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. |
| 17879 | Axiomatising set theory makes it all relative [Skolem] |
| Full Idea: Axiomatising set theory leads to a relativity of set-theoretic notions, and this relativity is inseparably bound up with every thoroughgoing axiomatisation. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.296) |
| 17878 | If a 1st-order proposition is satisfied, it is satisfied in a denumerably infinite domain [Skolem] |
| Full Idea: Löwenheim's theorem reads as follows: If a first-order proposition is satisfied in any domain at all, it is already satisfied in a denumerably infinite domain. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.293) |
| 17880 | Integers and induction are clear as foundations, but set-theory axioms certainly aren't [Skolem] |
| Full Idea: The initial foundations should be immediately clear, natural and not open to question. This is satisfied by the notion of integer and by inductive inference, by it is not satisfied by the axioms of Zermelo, or anything else of that kind. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.299) | |
| A reaction: This is a plea (endorsed by Almog) that the integers themselves should be taken as primitive and foundational. I would say that the idea of successor is more primitive than the integers. |
| 17881 | Mathematician want performable operations, not propositions about objects [Skolem] |
| Full Idea: Most mathematicians want mathematics to deal, ultimately, with performable computing operations, and not to consist of formal propositions about objects called this or that. | |
| From: Thoralf Skolem (Remarks on axiomatised set theory [1922], p.300) |
| 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. |
| 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. |
| 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 |
| 6613 | The natural kinds are objects, processes and properties/relations [Ellis] |
| Full Idea: There are three hierarchies of natural kinds: objects or substances (substantive universals), events or processes (dynamic universals), and properties or relations (tropic universals). | |
| From: Brian Ellis (Katzav on limitations of dispositions [2005], 91) | |
| A reaction: Most interesting here is the identifying of natural kinds with universals, making universals into the families of nature. Universals are high-level sets of natural kinds. To grasp universals you must see patterns, and infer the underlying order. |
| 6616 | Least action is not a causal law, but a 'global law', describing a global essence [Ellis] |
| Full Idea: The principle of least action is not a causal law, but is what I call a 'global law', which describes the essence of the global kind, which every object in the universe necessarily instantiates. | |
| From: Brian Ellis (Katzav on limitations of dispositions [2005]) | |
| A reaction: As a fan of essentialism I find this persuasive. If I inherit part of my essence from being a mammal, I inherit other parts of my essence from being an object, and all objects would share that essence, so it would look like a 'law' for all objects. |
| 6615 | A species requires a genus, and its essence includes the essence of the genus [Ellis] |
| Full Idea: A specific universal can exist only if the generic universal of which it is a species exists, but generic universals don't depend on species; …the essence of any genus is included in its species, but not conversely. | |
| From: Brian Ellis (Katzav on limitations of dispositions [2005], 91) | |
| A reaction: Thus the species 'electron' would be part of the genus 'lepton', or 'human' part of 'mammal'. The point of all this is to show how individual items connect up with the rest of the universe, giving rise to universal laws, such as Least Action. |
| 6614 | A hierarchy of natural kinds is elaborate ontology, but needed to explain natural laws [Ellis] |
| Full Idea: The hierarchy of natural kinds proposed by essentialism may be more elaborate than is strictly required for purposes of ontology, but it is necessary to explain the necessity of the laws of nature, and the universal applicability of global principles. | |
| From: Brian Ellis (Katzav on limitations of dispositions [2005], 91) | |
| A reaction: I am all in favour of elaborating ontology in the name of best explanation. There seem, though, to be some remaining ontological questions at the point where the explanations of essentialism run out. |
| 6612 | Without general principles, we couldn't predict the behaviour of dispositional properties [Ellis] |
| Full Idea: It is objected to dispositionalism that without the principle of least action, or some general principle of equal power, the specific dispositional properties of things could tell us very little about how these things would be disposed to behave. | |
| From: Brian Ellis (Katzav on limitations of dispositions [2005], 90) | |
| A reaction: Ellis attempts to meet this criticism, by placing dispositional properties within a hierarchy of broader properties. There remains a nagging doubt about how essentialism can account for space, time, order, and the existence of essences. |
| 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 |