18 ideas
| 343 | The unexamined life is not worth living for men [Socrates] |
| Full Idea: The unexamined life is not worth living for men. | |
| From: Socrates (reports of last days [c.399 BCE]), quoted by Plato - The Apology 38a | |
| A reaction: I wonder why? I can see Nietzsche offering aristocratic heroes and dancers as counterexamples. Compare Idea 3798. |
| 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. |
| 339 | Men fear death as a great evil when it may be a great blessing [Socrates] |
| Full Idea: No one knows whether death may not be the greatest of all blessings for a man, yet men fear it as if they knew that it is the greatest of evils. | |
| From: Socrates (reports of last days [c.399 BCE]), quoted by Plato - The Apology 29a | |
| A reaction: As a neutral observer, I see little sign of it being a blessing, except as a relief from misery. It seem wrong to view such a natural thing as evil, but it is the thing most of us least desire. |
| 344 | If death is like a night of dreamless sleep, such nights are very pleasant [Socrates] |
| Full Idea: If death is like a night of dreamless sleep it is an advantage, for such nights are very pleasant, and eternity would seem like a single night. | |
| From: Socrates (reports of last days [c.399 BCE]), quoted by Plato - The Apology 40d | |
| A reaction: Dreamless sleep is only pleasant if being awake is unpleasant. Very quiet days are only pleasant if the active days are horrible. A desire for a totally quiet life is absurd. |
| 16764 | The soul conserves the body, as we see by its dissolution when the soul leaves [Toletus] |
| Full Idea: Every accident of a living thing, as well as all its organs and temperaments and its dispositions are conserved by the soul. We see this from experience, since when that soul recedes, all these dissolve and become corrupted. | |
| From: Franciscus Toletus (Commentary on 'De Anima' [1572], II.1.1), quoted by Robert Pasnau - Metaphysical Themes 1274-1671 24.5 | |
| A reaction: A nice example of observing a phenemonon, but not being able to observe the dependence relation the right way round. Compare Descartes in Idea 16763. |
| 2 | We should not even harm someone who harms us [Socrates] |
| Full Idea: One should never return an injustice nor harm another human being no matter what one suffers at their hands. | |
| From: Socrates (reports of last days [c.399 BCE]), quoted by Plato - Crito 49c | |
| A reaction: Jesus of Nazareth was not the first person to make this suggestion. |
| 345 | A good man cannot be harmed, either in life or in death [Socrates] |
| Full Idea: A good man cannot be harmed, either in life or in death. | |
| From: Socrates (reports of last days [c.399 BCE]), quoted by Plato - The Apology 41d |
| 346 | One ought not to return a wrong or injury to any person, whatever the provocation [Socrates] |
| Full Idea: One ought not to return a wrong or an injury to any person, whatever the provocation is. | |
| From: Socrates (reports of last days [c.399 BCE]), quoted by Plato - Crito 49b | |
| A reaction: The same as the essential moral teachings of Jesus (see Idea 6288) and Lao Tzu (Idea 6324). The big target is not to be corrupted by the evil of other people. |
| 341 | Wealth is good if it is accompanied by virtue [Socrates] |
| Full Idea: Wealth does not bring about excellence, but excellence makes wealth and everything else good for men. | |
| From: Socrates (reports of last days [c.399 BCE]), quoted by Plato - The Apology 30b |
| 347 | Will I stand up against the law, simply because I have been unjustly judged? [Socrates] |
| Full Idea: Do I intend to destroy the laws, because the state wronged me by passing a faulty judgement at my trial? | |
| From: Socrates (reports of last days [c.399 BCE]), quoted by Plato - Crito 50c |
| 338 | Socrates is accused of denying the gods, saying sun is stone and moon is earth [Socrates, by Plato] |
| Full Idea: Socrates denies the gods, because he says the sun is stone and the moon is earth. | |
| From: report of Socrates (reports of last days [c.399 BCE]) by Plato - The Apology 26d |