Re: question about axiomatic set theory

David C. Ullrich wrote:
> It's impossible to define _everything_ in terms of
> previously defined terms. No matter how things are
> set up officially, there will always be a lowest
> level where we simply assume that the reader knows
> what we mean...
>
> Yes, we need a certain amount of set theory in the
> basic definitions for logic. But not that much set
> theory is required.

I guess that approach would exclude constructions such as nonstandard
models. Maybe it's more accurate to say that not much set theory is
required for MOST (especially applied) mathematics?

>
> On 20 Aug 2005 17:46:13 -0700, "Dani" <tictactictac@xxxxxxxxx> wrote:
>
> >I already know the axiomatic development of set theory. So my question
> >might seem absurd - I don't see how that development is possible. My
> >question - how IS it possible?
> >
> >Where this absurdity comes from: when I try to re-gain my
> >understanding, logic and set-theoretic approaches tangle together, and
> >trying to put one in front of the other just makes the problem worse. I
> >don't see how set theory can be axiomatically developed, if structures
> >are sets, and so are formal systems. As though it were not enough that
> >my thinking tangles set and logic, I began recently to read Nonstandard
> >Analysis by Abraham Robinson. Here, constructions like enlargements and
> >ultraproducts just invite the problem to get worse.
> >
> >I hope somebody might have some idea about this. But it seems to me
> >that maybe mathematics is just ambiguous to some extent - which can
> >mean that not everything in it can be stated on paper, but it open to
> >individual interpretation. But that would seem to be a contradiction,
> >given how universally accepted the mathematical theories are, despite
> >their complexity.
>
>
> ************************
>
> David C. Ullrich

.

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