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"However, she suggested that some mathematical entities are in fact concrete, unlike, notably, Gödel, who assumed all mathematical objects are abstract. She suggested that sets can be causally efficacious, and in fact share all the causal and spatiotemporal properties of their elements."
The article would be greatly improved if the philosophical terms were defined in plain language, if that is possible.
What does it mean for a mathematical object to be "abstract" or "concrete" ?
What does it mean for a set to be "causally efficacious" ?
I hope someone knowledgeable about these things can fill in the details so that non-expert readers can understand Maddy's philosophical positions, at least to some degree.
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