7 ideas
| 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. |
| 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. |
| 10180 | Mathematicians do not study objects, but relations between objects [Poincaré] |
| Full Idea: Mathematicians do not study objects, but relations between objects; it is a matter of indifference if the objects are replaced by others, provided the relations do not change. They are interested in form alone, not matter. | |
| From: Henri Poincaré (Science and Hypothesis [1902], p.20), quoted by E Reck / M Price - Structures and Structuralism in Phil of Maths §6 | |
| A reaction: This connects modern structuralism with Aritotle's interest in the 'form' of things. Contrary to the views of the likes of Frege, it is hard to see that the number '7' has any properties at all, apart from its relations. A daffodil would do just as well. |
| 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). |
| 18552 | Forget about beauty; just concentrate on the virtues of delicacy and discernment admired in critics [Hume, by Scruton] |
| Full Idea: Hume suggest we get away from the fruitless discussion of beauty, and simply concentrate on the qualities we admire, and ought to admire, in a critic - qualities such as delicacy and discernment. | |
| From: report of David Hume (Of the standard of taste [1757]) by Roger Scruton - Beauty: a very short introduction 6 | |
| A reaction: We might wonder how you can admire 'discernment' without some view of the thing being discern, which is in danger of being beauty. How do you judge delicacy and discernment without judging the objects of the critic's taste? Mere authority? |
| 6608 | Strong sense, delicate sentiment, practice, comparisons, and lack of prejudice, are all needed for good taste [Hume] |
| Full Idea: Strong sense, united to delicate sentiment, improved by practice, perfected by comparison, and cleared of all prejudice, can alone entitle critics to the valuable character of having 'taste'. | |
| From: David Hume (Of the standard of taste [1757]), quoted by Robert Fogelin - Walking the Tightrope of Reason Ch.6 | |
| A reaction: I agree entirely with this, but then I am a very politically incorrect elitist when it comes to taste. It just seems screamingly obvious that professional wine-tasters have a better appreciation of wine than me, and so on for the rest of the arts. |