Re: Implementable Set Theory and Consistency of ZFC

David C. Ullrich wrote:

On Mon, 05 Nov 2007 10:15:56 +0100, Han de Bruijn
<Han.deBruijn@xxxxxxxxxxxxxx> wrote:

David C. Ullrich wrote:

On Thu, 01 Nov 2007 13:27:16 +0100, Han de Bruijn
<Han.deBruijn@xxxxxxxxxxxxxx> wrote:

Sure. How could I forget: "if 2.2 = 4, then New York is a large city"
(from 'On the Sentential Calculus' by Alfred Tarski). What nonsense!

No, it would be nonsense if it worked the way you think it should.

For a second try to forget that you're right and everyone else
on the planet is wrong, and think about the following:

Suppose we know the following:

"If we assume blah-blah-blah then it follows that the
integral of 1/t is log(t)."

Now suppose that we assume blah-blah-blah, and we
_also_ assume that unicorns exist. It really makes
sense to you that just because we're assuming unicorns
exist, the fact that the integral of 1/t is log(t)
should somehow no longer follow from blah-blah-blah?

If someone in 'sci.math' would employ the idea that unicorns exist, in
a proof of Fermat's Last Theorem, wouldn't you respond to that person
that this premise is utterly _irrelevant_?

Yes. And the fact that I'd say that is utterly irrelevant here.
Your insistence that something follows from 1-4 but not from
1-8 is nonsense.

Pythagoras' theorem is proven with the axioms of Geometry. Is it true
then that Pythagoras' theorem is a premise for Pythagoras' theorem?
I mean, instead of assuming that unicorns exist, one could assume as
well that Pythagoras' theorem is true. That makes proving things MUCH
easier! (Hmm .. now I begin to understand how FLT was proved by Wiles)

Han de Bruijn

.

Relevant Pages

  • Re: Implementable Set Theory and Consistency of ZFC
    ... Han de Bruijn wrote: ... it would be nonsense if it worked the way you think it should. ... _also_ assume that unicorns exist. ... Pythagoras' theorem is proven with the axioms of Geometry. ...
    (sci.math)
  • Re: Implementable Set Theory and Consistency of ZFC
    ... "If we assume blah-blah-blah then it follows that the ... 1-8 is nonsense. ... then that Pythagoras' theorem is a premise for Pythagoras' theorem? ... but T does not follow from those axioms plus PT. ...
    (sci.math)
  • Re: Implementable Set Theory and Consistency of ZFC
    ... it would be nonsense if it worked the way you think it should. ... "If we assume blah-blah-blah then it follows that the ... _also_ assume that unicorns exist. ... And the fact that I'd say that is utterly irrelevant here. ...
    (sci.math)
  • Re: Implementable Set Theory and Consistency of ZFC
    ... it would be nonsense if it worked the way you think it should. ... "If we assume blah-blah-blah then it follows that the ... sense to you that just because we're assuming unicorns ... should somehow no longer follow from blah-blah-blah? ...
    (sci.math)
  • Re: Implementable Set Theory and Consistency of ZFC
    ... Han de Bruijn wrote: ... it would be nonsense if it worked the way you think it should. ... _also_ assume that unicorns exist. ...
    (sci.math)