Combining Texts

All the ideas for 'The Value of Science', 'Mathematical Explanation' and 'Reply to Foucher'

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5 ideas

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.

9. Objects / D. Essence of Objects / 3. Individual Essences

13230	Particular essence is often captured by generality [Steiner,M]
	Full Idea: Generality is often necessary for capturing the essence of a particular.
	From: Mark Steiner (Mathematical Explanation [1978], p.36)
	A reaction: The most powerful features of an entity are probably those which are universal, like intelligence or physical strength in a human. Those characteristics are powerful because they compete with the same characteristic in others (perhaps?).

14. Science / D. Explanation / 2. Types of Explanation / e. Lawlike explanations

13229	Maybe an instance of a generalisation is more explanatory than the particular case [Steiner,M]
	Full Idea: Maybe to deduce a theorem as an instance of a generalization is more explanatory than to deduce it correctly.
	From: Mark Steiner (Mathematical Explanation [1978], p.32)
	A reaction: Steiner eventually comes down against this proposal, on the grounds that some proofs are too general, and hence too far away from the thing they are meant to explain.

14. Science / D. Explanation / 2. Types of Explanation / m. Explanation by proof

13231	Explanatory proofs rest on 'characterizing properties' of entities or structure [Steiner,M]
	Full Idea: My proposal is that an explanatory proof makes reference to the 'characterizing property' of an entity or structure mentioned in the theorem, where the proof depends on the property. If we substitute a different object, the theory collapses.
	From: Mark Steiner (Mathematical Explanation [1978], p.34)
	A reaction: He prefers 'characterizing property' to 'essence', because he is not talking about necessary properties, since all properties are necessary in mathematics. He is, in fact, reverting to the older notion of an essence, as the core power of the thing.

26. Natural Theory / D. Laws of Nature / 11. Against Laws of Nature

15877	The aim of science is just to create a comprehensive, elegant language to describe brute facts [Poincaré, by Harré]
	Full Idea: In Poincaré's view, we try to construct a language within which the brute facts of experience are expressed as comprehensively and as elegantly as possible. The job of science is the forging of a language precisely suited to that purpose.
	From: report of Henri Poincaré (The Value of Science [1906], Pt III) by Rom Harré - Laws of Nature 2
	A reaction: I'm often struck by how obscure and difficult our accounts of self-evident facts can be. Chairs are easy, and the metaphysics of chairs is hideous. Why is that? I'm a robust realist, but I like Poincaré's idea. He permits facts.