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All the ideas for '', 'Mathematics and Indispensibility' and 'Nonexistent Objects'

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6 ideas

5. Theory of Logic / A. Overview of Logic / 1. Overview of Logic

11211	If a sound conclusion comes from two errors that cancel out, the path of the argument must matter [Rumfitt]
	Full Idea: If a designated conclusion follows from the premisses, but the argument involves two howlers which cancel each other out, then the moral is that the path an argument takes from premisses to conclusion does matter to its logical evaluation.
	From: Ian Rumfitt ("Yes" and "No" [2000], II)
	A reaction: The drift of this is that our view of logic should be a little closer to the reasoning of ordinary language, and we should rely a little less on purely formal accounts.

5. Theory of Logic / E. Structures of Logic / 2. Logical Connectives / a. Logical connectives

11210	Standardly 'and' and 'but' are held to have the same sense by having the same truth table [Rumfitt]
	Full Idea: If 'and' and 'but' really are alike in sense, in what might that likeness consist? Some philosophers of classical logic will reply that they share a sense by virtue of sharing a truth table.
	From: Ian Rumfitt ("Yes" and "No" [2000])
	A reaction: This is the standard view which Rumfitt sets out to challenge.

11212	The sense of a connective comes from primitively obvious rules of inference [Rumfitt]
	Full Idea: A connective will possess the sense that it has by virtue of its competent users' finding certain rules of inference involving it to be primitively obvious.
	From: Ian Rumfitt ("Yes" and "No" [2000], III)
	A reaction: Rumfitt cites Peacocke as endorsing this view, which characterises the logical connectives by their rules of usage rather than by their pure semantic value.

7. Existence / D. Theories of Reality / 11. Ontological Commitment / e. Ontological commitment problems

9558	All scientific tests will verify mathematics, so it is a background, not something being tested [Sober]
	Full Idea: If mathematical statements are part of every competing hypothesis, then no matter which hypothesis comes out best in the light of observations, they will be part of the best hypothesis. They are not tested, but are a background assumption.
	From: Elliott Sober (Mathematics and Indispensibility [1993], 45), quoted by Charles Chihara - A Structural Account of Mathematics
	A reaction: This is a very nice objection to the Quine-Putnam thesis that mathematics is confirmed by the ongoing successes of science.

9. Objects / A. Existence of Objects / 4. Impossible objects

18948	There is an object for every set of properties (some of which exist, and others don't) [Parsons,T, by Sawyer]
	Full Idea: According to Terence Parsons, there is an object corresponding to every set of properties. To some of those sets of properties there corresponds an object that exists, and to others there corresponds an object that does not exist (a nonexistent object).
	From: report of Terence Parsons (Nonexistent Objects [1980]) by Sarah Sawyer - Empty Names 5
	A reaction: This I take to be the main source of the modern revival of Meinong's notorious view of objects (attacked by Russell). I always find the thought 'a round square is square' to be true, and in need of a truthmaker. But must a round square be non-triangular?

19. Language / F. Communication / 3. Denial

11214	We learn 'not' along with affirmation, by learning to either affirm or deny a sentence [Rumfitt]
	Full Idea: The standard view is that affirming not-A is more complex than affirming the atomic sentence A itself, with the latter determining its sense. But we could learn 'not' directly, by learning at once how to either affirm A or reject A.
	From: Ian Rumfitt ("Yes" and "No" [2000], IV)
	A reaction: [compressed] This seems fairly anti-Fregean in spirit, because it looks at the psychology of how we learn 'not' as a way of clarifying what we mean by it, rather than just looking at its logical behaviour (and thus giving it a secondary role).