24 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. |
| 1630 | We can only see an alien language in terms of our own thought structures (e.g. physical/abstract) [Quine] |
| Full Idea: We are prone to talk about physical and abstract objects. It is hard to know how else to talk, because we are bound to adapt any alien pattern to our own in the very process of understanding or translating the alien sentences. | |
| From: Willard Quine (Speaking of Objects [1960], pt.I,p.1) |
| 5747 | "No entity without identity" - our ontology must contain items with settled identity conditions [Quine, by Melia] |
| Full Idea: Quine's well-known slogan "no entity without identity" means that no object should be admitted into our ontology unless its identity conditions, the conditions that say which object it is, have been settled. | |
| From: report of Willard Quine (Speaking of Objects [1960]) by Joseph Melia - Modality Ch.4 | |
| A reaction: This invites science fiction scenarios, where we admit the existence of something before we have a clue what it is (whether it is physical, hallucination, divine..). Quine's slogan seems attractive but optimistic. How 'settled'? |
| 7925 | There is no proper identity concept for properties, and it is hard to distinguish one from two [Quine] |
| Full Idea: The lack of a proper identity concept for attributes (properties) is a lack that philosophers feel impelled to supply; for, what sense is there in saying there are attributes when there is no sense in saying when there is one attribute and when two? | |
| From: Willard Quine (Speaking of Objects [1960], IV) | |
| A reaction: This strikes me as being a really crucial question. There is a mistaken tendency to take any possible linguistic predicate as implying a natural property. I sympathise with the sceptics here (see Ideas 4029, 3906, 3322). How to individuate properties? |
| 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) |
| 13387 | Our conceptual scheme becomes more powerful when we posit abstract objects [Quine] |
| Full Idea: There is no denying the access of power that accrues to our conceptual scheme through the positing of abstract objects. | |
| From: Willard Quine (Speaking of Objects [1960], §5) | |
| A reaction: This seems right, both in its use of the word 'posit', and in its general pragmatic claim. So why? If they enable us to grapple with the world better, it must be because of their power of generalisation. They are nets thrown over chunks of reality. |
| 8277 | I prefer 'no object without identity' to Quine's 'no entity without identity' [Lowe on Quine] |
| Full Idea: To adapt Quine's famous slogan ('no entity without identity'), I prefer to say 'no object without identity'. | |
| From: comment on Willard Quine (Speaking of Objects [1960], p.52) by E.J. Lowe - The Possibility of Metaphysics 7.1 | |
| A reaction: Quine was trying to make us all more scientific, but Lowe is closer to common sense. The sky is an entity, most of us would say, but with very shaky identity-conditions. A wave of the sea is a good example. |
| 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. |
| 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. |
| 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) |
| 1631 | You could know the complete behavioural conditions for a foreign language, and still not know their beliefs [Quine] |
| Full Idea: We could know the necessary and sufficient stimulatory conditions of every possible act of utterance, in a foreign language, and still not know how to determine what objects the speakers of that language believe in. | |
| From: Willard Quine (Speaking of Objects [1960], pt.III,p.11) | |
| A reaction: I just don't believe this, because the same scepticism then creeps into discussions of native speakers of a single language, and all communcation is blighted - which is nonsense. |
| 1632 | Translation of our remote past or language could be as problematic as alien languages [Quine] |
| Full Idea: Translation of our remote past or future discourse into the terms we now know could be about as tenuous and arbitrary a projection as translation of a heathen language was seen to be. | |
| From: Willard Quine (Speaking of Objects [1960], pt.V,p.25) | |
| A reaction: Is he seriously saying that we can't understand Shakespeare, because holism implies that we would have to be Elizabethans? So scholarship is in vain? Is yesterday the 'past'? |
| 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. |
| 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) |
| 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) |