15 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. |
| 13373 | Typically, paradoxes are dealt with by dividing them into two groups, but the division is wrong [Priest,G] |
| Full Idea: A natural principle is the same kind of paradox will have the same kind of solution. Standardly Ramsey's first group are solved by denying the existence of some totality, and the second group are less clear. But denial of the groups sink both. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §5) | |
| A reaction: [compressed] This sums up the argument of Priest's paper, which is that it is Ramsey's division into two kinds (see Idea 13334) which is preventing us from getting to grips with the paradoxes. Priest, notoriously, just lives with them. |
| 13368 | The 'least indefinable ordinal' is defined by that very phrase [Priest,G] |
| Full Idea: König: there are indefinable ordinals, and the least indefinable ordinal has just been defined in that very phrase. (Recall that something is definable iff there is a (non-indexical) noun-phrase that refers to it). | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §3) | |
| A reaction: Priest makes great subsequent use of this one, but it feels like a card trick. 'Everything indefinable has now been defined' (by the subject of this sentence)? König, of course, does manage to pick out one particular object. |
| 13370 | 'x is a natural number definable in less than 19 words' leads to contradiction [Priest,G] |
| Full Idea: Berry: if we take 'x is a natural number definable in less than 19 words', we can generate a number which is and is not one of these numbers. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §3) | |
| A reaction: [not enough space to spell this one out in full] |
| 13369 | By diagonalization we can define a real number that isn't in the definable set of reals [Priest,G] |
| Full Idea: Richard: φ(x) is 'x is a definable real number between 0 and 1' and ψ(x) is 'x is definable'. We can define a real by diagonalization so that it is not in x. It is and isn't in the set of reals. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §3) | |
| A reaction: [this isn't fully clear here because it is compressed] |
| 13366 | The least ordinal greater than the set of all ordinals is both one of them and not one of them [Priest,G] |
| Full Idea: Burali-Forti: φ(x) is 'x is an ordinal', and so w is the set of all ordinals, On; δ(x) is the least ordinal greater than every member of x (abbreviation: log(x)). The contradiction is that log(On)∈On and log(On)∉On. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §2) |
| 13367 | The next set up in the hierarchy of sets seems to be both a member and not a member of it [Priest,G] |
| Full Idea: Mirimanoff: φ(x) is 'x is well founded', so that w is the cumulative hierarchy of sets, V; &delta(x) is just the power set of x, P(x). If x⊆V, then V∈V and V∉V, since δ(V) is just V itself. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §2) |
| 13371 | If you know that a sentence is not one of the known sentences, you know its truth [Priest,G] |
| Full Idea: In the family of the Liar is the Knower Paradox, where φ(x) is 'x is known to be true', and there is a set of known things, Kn. By knowing a sentence is not in the known sentences, you know its truth. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §4) | |
| A reaction: [mostly my wording] |
| 13372 | There are Liar Pairs, and Liar Chains, which fit the same pattern as the basic Liar [Priest,G] |
| Full Idea: There are liar chains which fit the pattern of Transcendence and Closure, as can be seen with the simplest case of the Liar Pair. | |
| From: Graham Priest (The Structure of Paradoxes of Self-Reference [1994], §4) | |
| A reaction: [Priest gives full details] Priest's idea is that Closure is when a set is announced as complete, and Transcendence is when the set is forced to expand. He claims that the two keep coming into conflict. |
| 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 Castańeda 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. |
| 20959 | Concepts are only analytic once the predicate is absorbed into the subject [Schleiermacher] |
| Full Idea: The difference between analytic and synthetic judgements is an unimportant fluid one. 'Ice melts' is analytic if it is already taken up into the concept of ice, and synthetic if not yet taken up. It is just a different state of the formation of concepts. | |
| From: Friedrich Schleiermacher (Dialektik [1833], p.563), quoted by Andrew Bowie - Introduction to German Philosophy 8 'Scientific' | |
| A reaction: [compressed] I wonder if Quine ever encountered this quotation. The idea refers to Kant's notion of analyticity, and makes the good point that predicates only become 'contained in the subject' once the situation is very familiar. |