Combining Texts

All the ideas for 'Science and Method', 'Reply to Foucher' and 'On Relations of Universals and Particulars'

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4 ideas

6. Mathematics / A. Nature of Mathematics / 2. Geometry

10245	One geometry cannot be more true than another [Poincaré]
	Full Idea: One geometry cannot be more true than another; it can only be more convenient.
	From: Henri Poincaré (Science and Method [1908], p.65), quoted by Stewart Shapiro - Philosophy of Mathematics
	A reaction: This is the culminating view after new geometries were developed by tinkering with Euclid's parallels postulate.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / d. Actual infinite

19406	I strongly believe in the actual infinite, which indicates the perfections of its author [Leibniz]
	Full Idea: I am so much for the actual infinite that instead of admitting that nature abhors it, as is commonly said, I hold that it affects nature everywhere in order to indicate the perfections of its author.
	From: Gottfried Leibniz (Reply to Foucher [1693], p.99)
	A reaction: I would have thought that, for Leibniz, while infinities indicate the perfections of their author, that is not the reason why they exist. God wasn't, presumably, showing off. Leibniz does not think we can actually know these infinities.

7. Existence / C. Structure of Existence / 5. Supervenience / c. Significance of supervenience

16045	General facts supervene on particular facts, but cannot be inferred from them [Russell, by Bennett,K]
	Full Idea: Russell noted that you cannot arrive at general facts by inference from numerous particular facts, ..but general facts logically supervene on particular ones. So the general facts supervene, but are not entailed.
	From: report of Bertrand Russell (On Relations of Universals and Particulars [1911]) by Karen Bennett - Supervenience §3.2
	A reaction: The belief that the general facts supervene on the particular ones then seems to be more a matter of faith than of fact. Or maybe it is analytic, depending on what we understand by 'general'. Universal, or generalised?

8. Modes of Existence / B. Properties / 13. Tropes / b. Critique of tropes

14327	Trope theorists cannot explain how tropes resemble each other [Russell, by Mumford]
	Full Idea: The trope theorist cannot explain how a number of tropes resemble each other.
	From: report of Bertrand Russell (On Relations of Universals and Particulars [1911]) by Stephen Mumford - Dispositions 07.6
	A reaction: [My 13,000th Idea: 31/10/11] Every theory is left with something it cannot explain. Is it likely that we could come up with an explanation of resemblance? It seems like a combination of identity in the physics, and identity in the brain mechanisms.