Re: question about axiomatic set theory

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.

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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