Combining Texts

All the ideas for 'Mahaprajnaparamitashastra', 'The Logic of Boundaryless Concepts' and 'Mathematical Explanation'

unexpand these ideas     |    start again     |     specify just one area for these texts

---

6 ideas

5. Theory of Logic / A. Overview of Logic / 3. Value of Logic

9390	Logic guides thinking, but it isn't a substitute for it [Rumfitt]
	Full Idea: Logic is part of a normative theory of thinking, not a substitute for thinking.
	From: Ian Rumfitt (The Logic of Boundaryless Concepts [2007], p.13)
	A reaction: There is some sort of logicians' dream, going back to Leibniz, of a reasoning engine, which accepts propositions and outputs inferences. I agree with this idea. People who excel at logic are often, it seems to me, modest at philosophy.

9. Objects / B. Unity of Objects / 3. Unity Problems / e. Vague objects

9389	Vague membership of sets is possible if the set is defined by its concept, not its members [Rumfitt]
	Full Idea: Vagueness in respect of membership is consistency with determinacy of the set's identity, so long as a set's identity is taken to consist, not in its having such-and-such members, but in its being the extension of a concept.
	From: Ian Rumfitt (The Logic of Boundaryless Concepts [2007], p.5)
	A reaction: I find this view of sets much more appealing than the one that identifies a set with its members. The empty set is less of a problem, as well as non-existents. Logicians prefer the extensional view because it is tidy.

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.

23. Ethics / C. Virtue Theory / 3. Virtues / a. Virtues

7903	The six perfections are giving, morality, patience, vigour, meditation, and wisdom [Nagarjuna]
	Full Idea: The six perfections are of giving, morality, patience, vigour, meditation, and wisdom.
	From: Nagarjuna (Mahaprajnaparamitashastra [c.120], 88)
	A reaction: What is 'morality', if giving is not part of it? I like patience and vigour being two of the virtues, which immediately implies an Aristotelian mean (which is always what is 'appropriate').