Re: "Godel got it all wrong"


Peter_Smith wrote:

So why, I wonder, do people still get a bee in their bonnet about
this?! Very puzzling.

I think there are three points:

1/ First Godel's original proof sails pretty close to the rocks. By
that I mean, he played up the likeness of his sentence (for the First
Incompleteness Theorem) to Richard's and the Liar Paradox, and this is
how most people first approach the Theorem. Given that the Liar
Paradox creates such puzzlement, and also skepticism, it would seem
normal that a certain amount is transfered to Godel.

2/ I think a fair number of people consider mathematics intuitively as
just a bunch of symbolic manipulation - manipulation from a certain set
of axioms which are self-evident and obvious. It's a small step from
there to equate what is provable (from that certain set) to what is
true. But here comes Godel, whose Theorems seem to to break that
association.

3/ As someone said, there are a lot of wild conclusions drawn from
Godel, and people draw conclusions based on the
if-there-is-smoke-there-must-be-fire.

.

Relevant Pages

  • Re: Godel on BBC 4
    ... from the notion of 'truth' in the liar paradox. ... "Understanding Godel isn't about following his formal proof. ... they ought not to be comfortable with that analogy because the ...
    (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. ...
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  • Re: Godels Incompleteness theorem
    ... If Godel had created a statement S that said "S is not true", then Godel would have proved that mathematics is internally self-contradictory, i.e., the famous liar paradox. ... But you will see that you had to use the extra axiom "number theory is consistent" and hence all you have really proved is that it is not possible to prove "number theory is consistent" within number theory.) ... Actually you need to use an additional meta-assumption "provability implies truth" to make this work. ...
    (sci.math)