12 ideas
| 15787 | Maybe Ockham's Razor is a purely aesthetic principle [Lycan] |
| Full Idea: It might be said that Ockham's Razor is a purely aesthetic principle. | |
| From: William Lycan (The Trouble with Possible Worlds [1979], 02) | |
| A reaction: I don't buy this, if it meant to be dismissive of the relevance of the principle to truth. A deep question might be, what is so aesthetically attractive about simplicity? I'm inclined to think that application of the Razor has delivered terrific results. |
| 15784 | The Razor seems irrelevant for Meinongians, who allow absolutely everything to exist [Lycan] |
| Full Idea: A Meinongian has already posited everything that could, or even could not, be; how, then, can any subsequent brandishing of Ockham's Razor be to the point? | |
| From: William Lycan (The Trouble with Possible Worlds [1979], 02) | |
| A reaction: See the ideas of Alexius Meinong. Presumably these crazy Meinongians must make some distinction between what actually exists in front of your nose, and the rest. So the Razor can use that distinction too. |
| 15946 | Cantor developed sets from a progression into infinity by addition, multiplication and exponentiation [Cantor, by Lavine] |
| Full Idea: Cantor's development of set theory began with his discovery of the progression 0, 1, ....∞, ∞+1, ∞+2, ..∞x2, ∞x3, ...∞^2, ..∞^3, ...∞^∞, ...∞^∞^∞..... | |
| From: report of George Cantor (Grundlagen (Foundations of Theory of Manifolds) [1883]) by Shaughan Lavine - Understanding the Infinite VIII.2 |
| 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. |
| 15911 | Ordinals are generated by endless succession, followed by a limit ordinal [Cantor, by Lavine] |
| Full Idea: Ordinal numbers are generated by two principles: each ordinal has an immediate successor, and each unending sequence has an ordinal number as its limit (that is, an ordinal that is next after such a sequence). | |
| From: report of George Cantor (Grundlagen (Foundations of Theory of Manifolds) [1883]) by Shaughan Lavine - Understanding the Infinite III.4 |
| 15792 | Maybe non-existent objects are sets of properties [Lycan] |
| Full Idea: Meinong's Objects have sometimes been construed as sets of properties. | |
| From: William Lycan (The Trouble with Possible Worlds [1979], 09) | |
| A reaction: [Lycan cites Castaņeda and T.Parsons] You still seem to have the problem with any 'bundle' theory of anything. A non-existent object is as much intended to be an object as anything on my desk right now. It just fails to be. |
| 15795 | Treating possible worlds as mental needs more actual mental events [Lycan] |
| Full Idea: A mentalistic approach to possible worlds is daunted by the paucity of actual mental events. | |
| From: William Lycan (The Trouble with Possible Worlds [1979], 09) | |
| A reaction: Why do they have to be actual, any more than memories have to be conscious? The mental events just need to be available when you need them. They are never all required simultaneously. This isn't mathematical logic! |
| 15796 | Possible worlds must be made of intensional objects like propositions or properties [Lycan] |
| Full Idea: I believe the only promising choice of actual entities to serve as 'worlds' is that of sets of intensional objects, such as propositions or properties with stipulated interrelations. | |
| From: William Lycan (The Trouble with Possible Worlds [1979], 12) | |
| A reaction: This is mainly in response to Lewis's construction of them out of actual concrete objects. It strikes me as a bogus problem. It is just a convenient way to think precisely about possibilities, and occasionally outruns our mental capacity. |
| 15794 | If 'worlds' are sentences, and possibility their consistency, consistency may rely on possibility [Lycan] |
| Full Idea: If a 'world' is understood as a set of sentences, then possibility may be understood as consistency, ...but this seems circular, in that 'consistency' of sentences cannot adequately be defined save in terms of possibility. | |
| From: William Lycan (The Trouble with Possible Worlds [1979], 09) | |
| A reaction: [Carnap and Hintikka propose the view, Lewis 'Counterfactuals' p.85 objects] Worlds as sentences is not, of course, the same as worlds as propositions. There is a lot of circularity around in 'possible' worlds. |
| 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). |