13 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. |
| 5987 | Alcmaeon was the first to say the brain is central to thinking [Alcmaeon, by Staden, von] |
| Full Idea: Alcmaeon apparently was the first Greek to assign central cognitive and biological functions to the brain. | |
| From: report of Alcmaeon (fragments/reports [c.490 BCE]) by Heinrich von Staden - Alcmaeon | |
| A reaction: The name of Alcmaeon should be remembered with honour. This was 200 years before Aristotle, who still hadn't worked it out. I presume Alcmaeon inferred the truth from head injuries, which is overwhelming evidence, if you notice it. |
| 1477 | Being manly and brave is the result of convention, not of human nature [Plutarch] |
| Full Idea: Manliness is not a natural human attribute, otherwise women would be just as brave. It is due to pressure from laws, and this pressure has no free will, but is a slave of convention and criticism. | |
| From: Plutarch (64: Gryllus - on Rationality in Animals [c.85], 988c) | |
| A reaction: This is the first glimmerings of seeing gender as a cultural creation, rather than as a fact. Presumably he takes the same view of some of the supposed feminine virtues. |
| 1478 | Animals don't value pleasure, as they cease sexual intercourse after impregnation [Plutarch] |
| Full Idea: Animals of both sexes cease to have intercourse after impregnation; that shows how little animals value pleasure, and that nature is all that counts. | |
| From: Plutarch (64: Gryllus - on Rationality in Animals [c.85], 990d) | |
| A reaction: A famous monkey had an implant to stimulate pleasure, and a button to trigger it. It apparently would have starved to death rather than release the button. Animal sex is dull? |
| 1479 | Animals have not been led into homosexuality, because they value pleasure very little [Plutarch] |
| Full Idea: Because animals value pleasure very little, they have not been led into sex between males or between females. | |
| From: Plutarch (64: Gryllus - on Rationality in Animals [c.85], 990d) |
| 24043 | Soul must be immortal, since it continually moves, like the heavens [Alcmaeon, by Aristotle] |
| Full Idea: Alcmaeon says that the soul is immortal because it resembles immortal things and that this affection belongs to it because it is always in movement, like divine things, such the moon, the sun, the stars and the whole heaven. | |
| From: report of Alcmaeon (fragments/reports [c.490 BCE], DK 24) by Aristotle - De Anima 405a30 | |
| A reaction: Hm. Fish and rivers seem to be continually moving too. Presumably we are like gods, but then Greek gods seem awfully like humans. I don't know the history of belief in immortality; an interesting topic. |