Combining Texts

All the ideas for 'The Logic of Boundaryless Concepts', 'Pacidius Philalethi dialogue' and 'The Philosophy of Logic'

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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.

6. Mathematics / A. Nature of Mathematics / 5. The Infinite / i. Cardinal infinity

18200	Very large sets should be studied in an 'if-then' spirit [Putnam]
	Full Idea: Sets of a very high type or very high cardinality (higher than the continuum, for example), should today be investigated in an 'if-then' spirit.
	From: Hilary Putnam (The Philosophy of Logic [1971], p.347), quoted by Penelope Maddy - Naturalism in Mathematics
	A reaction: Quine says the large sets should be regarded as 'uninterpreted'.

6. Mathematics / C. Sources of Mathematics / 4. Mathematical Empiricism / b. Indispensability of mathematics

18199	Indispensability strongly supports predicative sets, and somewhat supports impredicative sets [Putnam]
	Full Idea: We may say that indispensability is a pretty strong argument for the existence of at least predicative sets, and a pretty strong, but not as strong, argument for the existence of impredicative sets.
	From: Hilary Putnam (The Philosophy of Logic [1971], p.346), quoted by Penelope Maddy - Naturalism in Mathematics II.2

8857	We must quantify over numbers for science; but that commits us to their existence [Putnam]
	Full Idea: Quantification over mathematical entities is indispensable for science..., therefore we should accept such quantification; but this commits us to accepting the existence of the mathematical entities in question.
	From: Hilary Putnam (The Philosophy of Logic [1971], p.57), quoted by Stephen Yablo - Apriority and Existence
	A reaction: I'm not surprised that Hartry Field launched his Fictionalist view of mathematics in response to such a counterintuitive claim. I take it we use numbers to slice up reality the way we use latitude to slice up the globe. No commitment to lines!

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 / C. Structure of Objects / 8. Parts of Objects / a. Parts of objects

12697	Indivisibles are not parts, but the extrema of parts [Leibniz]
	Full Idea: Indivisibles are not parts, but the extrema of parts.
	From: Gottfried Leibniz (Pacidius Philalethi dialogue [1676], A6.3.565-6), quoted by Daniel Garber - Leibniz:Body,Substance,Monad 1
	A reaction: This is incipient monadology, that the bottom level of division ceases to be parts of a thing, and arrives at a different order of entity, to explain the parts of things. Leibniz denies that this subdivision comes down to points.