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Matheology § 278
Posted:
Jun 3, 2013 12:43 PM


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 asyetunimagined 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 settheoretic 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



