Combining Texts

All the ideas for 'fragments/reports', 'The Web of Belief' and 'Mathematical Explanation'

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5 ideas

1. Philosophy / F. Analytic Philosophy / 1. Nature of Analysis

8460	Philosophers have given precise senses to deduction, probability, computability etc [Quine/Ullian]
	Full Idea: Successful explications (giving a precise sense to a term) have been found for the concepts of deduction, probability and computability, to name just three.
	From: W Quine / J Ullian (The Web of Belief [1970], 65), quoted by Alex Orenstein - W.V. Quine Ch.3
	A reaction: Quine also cites the concept of an 'ordered pair'. Orenstein adds Tarski's definition of truth, Russell's definite descriptions, and the explication of existence in terms of quantifications. Cf. Idea 2958.

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.

21. Aesthetics / C. Artistic Issues / 7. Art and Morality

468	Musical performance can reveal a range of virtues [Damon of Ath.]
	Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice.
	From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where?