19 ideas
192 | Only one thing can be contrary to something [Plato] |
Full Idea: To everything that admits of a contrary there is one contrary and no more. | |
From: Plato (Protagoras [c.380 BCE], 332c) | |
A reaction: The sort of thing for which a modern philosopher would demand a proof (and then reject when the proof couldn't be found), where a Greek is happy to assert it as self-evident. I can't think of a counterexample. |
8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
Full Idea: Hilbert wanted to derive ideal mathematics from the secure, paradox-free, finite mathematics (known as 'Hilbert's Programme'). ...Note that for the realist consistency is not something we need to prove; it is a precondition of thought. | |
From: report of David Hilbert (works [1900], 6.7) by Michčle Friend - Introducing the Philosophy of Mathematics | |
A reaction: I am an intuitive realist, though I am not so sure about that on cautious reflection. Compare the claims that there are reasons or causes for everything. Reality cannot contain contradicitions (can it?). Contradictions would be our fault. |
10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
Full Idea: The solid philosophical attitude that I think is required for the grounding of pure mathematics is this: In the beginning was the sign. | |
From: David Hilbert (works [1900]), quoted by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
A reaction: Why did people invent those particular signs? Presumably they were meant to designate something, in the world or in our experience. |
10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
Full Idea: Hilbert replaced a semantic construal of inconsistency (that the theory entails a statement that is necessarily false) by a syntactic one (that the theory formally derives the statement (0 =1 ∧ 0 not-= 1). | |
From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
A reaction: Finding one particular clash will pinpoint the notion of inconsistency, but it doesn't seem to define what it means, since the concept has very wide application. |
10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
Full Idea: Hilbert's project was to establish the consistency of classical mathematics using just finitary means, to convince all parties that no contradictions will follow from employing the infinitary notions and reasoning. | |
From: report of David Hilbert (works [1900]) by A.George / D.J.Velleman - Philosophies of Mathematics Ch.6 | |
A reaction: This is the project which was badly torpedoed by Gödel's Second Incompleteness Theorem. |
190 | If asked whether justice itself is just or unjust, you would have to say that it is just [Plato] |
Full Idea: If someone asked me 'Is justice itself just or unjust?' I should answer that it was just, wouldn't you? I agree. | |
From: Plato (Protagoras [c.380 BCE], 330c) |
20184 | The only real evil is loss of knowledge [Plato] |
Full Idea: The only real kind of faring ill is the loss of knowledge. | |
From: Plato (Protagoras [c.380 BCE], 345b) | |
A reaction: This must crucially involve the intellectualist view (of Socrates) that virtuos behaviour results from knowledge, and moral wickedness is the result of ignorance. It is hard to see how forgetting a phone number is evil. |
20185 | The most important things in life are wisdom and knowledge [Plato] |
Full Idea: It would be shameful indeed to say that wisdom and knowledge are anything but the most powerful forces in human activity. | |
From: Plato (Protagoras [c.380 BCE], 352d) | |
A reaction: He lumps wisdom and knowledge together, and I think we can take 'knowledge' to mean something like understanding, because obviously mere atomistic propositional knowledge can be utterly trivial. |
191 | Everything resembles everything else up to a point [Plato] |
Full Idea: Everything resembles everything else up to a point. | |
From: Plato (Protagoras [c.380 BCE], 331d) |
203 | Courage is knowing what should or shouldn't be feared [Plato] |
Full Idea: Knowledge of what is and is not to be feared is courage. | |
From: Plato (Protagoras [c.380 BCE], 360d) |
202 | No one willingly and knowingly embraces evil [Plato] |
Full Idea: No one willingly goes to meet evil, or what he thinks is evil. | |
From: Plato (Protagoras [c.380 BCE], 358d) | |
A reaction: Presumably people who actively choose satanism can override this deep-seated attitude. But their adherence to evil usually seems to be rather restrained. A danger of tautology with ideas like this. |
193 | Some things are good even though they are not beneficial to men [Plato] |
Full Idea: 'Do you mean by good those things that are beneficial to men?' 'Not only those. I call some things which are not beneficial good as well'. | |
From: Plato (Protagoras [c.380 BCE], 333e) | |
A reaction: Examples needed, but this would be bad news for utilitarians. Good health is not seen as beneficial if it is taken for granted. Not being deaf. |
197 | Some pleasures are not good, and some pains are not evil [Plato] |
Full Idea: There are some pleasures which are not good, and some pains which are not evil. | |
From: Plato (Protagoras [c.380 BCE], 351d) | |
A reaction: Sadism and child birth. Though Bentham (I think) says that there is nothing good about the pain, since the event would obviously be better without it. |
200 | People tend only to disapprove of pleasure if it leads to pain, or prevents future pleasure [Plato] |
Full Idea: The only reason the common man disapproves of pleasures is if they lead to pain and deprive us of future pleasures. | |
From: Plato (Protagoras [c.380 BCE], 354a) | |
A reaction: Plato has a strong sense that some pleasures are just innately depraved and wicked. If those pleasure don't hurt anyone, it is very hard to pinpoint what is wrong with them. |
189 | If we punish wrong-doers, it shows that we believe virtue can be taught [Plato] |
Full Idea: Athenians inflict punishment on wrong-doers, which shows that they too think it possible to impart and teach goodness. | |
From: Plato (Protagoras [c.380 BCE], 324c) |
188 | Socrates did not believe that virtue could be taught [Plato] |
Full Idea: Socrates: I do not believe that virtue can be taught. | |
From: Plato (Protagoras [c.380 BCE], 320b) |
204 | Socrates is contradicting himself in claiming virtue can't be taught, but that it is knowledge [Plato] |
Full Idea: Socrates is contradicting himself by saying virtue is not teachable, and yet trying to demonstrate that every virtue is knowledge. | |
From: Plato (Protagoras [c.380 BCE], 361b) |
1868 | The world was made as much for animals as for man [Celsus] |
Full Idea: The world was made as much for the irrational animals as for men. | |
From: Celsus (On the True Doctrine (Against Christians) [c.178], §V) | |
A reaction: A good remark. It seems to be a classic distortion of European Christianity that the world is made for us, and that animals only exist to fill our sandwiches. |
1867 | Christians presented Jesus as a new kind of logos to oppose that of the philosophers [Celsus] |
Full Idea: Christians put forth this Jesus not only as the son of God, but as the very Logos - not the pure and holy Logos known to the philosophers, but a new kind of Logos. | |
From: Celsus (On the True Doctrine (Against Christians) [c.178], III) |