Re: Godel on BBC 4

On Oct 28, 12:40 pm, Chris Menzel <cmen...@xxxxxxxxxxxxxxxxxxxx>
wrote:
On Sun, 26 Oct 2008 21:07:11 -0700 (PDT), Newberry
<newberr...@xxxxxxxxx> said:





Chris Menzel wrote:
On Thu, 09 Oct 2008 19:03:08 +0100, John Jones <jonescard...@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.

I think that divorcing truth and provability is paradoxical.

Perhaps in your own understanding of truth and provability.  But the
fact is that those concepts in Goedel's theorem are provably distinct,
and consistently so. If you think otherwise, then you simply don't
understand the theorem.

Well, P & ~P is not the only example of inconsistency. Other examples
are omega-inconsistency, and provability not equivalent to truth.
.

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. ... 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
    ... 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
    ... 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. ... paradox -- is replaced by provability in the former. ... from the notion of 'truth' in the liar paradox. ...
    (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)
Loading