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Ideas for 'Mahaprajnaparamitashastra', 'works' and 'Phil of Mathematics: why nothing works'

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2 ideas

6. Mathematics / C. Sources of Mathematics / 1. Mathematical Platonism / b. Against mathematical platonism

3663	How can you contemplate Platonic entities without causal transactions with them? [Putnam]
	Full Idea: Platonism has the attendant problem of how we can succeed in thinking about and referring to entities we can have no causal transactions with.
	From: Hilary Putnam (Phil of Mathematics: why nothing works [1979], Modalism)

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / a. Mathematical empiricism

8631	Cantor says that maths originates only by abstraction from objects [Cantor, by Frege]
	Full Idea: Cantor calls mathematics an empirical science in so far as it begins with consideration of things in the external world; on his view, number originates only by abstraction from objects.
	From: report of George Cantor (works [1880]) by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §21
	A reaction: Frege utterly opposed this view, and he seems to have won the day, but I am rather thrilled to find the great Cantor endorsing my own intuitions on the subject. The difficulty is to explain 'abstraction'.