14 ideas
| 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. |
| 18415 | The actual world is just the world you are in [Lewis, by Cappelen/Dever] |
| Full Idea: Lewis equates knowing which world is actual with knowing which world one is in. | |
| From: report of David Lewis (Attitudes De Dicto and De Se [1979]) by Cappelen,H/Dever,Josh - The Inessential Indexical 05.1 | |
| A reaction: [This view is not, of course, Actualism, but an alternative treatment of actuality, within a multitude of possibilities]. |
| 16392 | A content is a property, and believing it is self-ascribing that property [Lewis, by Recanati] |
| Full Idea: For Lewis, a belief mode is analysed by saying that to believe a content (analysed as a property) is for the subject of thought to 'self-ascribe' that property. | |
| From: report of David Lewis (Attitudes De Dicto and De Se [1979]) by François Recanati - Mental Files 18.3 | |
| A reaction: Lewis is weird. I would have thought you only self-ascribe the 'property' when you find yourself believing it. Lewis seems desperate to eliminate mental language. Belief can be a primitive concept without being primitive in ontology. |
| 18416 | Attitudes involve properties (not propositions), and belief is self-ascribing the properties [Lewis, by Solomon] |
| Full Idea: Lewis suggests that we take attitudes to have properties, rather than propositions, as contents. To stand in the belief relation to a property is to self-ascribe that property. | |
| From: report of David Lewis (Attitudes De Dicto and De Se [1979]) by Robert C. Solomon - Erotic Love as a Moral Virtue 05.1 | |
| A reaction: This is the sort of convoluted suggestion that Lewis has to come up with, in pursuit of his project of a wholly consistent metaphysics. Examine Lewis's account of properties before you judge this proposal! Self-ascribing is joining a set! |
| 16390 | Lewis's popular centred worlds approach gives an attitude an index of world, subject and time [Lewis, by Recanati] |
| Full Idea: Many philosophers now prefer Lewis's centred worlds framework for indexicals It is two-dimensional, saying an attitude only has a truth-value when evaluated with respect to a contextual index, containing a subject and time, as well as a world. | |
| From: report of David Lewis (Attitudes De Dicto and De Se [1979]) by François Recanati - Mental Files 18.2 | |
| A reaction: [compressed; this is said to have largely ousted the older Kaplan-Perry view] You only begin to understand the possible worlds game when you see how many problems find proposed 'solutions' there. |
| 18418 | A theory of perspectival de se content gives truth conditions relative to an agent [Lewis, by Cappelen/Dever] |
| Full Idea: Lewis's theory of a perspectival 'de se' content ...delivers truth conditions not absolutely, but only relative to a choice of agent/center. | |
| From: report of David Lewis (Attitudes De Dicto and De Se [1979]) by Cappelen,H/Dever,Josh - The Inessential Indexical 05.7 | |
| A reaction: The proposal rests on a theory of 'centred' possible worlds, specifying the viewpoint of some agent within the whole system. It relies on accepting the idea that indexicals are special, which Cappelen and Dever reject. |
| 468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
| Full Idea: In singing and playing the lyre, a boy will be likely to reveal not only courage and moderation, but also justice. | |
| From: Damon (fragments/reports [c.460 BCE], B4), quoted by (who?) - where? |