Combining Texts

All the ideas for 'The Origin of the Work of Art', 'Mathematical Explanation' and 'Later Letters to Dedekind'

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5 ideas

1. Philosophy / D. Nature of Philosophy / 5. Aims of Philosophy / b. Philosophy as transcendent

15585	Later Heidegger sees philosophy as more like poetry than like science [Heidegger, by Polt]
	Full Idea: In his later work Heidegger came to view philosophy as closer to poetry than to science.
	From: report of Martin Heidegger (The Origin of the Work of Art [1935], p.178) by Richard Polt - Heidegger: an introduction 5 'Signs'

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / a. Axioms for sets

17831	Cantor gives informal versions of ZF axioms as ways of getting from one set to another [Cantor, by Lake]
	Full Idea: Cantor gives informal versions of the axioms of ZF as ways of getting from one set to another.
	From: report of George Cantor (Later Letters to Dedekind [1899]) by John Lake - Approaches to Set Theory 1.6
	A reaction: Lake suggests that it should therefore be called CZF.

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.