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All the ideas for 'Reply to Fourth Objections', 'Ontological Ground of Alethic Modality' and 'works'

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4 ideas

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / k. Infinitesimals

18086	Weierstrass eliminated talk of infinitesimals [Weierstrass, by Kitcher]
	Full Idea: Weierstrass effectively eliminated the infinitesimalist language of his predecessors.
	From: report of Karl Weierstrass (works [1855]) by Philip Kitcher - The Nature of Mathematical Knowledge 10.6

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / l. Limits

18092	Weierstrass made limits central, but the existence of limits still needed to be proved [Weierstrass, by Bostock]
	Full Idea: After Weierstrass had stressed the importance of limits, one now needed to be able to prove the existence of such limits.
	From: report of Karl Weierstrass (works [1855]) by David Bostock - Philosophy of Mathematics 4.4
	A reaction: The solution to this is found in work on series (going back to Cauchy), and on Dedekind's cuts.

10. Modality / E. Possible worlds / 1. Possible Worlds / e. Against possible worlds

9220	Lewis must specify that all possibilities are in his worlds, making the whole thing circular [Shalkowski, by Sider]
	Full Idea: If purple cows are simply absent from Lewis's multiverse, then certain correct propositions turn out to be impossible. Lewis must require a world for every possibility. But then it is circular, as the multiverse needs modal notions to characterize it.
	From: report of Scott Shalkowski (Ontological Ground of Alethic Modality [1994], 3.9) by Theodore Sider - Reductive Theories of Modality 3.9
	A reaction: [Inversely, a world containing a round square would make that possible] This sounds very nice, though Sider rejects it (p.197). I've never seen how you could define possibility using the concept of 'possible' worlds.

17. Mind and Body / E. Mind as Physical / 6. Conceptual Dualism

3643	The concept of mind excludes body, and vice versa [Descartes]
	Full Idea: The concept of body includes nothing at all which belongs to the mind, and the concept of mind includes nothing at all which belongs to the body.
	From: René Descartes (Reply to Fourth Objections [1641], 225)
	A reaction: A headache? Hunger? The mistake, I think, is to regard the mind as entirely conscious, thus creating a sharp boundary between two aspects of our lives. As shown by blindsight, I take many of my central mental operations to be pre- or non-conscious.