35 ideas
| 354 | Wisdom makes virtue and true goodness possible [Plato] |
| Full Idea: It is wisdom that makes possible courage and self-control and integrity or, in a word, true goodness. | |
| From: Plato (Phaedo [c.382 BCE], 069b) | |
| A reaction: Aristotle also says that prudence (phronesis) makes virtue possible. |
| 370 | Philosophy is a purification of the soul ready for the afterlife [Plato] |
| Full Idea: Souls which have purified themselves sufficiently by philosophy will live after death without bodies. | |
| From: Plato (Phaedo [c.382 BCE], 114b) | |
| A reaction: Purifying it of what? Error, or desire, or narrow-mindedness, or the physical? |
| 350 | In investigation the body leads us astray, but the soul gets a clear view of the facts [Plato] |
| Full Idea: When philosophers investigate with the help of the body they are led astray, but through reflection the soul gets a clear view of the facts. | |
| From: Plato (Phaedo [c.382 BCE], 065c) |
| 362 | The greatest misfortune for a person is to develop a dislike for argument [Plato] |
| Full Idea: No greater misfortune could happen to anyone than developing a dislike for argument. | |
| From: Plato (Phaedo [c.382 BCE], 089d) |
| 8623 | Proof reveals the interdependence of truths, as well as showing their certainty [Euclid, by Frege] |
| Full Idea: Euclid gives proofs of many things which anyone would concede to him without question. ...The aim of proof is not merely to place the truth of a proposition beyond doubt, but also to afford us insight into the dependence of truths upon one another. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Gottlob Frege - Grundlagen der Arithmetik (Foundations) §02 | |
| A reaction: This connects nicely with Shoemaker's view of analysis (Idea 8559), which I will adopt as my general view. I've always thought of philosophy as the aspiration to wisdom through the cartography of concepts. |
| 13907 | If you pick an arbitrary triangle, things proved of it are true of all triangles [Euclid, by Lemmon] |
| Full Idea: Euclid begins proofs about all triangles with 'let ABC be a triangle', but ABC is not a proper name. It names an arbitrarily selected triangle, and if that has a property, then we can conclude that all triangles have the property. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by E.J. Lemmon - Beginning Logic 3.2 | |
| A reaction: Lemmon adds the proviso that there must be no hidden assumptions about the triangle we have selected. You must generalise the properties too. Pick a triangle, any triangle, say one with three angles of 60 degrees; now generalise from it. |
| 6297 | Euclid's geometry is synthetic, but Descartes produced an analytic version of it [Euclid, by Resnik] |
| Full Idea: Euclid's geometry is a synthetic geometry; Descartes supplied an analytic version of Euclid's geometry, and we now have analytic versions of the early non-Euclidean geometries. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Michael D. Resnik - Maths as a Science of Patterns One.4 | |
| A reaction: I take it that the original Euclidean axioms were observations about the nature of space, but Descartes turned them into a set of pure interlocking definitions which could still function if space ceased to exist. |
| 9603 | An assumption that there is a largest prime leads to a contradiction [Euclid, by Brown,JR] |
| Full Idea: Assume a largest prime, then multiply the primes together and add one. The new number isn't prime, because we assumed a largest prime; but it can't be divided by a prime, because the remainder is one. So only a larger prime could divide it. Contradiction. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by James Robert Brown - Philosophy of Mathematics Ch.1 | |
| A reaction: Not only a very elegant mathematical argument, but a model for how much modern logic proceeds, by assuming that the proposition is false, and then deducing a contradiction from it. |
| 9894 | A unit is that according to which each existing thing is said to be one [Euclid] |
| Full Idea: A unit is that according to which each existing thing is said to be one. | |
| From: Euclid (Elements of Geometry [c.290 BCE], 7 Def 1) | |
| A reaction: See Frege's 'Grundlagen' §29-44 for a sustained critique of this. Frege is good, but there must be something right about the Euclid idea. If I count stone, paper and scissors as three, each must first qualify to be counted as one. Psychology creeps in. |
| 13155 | If you add one to one, which one becomes two, or do they both become two? [Plato] |
| Full Idea: I cannot convince myself that when you add one to one either the first or the second one becomes two, or they both become two by the addition of the one to the other, ...or that when you divide one, the cause of becoming two is now the division. | |
| From: Plato (Phaedo [c.382 BCE], 097d) | |
| A reaction: Lovely questions, all leading to the conclusion that two consists of partaking in duality, to which you can come by several different routes. |
| 8738 | Postulate 2 says a line can be extended continuously [Euclid, by Shapiro] |
| Full Idea: Euclid's Postulate 2 says the geometer can 'produce a finite straight line continuously in a straight line'. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Stewart Shapiro - Thinking About Mathematics 4.2 | |
| A reaction: The point being that this takes infinity for granted, especially if you start counting how many points there are on the line. The Einstein idea that it might eventually come round and hit you on the back of the head would have charmed Euclid. |
| 22278 | Euclid relied on obvious properties in diagrams, as well as on his axioms [Potter on Euclid] |
| Full Idea: Euclid's axioms were insufficient to derive all the theorems of geometry: at various points in his proofs he appealed to properties that are obvious from the diagrams but do not follow from the stated axioms. | |
| From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Michael Potter - The Rise of Analytic Philosophy 1879-1930 03 'aim' | |
| A reaction: I suppose if the axioms of a system are based on self-evidence, this would licence an appeal to self-evidence elsewhere in the system. Only pedants insist on writing down what is obvious to everyone! |
| 8673 | Euclid's parallel postulate defines unique non-intersecting parallel lines [Euclid, by Friend] |
| Full Idea: Euclid's fifth 'parallel' postulate says if there is an infinite straight line and a point, then there is only one straight line through the point which won't intersect the first line. This axiom is independent of Euclid's first four (agreed) axioms. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Michèle Friend - Introducing the Philosophy of Mathematics 2.2 | |
| A reaction: This postulate was challenged in the nineteenth century, which was a major landmark in the development of modern relativist views of knowledge. |
| 10250 | Euclid needs a principle of continuity, saying some lines must intersect [Shapiro on Euclid] |
| Full Idea: Euclid gives no principle of continuity, which would sanction an inference that if a line goes from the outside of a circle to the inside of circle, then it must intersect the circle at some point. | |
| From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Stewart Shapiro - Philosophy of Mathematics 6.1 n2 | |
| A reaction: Cantor and Dedekind began to contemplate discontinuous lines. |
| 10302 | Euclid says we can 'join' two points, but Hilbert says the straight line 'exists' [Euclid, by Bernays] |
| Full Idea: Euclid postulates: One can join two points by a straight line; Hilbert states the axiom: Given any two points, there exists a straight line on which both are situated. | |
| From: report of Euclid (Elements of Geometry [c.290 BCE]) by Paul Bernays - On Platonism in Mathematics p.259 |
| 14157 | Modern geometries only accept various parts of the Euclid propositions [Russell on Euclid] |
| Full Idea: In descriptive geometry the first 26 propositions of Euclid hold. In projective geometry the 1st, 7th, 16th and 17th require modification (as a straight line is not a closed series). Those after 26 depend on the postulate of parallels, so aren't assumed. | |
| From: comment on Euclid (Elements of Geometry [c.290 BCE]) by Bertrand Russell - The Principles of Mathematics §388 |
| 1600 | Euclid's common notions or axioms are what we must have if we are to learn anything at all [Euclid, by Roochnik] |
| Full Idea: The best known example of Euclid's 'common notions' is "If equals are subtracted from equals the remainders are equal". These can be called axioms, and are what "the man who is to learn anything whatever must have". | |
| From: report of Euclid (Elements of Geometry [c.290 BCE], 72a17) by David Roochnik - The Tragedy of Reason p.149 |
| 21347 | If Simmias is taller than Socrates, that isn't a feature that is just in Simmias [Plato] |
| Full Idea: When you say Simmias is taller than Socrates but shorter than Phaedo, so you mean there is in Simmias both tallness and shortness? - I do. ...But surely he is not taller than Socrates because he is Simmias but because of the tallness he happens to have? | |
| From: Plato (Phaedo [c.382 BCE], 102b-c) | |
| A reaction: He adds that both people must be cited. This appears to be what we now call a rejection relative height as an 'internal' relation, which is it would presumably be if it was a feature of one or of both men. |
| 360 | We must have a prior knowledge of equality, if we see 'equal' things and realise they fall short of it [Plato] |
| Full Idea: We must have some previous knowledge of equality, before the time when we saw equal things, but realised that they fell short of it. | |
| From: Plato (Phaedo [c.382 BCE], 075a) |
| 1 | There is only one source for all beauty [Plato] |
| Full Idea: If anything is beautiful other than beauty itself, it is beautiful for no other reason but because it participates in that beautiful. | |
| From: Plato (Phaedo [c.382 BCE], 100c) | |
| A reaction: The Greek word will be 'kalon' (beautiful, fine, noble). Like Aristotle, I find it baffling that such diversity could have a single source. Beautiful things have diverse aims. |
| 368 | Other things are named after the Forms because they participate in them [Plato] |
| Full Idea: The reason why other things are called after the forms is that they participate in the forms. | |
| From: Plato (Phaedo [c.382 BCE], 102a) |
| 16516 | The ship which Theseus took to Crete is now sent to Delos crowned with flowers [Plato] |
| Full Idea: The day before the trial the prow of the ship that the Athenians send to Delos had been crowned with garlands. - Which ship is that? - It is the ship in which, the Athenians say, Theseus once sailed to Crete, taking the victims. | |
| From: Plato (Phaedo [c.382 BCE], 058a) | |
| A reaction: Not philosophical, but this is the Ship of Theseus whose subsequent identity, Plutarch tells us, became a matter of dispute. |
| 357 | People are obviously recollecting when they react to a geometrical diagram [Plato] |
| Full Idea: The way in which people react to a geometrical diagram or anything like that is unmistakable proof of the theory of recollection. | |
| From: Plato (Phaedo [c.382 BCE], 073a) |
| 359 | If we feel the inadequacy of a resemblance, we must recollect the original [Plato] |
| Full Idea: If someone sees a resemblance, but feels that it falls far short of the original, they must therefore have a recollection of the original. | |
| From: Plato (Phaedo [c.382 BCE], 074e) |
| 9343 | To achieve pure knowledge, we must get rid of the body and contemplate things with the soul [Plato] |
| Full Idea: We are convinced that if we are ever to have pure knowledge of anything, we must get rid of the body and contemplate things by themselves with the soul by itself. | |
| From: Plato (Phaedo [c.382 BCE], 066c) | |
| A reaction: This seems to be the original ideal which motivates the devotion to a priori knowledge - that it will lead to a 'pure' knowledge, which in Plato's case will be eternal and necessary knowledge, like taking lessons from the gods. Wrong. |
| 15859 | To investigate the causes of things, study what is best for them [Plato] |
| Full Idea: If one wished to know the cause of each thing, why it comes to be or perishes or exists, one had to find what was the best way for it to be, or to be acted upon, or to act. Then it befitted a man to investigate only ...what is best. | |
| From: Plato (Phaedo [c.382 BCE], 097d) | |
| A reaction: A reversal of the modern idea of 'best explanation'. Socrates is citing Anaxagoras's proposal to understand things by interpreting the workings of a supreme Mind. It is the religious version of best explanation. |
| 13154 | Do we think and experience with blood, air or fire, or could it be our brain? [Plato] |
| Full Idea: Is it with the blood that we think, or with the air or the fire that is in us? Or is it none of these, but the brain that supplies our senses of hearing and sight and smell. | |
| From: Plato (Phaedo [c.382 BCE], 097a) | |
| A reaction: In retrospect it seems surprising that such clever people hadn't worked this one out, given the evidence of anatomy, in animals and people, and given brain injuries. By the time of Galen they appear to have got the answer. |
| 364 | One soul can't be more or less of a soul than another [Plato] |
| Full Idea: Is one soul, even minutely, more or less of a soul than another? Not in the least. | |
| From: Plato (Phaedo [c.382 BCE], 093b) | |
| A reaction: This idea is attractive because unconsciousness and death seem to be abrupt procedures, and so appear to be all-or-nothing, but I would personally view extreme Alzheimer's as an erasing of the soul, though a minimum level of it seems all-or-nothing. |
| 361 | It is a mistake to think that the most violent pleasure or pain is therefore the truest reality [Plato] |
| Full Idea: When anyone's soul feels a keen pleasure or pain it cannot help supposing that whatever causes the most violent emotion is the plainest and truest reality - which it is not. | |
| From: Plato (Phaedo [c.382 BCE], 084c) | |
| A reaction: Do people think that? Most people distinguish subjective from objective. Wounded soldiers are also aware of victory or defeat. |
| 351 | War aims at the acquisition of wealth, because we are enslaved to the body [Plato] |
| Full Idea: All wars are undertaken for the acquisition of wealth, and we want this because of the body, to which we are slave. | |
| From: Plato (Phaedo [c.382 BCE], 066c) |
| 22745 | Pherecydes said the first principle and element is earth [Pherecydes, by Sext.Empiricus] |
| Full Idea: Pherecydes of Syros said that the principle and element of all things is earth. | |
| From: report of Pherecydes (fragments/reports [c.600 BCE]) by Sextus Empiricus - Against the Physicists (two books) I.360 | |
| A reaction: Sextus is giving the history, and mentions it before saying that Thales thought it was water. Earth seems a sensible starting point, and I am guessing that Thales was trying to think a bit more deeply than Pherecydes about it. |
| 13156 | Fancy being unable to distinguish a cause from its necessary background conditions! [Plato] |
| Full Idea: Fancy being unable to distinguish between the cause of a thing, and the condition without which it could not be a cause. | |
| From: Plato (Phaedo [c.382 BCE], 099c) | |
| A reaction: Not as simple as he thinks. It seems fairly easy to construct a case where the immediately impacting event remains constant, and the background condition is changed. Even worse when negligence is held to be the cause. |
| 369 | If the Earth is spherical and in the centre, it is kept in place by universal symmetry, not by force [Plato] |
| Full Idea: If the earth is spherical and in the middle of the heavens, it needs neither air nor force to keep it from falling. The uniformity of heaven and equilibrium of earth are sufficient support. | |
| From: Plato (Phaedo [c.382 BCE], 108e) |
| 5883 | Pherecydes was the first to say that the soul is eternal [Pherecydes, by Cicero] |
| Full Idea: As far as the literature tells us, Pherecydes of Syros was the first who pronounced the souls of men to be eternal. | |
| From: report of Pherecydes (fragments/reports [c.600 BCE]) by M. Tullius Cicero - Tusculan Disputations I.xvi.38 | |
| A reaction: Presumably before that it was the physical person who arrived in the Underworld. The Hindu tradition seems to require the soul to be very long-lived, if not eternal. Why did Pherecydes come up with this idea? |
| 363 | Whether the soul pre-exists our body depends on whether it contains the ultimate standard of reality [Plato] |
| Full Idea: The theory that our soul exists even before it enters the body surely stands or falls with the soul's possession of the ultimate standard of reality. | |
| From: Plato (Phaedo [c.382 BCE], 092d) |