Combining Texts

All the ideas for 'The Logic of Boundaryless Concepts', 'Many, but almost one' and 'Introduction to Russell's Theory of Types'

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7 ideas

4. Formal Logic / F. Set Theory ST / 4. Axioms for Sets / p. Axiom of Reducibility

18170	The Axiom of Reducibility is self-effacing: if true, it isn't needed [Quine]
	Full Idea: The Axiom of Reducibility is self-effacing: if it is true, the ramification it is meant to cope with was pointless to begin with.
	From: Willard Quine (Introduction to Russell's Theory of Types [1967], p.152), quoted by Penelope Maddy - Naturalism in Mathematics I.1
	A reaction: Maddy says the rejection of Reducibility collapsed the ramified theory of types into the simple theory.

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.

7. Existence / D. Theories of Reality / 10. Vagueness / d. Vagueness as linguistic

15538	Semantic indecision explains vagueness (if we have precisifications to be undecided about) [Lewis]
	Full Idea: Semantic indecision will suffice to explain the phenomenon of vagueness. [note] Provided that there exist the many precisifications for us to be undecided between. If you deny this, you will indeed have need of vague objects.
	From: David Lewis (Many, but almost one [1993], 'Two solutions')
	A reaction: [He mentions Van Inwagen 1990:213-83] There seem to be three solutions to vague objects: that they really are vague, that they are precise but we can't know precisely, or Lewis's view. I like Lewis's view. Do animals have any problem with vagueness?

9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail

15537	If cats are vague, we deny that the many cats are one, or deny that the one cat is many [Lewis]
	Full Idea: To deny that there are many cats on the mat (because removal of a few hairs seems to produce a new one), we must either deny that the many are cats, or else deny that the cats are many. ...I think both alternatives lead to successful solutions.
	From: David Lewis (Many, but almost one [1993], 'The paradox')
	A reaction: He credits the problem to Geach (and Tibbles), and says it is the same as Unger's 'problem of the many' (Idea 15536).

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

15536	We have one cloud, but many possible boundaries and aggregates for it [Lewis]
	Full Idea: Many surfaces are equally good candidates to be boundaries of a cloud; therefore many aggregates of droplets are equally good candidates to be the cloud. How is it that we have just one cloud? And yet we do. This is Unger's (1980) 'problem of the many'.
	From: David Lewis (Many, but almost one [1993], 'The problem')
	A reaction: This is the problem of vague objects, as opposed to the problem of vague predicates, or the problem of vague truths, or the problem of vague prepositions (like 'towards').

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.

19. Language / F. Communication / 6. Interpreting Language / c. Principle of charity

15539	Basic to pragmatics is taking a message in a way that makes sense of it [Lewis]
	Full Idea: The cardinal principle of pragmatics is that the right way to take what is said, if at all possible, is the way that makes sense of the message.
	From: David Lewis (Many, but almost one [1993], 'A better solution')
	A reaction: Thus when someone misuses a word, suggesting nonsense, we gloss over it, often without even mentioning it, because the underlying sense is obvious. A good argument for the existence of propositions. Lewis doesn't mention truth.