Re: Implementable Set Theory and Consistency of ZFC

Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> writes:

MoeBlee wrote:

On Oct 15, 7:18 am, Han de Bruijn <Han.deBru...@xxxxxxxxxxxxxx> wrote:

Hereditarily finite sets = naturals : implementable set theory
_ Mainstream mathematics : naturals = finite ordinals

So the naturals are a common factor in two theories. And they join the
finite ordinals (that is: axiom of Infinity) with the "set of all sets"
in implementable set theory. The latter does not exist, though.

Doesn't that say something? Isn't there an analogous pattern, somewhere
in common model theory?
There is no principle of model theory or mathemtatical logic that
permits the inference you are trying to make.

Can it be assumed that you are knowledgable enough, so that I can trust
this assertion of yours?

Your argument is ludicrous; it's based on your manifest ignorance and
misunderstanding of the basics of the subject.

The usual mainstream reaction when they are running out of
"arguments".

It's also the usual mainstream reaction when faced with someone who
gives a silly argument. You know, like "N is in both theories, but
doesn't exist in one of the theories it's in. Doesn't that say
something?"

Now, how do we tell which situation this is: mainstream in retreat, or
mainstream reacting to a silly person?

--
"Britney thought the idea of a pre-nup was vile, because she is
loved-up with Kevin and cannot envisage breaking up. However, [...] no
one in Hollywood these days get married without brokering a
deal. [...] She had a long chat with Kevin and he was cool about it."
.

Relevant Pages