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Topic: Matheology § 278
Replies: 4   Last Post: Jun 3, 2013 2:59 PM

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Registered: 1/6/11
Re: Matheology � 278
Posted: Jun 3, 2013 2:27 PM
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In article
WM <> wrote:

> Matheology § 278
> If, for example, our set theory includes sufficient large cardinals,
> we might count Banach­Tarski as a good reason to model physical space
> [...] From this I think it is clear that considerations from
> applications are quite unlikely to prompt mathematicians to restrict
> the range of abstract structures they admit. It is just possible that
> as-yet-unimagined pressures from science will lead to profound
> expansions of the ontology of mathematics, as with Newton and Euler,
> but this seems considerably less likely than in the past, given that
> contemporary set theory is explicitly designed to be as inclusive as
> possible. More likely, pressures from applications will continue to
> influence which parts of the set-theoretic universe we attend to, as
> they did in the case of Dirac¹s delta function; in contemporary
> science, for example, the needs of quantum field theory and string
> theory have both led to the study of new provinces of the set-
> theoretic universe

For a long time, number theory was though to have no useful applications
outside of pure mathematics.

But now would commerce would crash without it.

So to claim, as WM so often does, that set theory will never have any
utility outside of pure mathematics, is the height of arrogance.

But, of course, unwarranted arrogance is one of WM's less pleasant

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