Re: Newberry's Theses

On Apr 26, 11:36 am, Aatu Koskensilta <aatu.koskensi...@xxxxxxxxx>
wrote:
On 2008-04-26, in sci.logic, Newberry wrote:

How do these principles come about?

They were discovered in the course of mathematical research. In
particular, in the development of set theory it become apparent that
the basic set theoretic principles can be justified in terms of the
picture of the world of sets provided by the cumulative hierarchy.

Can a machine produce them?

How is that relevant? A machine certainly can produce them in the
sense of outputting a list containing these principles.

It may be irrelevant to the immediate point, but it's certainly
an interesting question.

It's not immediately obvious to me how such a thing would
work. The obviously-difficult one is induction. But I don't even
see a way that a program could figure out multiplicative identity
without being told about it, at least not in finite time.


Marshall
.

Relevant Pages

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