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Inverse View
It is not the case that Maddy's early immanent realism can account for the massive infinities in mathematics.
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Reasons For
2 perspectives
Reason for 1 of 2
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1.
Immanent realism ties mathematical existence to physical instantiation, yet modern set theory posits sets of cardinality far exceeding any physical objects.
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2.
If sets exist only where physical objects are located, the transfinite hierarchy beyond beth-omega lacks any spatiotemporal grounding, undermining the account.
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Reason for 2 of 2
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1.
Maddy's positing of infinitely many sets at each physical location is ontologically profligate in ways that violate parsimony constraints defended by nominalists like Field.
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2.
An account that multiplies unobservable infinitary entities at every spacetime point inherits Platonism's epistemic access problems without gaining its ontological clarity.
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Reasons Against
1 perspective
Reason against
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On Maddy's view, corresponding to every physical object there is a huge infinity of sets existing in spacetime at the location of that physical object.
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