Combining Philosophers

Ideas for H.Putnam/P.Oppenheim, George Cantor and Georges Rey

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2 ideas

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'.

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics

3143	Physics requires the existence of properties, and also the abstract objects of arithmetic [Rey]
	Full Idea: Physics is committed to arithmetic, which seems committed to abstract objects such as numbers, and its causal explanations seem to appeal to properties, such as mass and charge.
	From: Georges Rey (Contemporary Philosophy of Mind [1997], 2.3)