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

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Posts: 18,076
Registered: 1/29/05
Matheology § 278
Posted: Jun 3, 2013 12:43 PM
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Matheology § 278

If, for example, our set theory includes sufficient large cardinals,
we might count Banach?Tarski 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 Dirac?s 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 {{with negative result. There is no meaningful
application of a meaningless theory possible}}.
[Penelope Maddy: "How applied mathematics became pure", Reviev
Symbolic Logic 1 (2008) 16 - 41]

Regards, WM

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