Combining Texts

All the ideas for 'A Puzzle Concerning Matter and Form', 'Cours d'Analyse' and 'Identity, Essence and Indiscernibility'

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4 ideas

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

18085	Values that approach zero, becoming less than any quantity, are 'infinitesimals' [Cauchy]
	Full Idea: When the successive absolute values of a variable decrease indefinitely in such a way as to become less than any given quantity, that variable becomes what is called an 'infinitesimal'. Such a variable has zero as its limit.
	From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4
	A reaction: The creator of the important idea of the limit still talked in terms of infinitesimals. In the next generation the limit took over completely.

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

18084	When successive variable values approach a fixed value, that is its 'limit' [Cauchy]
	Full Idea: When the values successively attributed to the same variable approach indefinitely a fixed value, eventually differing from it by as little as one could wish, that fixed value is called the 'limit' of all the others.
	From: Augustin-Louis Cauchy (Cours d'Analyse [1821], p.19), quoted by Philip Kitcher - The Nature of Mathematical Knowledge 10.4
	A reaction: This seems to be a highly significan proposal, because you can now treat that limit as a number, and adds things to it. It opens the door to Cantor's infinities. Is the 'limit' just a fiction?

8. Modes of Existence / C. Powers and Dispositions / 4. Powers as Essence

16755	The possible Aristotelian view that forms are real and active principles is clearly wrong [Fine,K, by Pasnau]
	Full Idea: Aristotle seems to have a possible basis for the belief [in individual forms], namely that forms are real and active principles in the world, which is denied by any right-minded modern.
	From: report of Kit Fine (A Puzzle Concerning Matter and Form [1994], p.19) by Robert Pasnau - Metaphysical Themes 1274-1671 24.3 n8
	A reaction: Pasnau says this is the view of forms promoted by the scholastics, whereas Aristotle's own view should be understood as 'metaphysical'.

9. Objects / B. Unity of Objects / 3. Unity Problems / c. Statue and clay

14381	A statue is essentially the statue, but its lump is not essentially a statue, so statue isn't lump [Yablo, by Rocca]
	Full Idea: Yablo proposes the argument that Statue A is essentially a statue, and Lump 1 is not essentially a statue, so Statue A is not identical with Lump 1.
	From: report of Stephen Yablo (Identity, Essence and Indiscernibility [1987]) by Michael della Rocca - Essentialists and Essentialism I
	A reaction: Della Rocca and Yablo unashamedly elide necessary properties with essential properties, so this argument doesn't bother me too much. It concerns the statue and the clay having different modal properties.