Combining Texts

All the ideas for 'The Problem of Empty Names', 'On the Nature of Mathematical Reasoning' and 'Definitiones cogitationesque metaphysicae'

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4 ideas

5. Theory of Logic / F. Referring in Logic / 1. Naming / e. Empty names

18946	Unreflectively, we all assume there are nonexistents, and we can refer to them [Reimer]
	Full Idea: As speakers of the language, we unreflectively assume that there are nonexistents, and that reference to them is possible.
	From: Marga Reimer (The Problem of Empty Names [2001], p.499), quoted by Sarah Sawyer - Empty Names 4
	A reaction: Sarah Swoyer quotes this as a good solution to the problem of empty names, and I like it. It introduces a two-tier picture of our understanding of the world, as 'unreflective' and 'reflective', but that seems good. We accept numbers 'unreflectively'.

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

15923	Poincaré rejected the actual infinite, claiming definitions gave apparent infinity to finite objects [Poincaré, by Lavine]
	Full Idea: Poincaré rejected the actual infinite. He viewed mathematics that is apparently concerned with the actual infinite as actually concerning the finite linguistic definitions the putatively describe actually infinite objects.
	From: report of Henri Poincaré (On the Nature of Mathematical Reasoning [1894]) by Shaughan Lavine - Understanding the Infinite

9. Objects / B. Unity of Objects / 2. Substance / d. Substance defined

12712	Substance is that which can act [Leibniz]
	Full Idea: I define substance as that which can act.
	From: Gottfried Leibniz (Definitiones cogitationesque metaphysicae [1678], A6.4.1398), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 3
	A reaction: This is in tune with the notion that to exist is to have causal powers. I find the view congenial, and the middle period of Leibniz's thought, before monads became too spiritual, chimes in with my view.

14. Science / D. Explanation / 3. Best Explanation / b. Ultimate explanation

12737	Nature can be fully explained by final causes alone, or by efficient causes alone [Leibniz]
	Full Idea: All the phenomena of nature can be explained solely by final causes, exactly as if there were no efficient causes; and all the phenomena of nature can be explained solely by efficient causes, as if there were no final causes.
	From: Gottfried Leibniz (Definitiones cogitationesque metaphysicae [1678], A6.4.1403), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 6
	A reaction: Somewhat speculative (a virtue!), but it is interesting to see him suggesting that there might be two complete and satisfactory explanations, which never touched one another. I can't see Aristotle agreeing with that.