/Newtonian project"
of the calculus. Abysmally ignorant as you are of the actual
mathematics, however, no doubt you have some screwball idea of what
Goedel's project was.

Any project that makes substantive claims based on assumptions made
in the formulation of the liar paradox can't be credible.
Case in point.

The respondents on the programme seemed ok with the idea that Godel
was about liar paradox stuff.

Sure, properly framed. There is, in Goedel's proof, an *analogy* with
"liar paradox stuff", the critical difference being that the notion of
truth in the latter -- which is essential to the generation of the
paradox -- is replaced by provability in the former. In the liar
paradox, you get a sentence that is true if and only if it is not true,
a genuine contradiction. In Goedel's proof, you get a sentence that it
is true (in the natural numbers) if and only if it is not provable (in
the system at hand), which is perfectly consistent.

You haven't given an argument. To make the argument stick and bear fruit
you must say what is meant by 'provability' and why you think it differs
from the notion of 'truth' in the liar paradox.

Without this explanation what may appear as an argument can be no more
than a restatement or translation of what has already been said.

And again, case in point. Because you are profoundly (and, to my
ceaseless, amazement, willfully) ignorant of even the rather elementary
concepts of mathematical logic that constitute the backdrop of Goedel's
theorem, you have no idea that both "provability" and "truth" are
rigorously defined and, so defined, provably distinct. Thus, you create
a pseudo-issue in your own apparently uneducable mind where there is in
fact none. Do you not realize how foolish this makes you look?

.

Relevant Pages

  • Re: Godel on BBC 4
    ... classical geometry or "challenging the Leibnizian/Newtonian project" ... in the formulation of the liar paradox can't be credible. ... I think that divorcing truth and provability is paradoxical. ...
    (sci.logic)
  • Re: Godel on BBC 4
    ... classical geometry or "challenging the Leibnizian/Newtonian project" ... in the formulation of the liar paradox can't be credible. ... The respondents on the programme seemed ok with the idea that Godel ... paradox -- is replaced by provability in the former. ...
    (sci.logic)
  • Re: Godel on BBC 4
    ... classical geometry or "challenging the Leibnizian/Newtonian project" ... in the formulation of the liar paradox can't be credible. ... Perhaps in your own understanding of truth and provability. ...
    (sci.logic)
  • Re: Godel on BBC 4
    ... classical geometry or "challenging the Leibnizian/Newtonian project" ... in the formulation of the liar paradox can't be credible. ... To make the argument stick and bear fruit you must say what is meant by 'provability' and why you think it differs from the notion of 'truth' in the liar paradox. ...
    (sci.logic)
  • Re: Godel on BBC 4
    ... you must say what is meant by 'provability' and why you think it differs from the notion of 'truth' in the liar paradox. ... You MUST say what is meant by provability and why it is not the same as truth if you want to argue against a proposal that places their relationship in doubt. ...
    (sci.logic)
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