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Ideas for 'works (fragments)', 'Making It Explicit' and 'Models and Reality'

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2 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / a. The Infinite

7555	Zeno achieved the statement of the problems of infinitesimals, infinity and continuity [Russell on Zeno of Citium]
	Full Idea: Zeno was concerned with three increasingly abstract problems of motion: the infinitesimal, the infinite, and continuity; to state the problems is perhaps the hardest part of the philosophical task, and this was done by Zeno.
	From: comment on Zeno (Citium) (fragments/reports [c.294 BCE]) by Bertrand Russell - Mathematics and the Metaphysicians p.81
	A reaction: A very nice tribute, and a beautiful clarification of what Zeno was concerned with.

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

9914	It is unfashionable, but most mathematical intuitions come from nature [Putnam]
	Full Idea: Experience with nature is undoubtedly the source of our most basic 'mathematical intuitions', even if it is unfashionable to say so.
	From: Hilary Putnam (Models and Reality [1977], p.424)
	A reaction: Correct. I find it quite bewildering how Frege has managed to so discredit all empirical and psychological approaches to mathematics that it has become a heresy to say such things.