35 ideas
| 13786 | Wisdom is called 'beautiful', because it performs fine works [Plato] |
| Full Idea: Wisdom [phronesis] is correctly given the name 'kalon' [beautiful], since it performs the works that we say are beautiful and welcome as such. | |
| From: Plato (Cratylus [c.377 BCE], 416d) | |
| A reaction: 'Phronesis' in Aristotle is more like prudence, or common sense, rather than wisdom ['sophia']. 'Kalon' also means fine or noble. This translation seems fair enough, though. |
| 13780 | Good people are no different from wise ones [Plato] |
| Full Idea: Socrates: Are good people any different from wise ones? No, they aren't. | |
| From: Plato (Cratylus [c.377 BCE], 398b) | |
| A reaction: This is Socrates's 'intellectualism', his view that being good is entirely a matter of reason and knowledge, and not a matter of habit or emotion. Do we still accept the traditional assumption that wise people are thereby morally good? |
| 17641 | Discoveries in mathematics can challenge philosophy, and offer it a new foundation [Russell] |
| Full Idea: Any new discovery as to mathematical method and principles is likely to upset a great deal of otherwise plausible philosophising, as well as to suggest a new philosophy which will be solid in proportion as its foundations in mathematics are securely laid. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.283) | |
| A reaction: This is a manifesto for modern analytic philosophy. I'm not convinced, especially if a fictionalist view of maths is plausible. What Russell wants is rigour, but there are other ways of getting that. Currently I favour artificial intelligence. |
| 17638 | If one proposition is deduced from another, they are more certain together than alone [Russell] |
| Full Idea: Two obvious propositions of which one can be deduced from the other both become more certain than either in isolation; thus in a complicated deductive system, many parts of which are obvious, the total probability may become all but absolute certainty. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.279) | |
| A reaction: Thagard picked this remark out, in support of his work on coherence. |
| 17632 | Non-contradiction was learned from instances, and then found to be indubitable [Russell] |
| Full Idea: The law of contradiction must have been originally discovered by generalising from instances, though, once discovered, it was found to be quite as indubitable as the instances. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.274) |
| 13778 | A dialectician is someone who knows how to ask and to answer questions [Plato] |
| Full Idea: What would you call someone who knows how to ask and answer questions? Wouldn't you call him a dialectician? | |
| From: Plato (Cratylus [c.377 BCE], 390c) | |
| A reaction: Asking good questions and giving good answers sound like two very different skills. I presume dialectic is the process of arriving at answers by means of asking the right questions. |
| 10882 | Predicative definitions only refer to entities outside the defined collection [Horsten] |
| Full Idea: Definitions are called 'predicative', and are considered sound, if they only refer to entities which exist independently from the defined collection. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §2.4) |
| 13776 | Truths say of what is that it is, falsehoods say of what is that it is not [Plato] |
| Full Idea: Those statements that say of the things that are that they are, are true, while those that say of the things that are that they are not, are false. | |
| From: Plato (Cratylus [c.377 BCE], 385b) | |
| A reaction: It was quite a shock to discover this, because the famous Aristotle definition (Idea 586) is always quoted, and no modern writers seem to have any awareness of the Plato remark. Classical scholarship is very poor in analytic philosophy. |
| 13777 | A name is a sort of tool [Plato] |
| Full Idea: A name is a sort of tool. | |
| From: Plato (Cratylus [c.377 BCE], 388a) | |
| A reaction: Idea 13775 gives a background for this metaphor, from earlier in the text. Wittgenstein has a famous toolkit metaphor for language. The whole of this text, 'Cratylus', is about names. |
| 13790 | A name-giver might misname something, then force other names to conform to it [Plato] |
| Full Idea: The name-giver might have made a mistake at the beginning and then forced the other names to be consistent with it. | |
| From: Plato (Cratylus [c.377 BCE], 436c) | |
| A reaction: Lovely. This is Gareth Evans's 'Madagascar' example. See Idea 9041. |
| 13791 | Things must be known before they are named, so it can't be the names that give us knowledge [Plato] |
| Full Idea: If things cannot be learned except from their names, how can we possibly claim that the name-givers or rule-setters have knowledge before any names had been given for them to know? | |
| From: Plato (Cratylus [c.377 BCE], 438b) | |
| A reaction: Running through this is a hostility to philosophy of language, so I find it very congenial. We are animals who relate to the world before language takes a grip. We have full-blown knowledge of things, with no intervention of words. |
| 13789 | Anyone who knows a thing's name also knows the thing [Plato] |
| Full Idea: The simple truth is that anyone who knows a thing's name also knows the thing. | |
| From: Plato (Cratylus [c.377 BCE], 435d) | |
| A reaction: A nice slogan, but it seems to be blatantly false. The best example is Gareth Evans's of joining in a conversation about a person ('Louis'?), and only gradually tuning in to the person to which the name refers. |
| 10884 | A theory is 'categorical' if it has just one model up to isomorphism [Horsten] |
| Full Idea: If a theory has, up to isomorphism, exactly one model, then it is said to be 'categorical'. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §5.2) |
| 17629 | Which premises are ultimate varies with context [Russell] |
| Full Idea: Premises which are ultimate in one investigation may cease to be so in another. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.273) |
| 17630 | The sources of a proof are the reasons why we believe its conclusion [Russell] |
| Full Idea: In mathematics, except in the earliest parts, the propositions from which a given proposition is deduced generally give the reason why we believe the given proposition. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.273) |
| 17640 | Finding the axioms may be the only route to some new results [Russell] |
| Full Idea: The premises [of a science] ...are pretty certain to lead to a number of new results which could not otherwise have been known. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.282) | |
| A reaction: I identify this as the 'fruitfulness' that results when the essence of something is discovered. |
| 10885 | Computer proofs don't provide explanations [Horsten] |
| Full Idea: Mathematicians are uncomfortable with computerised proofs because a 'good' proof should do more than convince us that a certain statement is true. It should also explain why the statement in question holds. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §5.3) |
| 17627 | It seems absurd to prove 2+2=4, where the conclusion is more certain than premises [Russell] |
| Full Idea: It is an apparent absurdity in proceeding ...through many rather recondite propositions of symbolic logic, to the 'proof' of such truisms as 2+2=4: for it is plain that the conclusion is more certain than the premises, and the supposed proof seems futile. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.272) | |
| A reaction: Famously, 'Principia Mathematica' proved this fact at enormous length. I wonder if this thought led Moore to his common sense view of his own hand - the conclusion being better than the sceptical arguments? |
| 10881 | The concept of 'ordinal number' is set-theoretic, not arithmetical [Horsten] |
| Full Idea: The notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept. | |
| From: Leon Horsten (Philosophy of Mathematics [2007], §2.3) |
| 17628 | Arithmetic was probably inferred from relationships between physical objects [Russell] |
| Full Idea: When 2 + 2 =4 was first discovered, it was probably inferred from the case of sheep and other concrete cases. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.272) |
| 2063 | How can beauty have identity if it changes? [Plato] |
| Full Idea: If beauty never stays the same, how can it be something? | |
| From: Plato (Cratylus [c.377 BCE], 439e) | |
| A reaction: A rather Platonic question! I presume that Heraclitus had a sense of beauty, and things regarded as 'sublime' are often tumultuous. |
| 13775 | We only succeed in cutting if we use appropriate tools, not if we approach it randomly [Plato] |
| Full Idea: If we undertake to cut something and make the cut in whatever way we choose and with whatever tool we choose, we will not succeed. If we cut according to the nature of cutting and being cut, and with the natural tool, we'll succeed and cut correctly. | |
| From: Plato (Cratylus [c.377 BCE], 387a) | |
| A reaction: I take this passage to be the creed for realists about the physical world - a commitment not merely to the existence of an external world, but to the existence of facts about it, which we may or may not be able to discover. |
| 13787 | Doesn't each thing have an essence, just as it has other qualities? [Plato] |
| Full Idea: Don't you think that just as each thing has a colour or some of those other qualities we mentioned, it also has a being or essence? | |
| From: Plato (Cratylus [c.377 BCE], 423e) | |
| A reaction: The Greek here seems to be 'ousia', which I increasingly think should be translated as 'distinct identity', rather than as 'existence' or as 'essence'. Maybe the philosophical term 'haecceity' captures it best. |
| 13774 | Things don't have every attribute, and essence isn't private, so each thing has an essence [Plato] |
| Full Idea: If Euthydemus is wrong that everything always has every attribute simultaneously, or that being or essence is private for each person, then it is clear that things have some fixed being or essence of their own. | |
| From: Plato (Cratylus [c.377 BCE], 386d) | |
| A reaction: I'm not sure what 'being or essence' translates. If it translates 'ousia' then I wouldn't make too much of this remark from an essentialist point of view. |
| 13772 | Is the being or essence of each thing private to each person? [Plato] |
| Full Idea: Is the being or essence of each of the things that are something private to each person, as Protagoras tells us? | |
| From: Plato (Cratylus [c.377 BCE], 385e) | |
| A reaction: This kind of drastic personal relativism about essences doesn't sound very plausible, but the idea that essences are private to each culture, or to each language, must certainly be taken seriously. |
| 13788 | If we made a perfect duplicate of Cratylus, there would be two Cratyluses [Plato] |
| Full Idea: Soc: Suppose we made a duplicate of everything you have and put it beside you; would there then be two Cratyluses, or Cratylus and an image of Cratylus? Crat: It seems to me, Socrates, that there would be two Cratyluses. | |
| From: Plato (Cratylus [c.377 BCE], 432c) | |
| A reaction: Don't think that science fiction examples are a modern development in philosophy. Plato has just invented the Startrek transporter. The two Cratyluses are the two spheres in Max Black's famous example. |
| 17637 | The most obvious beliefs are not infallible, as other obvious beliefs may conflict [Russell] |
| Full Idea: Even where there is the highest degree of obviousness, we cannot assume that we are infallible - a sufficient conflict with other obvious propositions may lead us to abandon our belief, as in the case of a hallucination afterwards recognised as such. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.279) | |
| A reaction: This approach to fallibilism seems to arise from the paradox that undermined Frege's rather obvious looking axioms. After Peirce and Russell, fallibilism has become a secure norm of modern thought. |
| 17639 | Believing a whole science is more than believing each of its propositions [Russell] |
| Full Idea: Although intrinsic obviousness is the basis of every science, it is never, in a fairly advanced science, the whole of our reason for believing any one proposition of the science. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.279) |
| 13792 | There can't be any knowledge if things are constantly changing [Plato] |
| Full Idea: It isn't even reasonable to say that there is such a thing as knowledge, Cratylus, if all things are passing on and none remain. | |
| From: Plato (Cratylus [c.377 BCE], 440a) | |
| A reaction: This encapsulates Plato's horror at Heraclitus scepticism about the stable identity of things. It leads to the essentialism of Aristotle and Leibniz, who fear that there is no knowledge if we can't pin down individual identities. Know processes? |
| 17631 | Induction is inferring premises from consequences [Russell] |
| Full Idea: The inferring of premises from consequences is the essence of induction. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.274) | |
| A reaction: So induction is just deduction in reverse? Induction is transcendental deduction? Do I deduce the premises from observing a lot of white swans? Hm. |
| 13781 | Soul causes the body to live, and gives it power to breathe and to be revitalized [Plato] |
| Full Idea: Those who named the soul thought that when the soul is present in the body, it causes it to live and gives it the power to breathe the air and be revitalized [anapsuchon]. | |
| From: Plato (Cratylus [c.377 BCE], 399d) | |
| A reaction: I quote this to emphasis that Greek psuché is very different from the consciousness which is largely discussed in modern philosophy of mind. I find it helpful to make a real effort to grasp the Greek concept. The feeling of life within you. |
| 13785 | 'Arete' signifies lack of complexity and a free-flowing soul [Plato] |
| Full Idea: 'Areté' signifies lack of perplexity [euporia, ease of movement], and that the flow of a good soul is unimpeded. | |
| From: Plato (Cratylus [c.377 BCE], 415d) | |
| A reaction: Some highly dubious etymology going on here, and throughout 'Cratylus', but it gives a nice feeling for the way Socrates and Plato saw virtue. |
| 17633 | The law of gravity has many consequences beyond its grounding observations [Russell] |
| Full Idea: The law of gravitation leads to many consequences which could not be discovered merely from the apparent motions of the heavenly bodies. | |
| From: Bertrand Russell (Regressive Method for Premises in Mathematics [1907], p.275) |
| 13779 | The natural offspring of a lion is called a 'lion' (but what about the offspring of a king?) [Plato] |
| Full Idea: It seems to me that it is right to call a lion's offspring a 'lion' and a horse's offspring a 'horse' (I'm talking about natural offspring, not some monster). ...but by the same argument any offspring of a king should be called a 'king'. | |
| From: Plato (Cratylus [c.377 BCE], 393b) | |
| A reaction: The standard modern difficulty is whether all descendants of dinosaurs are still called 'dinosaur', which they are not. |
| 13783 | Even the gods love play [Plato] |
| Full Idea: Even the gods love play. | |
| From: Plato (Cratylus [c.377 BCE], 406c) |