Re: What is a proof, exactly?

From: Jasper Stein (J.J.Stein.Stein_at_cs.cs.ru.ru.nl.nl)
Date: 12/02/04 

Date: Thu, 02 Dec 2004 14:52:59 +0000

J.E. wrote:

> it to what is inside the five in the blue set. If you don't have sets
> all the way down, then evetually you get to something that doesn't
> have equality defined and it causes equality to become undefined for
> everything that contained it, and everything that contained that and
> so on transfinitely.

Do you mean set equality specifically, or is this more generally a denial of
my question "Can we equate any two mathematical objects?"?

> mean the usual things. The thing is that set equality itself is an
> equivalence relation itself that is "too big" to be a set. So sets
> can do relations on specific sets, but sets can't do relations on all
> sets in general.

So - would you say we'd need two different kinds of equalities, the set
theoretic ones (equality between members of a set), and another one that
spans all sets simultaneously? Would this be a logical equality? And since
this equality is a proper class, what would this equality be if we consider
G"odel-Bernays instead of Zermelo-Fr"ankel?

Jasper 

-- 
The problem with having an open mind is that people toss in garbage