11 ideas
| 8207 | The quest for simplicity drove scientists to posit new entities, such as molecules in gases [Quine] |
| Full Idea: It is the quest for system and simplicity that has kept driving the scientist to posit further entities as values of his variables. By positing molecules, Boyles' law of gases could be assimilated into a general theory of bodies in motion. | |
| From: Willard Quine (On Multiplying Entities [1974], p.262) | |
| A reaction: Interesting that a desire for simplicity might lead to multiplications of entities. In fact, I presume molecules had been proposed elsewhere in science, and were adopted in gas-theory because they were thought to exist, not because simplicity is nice. |
| 8208 | In arithmetic, ratios, negatives, irrationals and imaginaries were created in order to generalise [Quine] |
| Full Idea: In classical arithmetic, ratios were posited to make division generally applicable, negative numbers to make subtraction generally applicable, and irrationals and finally imaginaries to make exponentiation generally applicable. | |
| From: Willard Quine (On Multiplying Entities [1974], p.263) | |
| A reaction: This is part of Quine's proposal (c.f. Idea 8207) that entities have to be multiplied in order to produce simplicity. He is speculating. Maybe they are proposed because they are just obvious, and the generality is a nice side-effect. |
| 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. |
| 8205 | Explaining events just by bodies can't explain two events identical in space-time [Quine] |
| Full Idea: An account of events just in terms of physical bodies does not distinguish between events that happen to take up just the same portion of space-time. A man's whistling and walking would be identified with the same temporal segment of the man. | |
| From: Willard Quine (On Multiplying Entities [1974], p.260) | |
| A reaction: We wouldn't want to make his 'walking' and his 'strolling' two events. Whistling and walking are different because different objects are involved (lips and legs). Hence a man is not (ontologically) a single object. |
| 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?). |
| 8206 | Necessity could be just generalisation over classes, or (maybe) quantifying over possibilia [Quine] |
| Full Idea: The need to add a note of necessity to 'all black crows are black' could be met by a generalisation over classes (what belongs to sets x and y belongs to y), or maybe be quantifying over possible particulars. | |
| From: Willard Quine (On Multiplying Entities [1974], p.262) | |
| A reaction: He dislikes the second strategy because 'unactualized particulars are an obscure and troublesome lot'. The second is the strategy of Lewis. I think necessity starts to creep back in as soon as you ask WHY a generalisation holds true. |
| 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. |
| 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. |
| 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). |