Re: Implementable Set Theory and Consistency of ZFC

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

David C. Ullrich wrote:

On Wed, 31 Oct 2007 12:13:48 +0100, Han de Bruijn
<Han.deBruijn@xxxxxxxxxxxxxx> wrote:

So, even if I don't make use of (5-8), a proof of A from (1-4) is a
proof from (1-8) ?

Yes. Evidently this is news to you - that's just proof
that you have no idea what "this follows from that"
means, exactly as people have said.

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?

So, even if I say "there exists a Foo", then such
a statement is a valid premise for proving that the integral of 1/t
from 1 to x is ln(x) ?

If we have a set of axioms S that implies that the integral
of 1/t from 1 to x is log(x) then yes, that statement also
follows from S together with "there exists a Foo".

Weird ..

So? First, it's how things are, whether you think it's
weird or not. Second, it shows that the things you've
been saying about how whatever follows from 1-4 but
does not follow from 1-8 are simply false.

Mathematical logic is a perversion of common speech logic, that's why.

Han de Bruijn


************************

David C. Ullrich
.

Relevant Pages

  • Re: Implementable Set Theory and Consistency of ZFC
    ... (from 'On the Sentential Calculus' by Alfred Tarski). ... What nonsense! ... "If we assume blah-blah-blah then it follows that the ... sense to you that just because we're assuming unicorns ...
    (sci.math)
  • Re: Implementable Set Theory and Consistency of ZFC
    ... "If we assume blah-blah-blah then it follows that the ... _also_ assume that unicorns exist. ... 1-8 is nonsense. ... then that Pythagoras' theorem is a premise for Pythagoras' theorem? ...
    (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)