38 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) |
| 10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
| Full Idea: Set theory has three roles: as a means of taming the infinite, as a supplier of the subject-matter of mathematics, and as a source of its modes of reasoning. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], Intro 1) | |
| A reaction: These all seem to be connected with mathematics, but there is also ontological interest in set theory. Potter emphasises that his second role does not entail a commitment to sets 'being' numbers. |
| 10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
| Full Idea: It is rare to find any direct reason given for believing that the empty set exists, except for variants of Dedekind's argument from convenience. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.3) |
| 13044 | Infinity: There is at least one limit level [Potter] |
| Full Idea: Axiom of Infinity: There is at least one limit level. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.9) | |
| A reaction: A 'limit ordinal' is one which has successors, but no predecessors. The axiom just says there is at least one infinity. |
| 10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
| Full Idea: It is only quite recently that the idea has emerged of deriving our conception of collections from a relation of dependence between them. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.2) | |
| A reaction: This is the 'iterative' view of sets, which he traces back to Gödel's 'What is Cantor's Continuum Problem?' |
| 13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
| Full Idea: We group under the heading 'limitation of size' those principles which classify properties as collectivizing or not according to how many objects there are with the property. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 13.5) | |
| A reaction: The idea was floated by Cantor, toyed with by Russell (1906), and advocated by von Neumann. The thought is simply that paradoxes start to appear when sets become enormous. |
| 10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
| Full Idea: Mereology tends to elide the distinction between the cards in a pack and the suits. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 02.1) | |
| A reaction: The example is a favourite of Frege's. Potter is giving a reason why mathematicians opted for set theory. I'm not clear, though, why a pack cannot have either 4 parts or 52 parts. Parts can 'fall under a concept' (such as 'legs'). I'm puzzled. |
| 10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
| Full Idea: In second-order logic only the formation rules are completely formalizable, not the inference rules. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 01.2) | |
| A reaction: He cites Gödel's First Incompleteness theorem for this. |
| 10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
| Full Idea: A 'supposition' axiomatic theory is as concerned with truth as a 'realist' one (with undefined terms), but the truths are conditional. Satisfying the axioms is satisfying the theorem. This is if-thenism, or implicationism, or eliminative structuralism. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 01.1) | |
| A reaction: Aha! I had failed to make the connection between if-thenism and eliminative structuralism (of which I am rather fond). I think I am an if-thenist (not about all truth, but about provable truth). |
| 10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
| Full Idea: Even if set theory's role as a foundation for mathematics turned out to be wholly illusory, it would earn its keep through the calculus it provides for counting infinite sets. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.8) |
| 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. |
| 17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
| Full Idea: It is a remarkable fact that all the arithmetical properties of the natural numbers can be derived from such a small number of assumptions (as the Peano Axioms). | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 05.2) | |
| A reaction: If one were to defend essentialism about arithmetic, this would be grist to their mill. I'm just saying. |
| 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. |
| 13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
| Full Idea: A set is called a 'relation' if every element of it is an ordered pair. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 04.7) | |
| A reaction: This is the modern extensional view of relations. For 'to the left of', you just list all the things that are to the left, with the things they are to the left of. But just listing the ordered pairs won't necessarily reveal how they are related. |
| 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) |
| 13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
| Full Idea: The argument that the relation of dependence is well-founded ...is a version of the classical arguments for substance. ..Any conceptual scheme which genuinely represents a world cannot contain infinite backward chains of meaning. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.3) | |
| A reaction: Thus the iterative conception of set may imply a notion of substance, and Barwise's radical attempt to ditch the Axiom of Foundation (Idea 13039) was a radical attempt to get rid of 'substances'. Potter cites Wittgenstein as a fan of substances here. |
| 13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
| Full Idea: A collection has a determinate number of members, whereas a fusion may be carved up into parts in various equally valid (although perhaps not equally interesting) ways. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 02.1) | |
| A reaction: This seems to sum up both the attraction and the weakness of mereology. If you doubt the natural identity of so-called 'objects', then maybe classical mereology is the way to go. |
| 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. |
| 10709 | Priority is a modality, arising from collections and members [Potter] |
| Full Idea: We must conclude that priority is a modality distinct from that of time or necessity, a modality arising in some way out of the manner in which a collection is constituted from its members. | |
| From: Michael Potter (Set Theory and Its Philosophy [2004], 03.3) | |
| A reaction: He is referring to the 'iterative' view of sets, and cites Aristotle 'Metaphysics' 1019a1-4 as background. |
| 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. |
| 19540 | Don't confuse justified belief with justified believers [Dougherty/Rysiew] |
| Full Idea: Much theorizing about justification conflates issues of justified belief with issues of justified/blameless believers. | |
| From: Dougherty,T/Rysiew,P (What is Knowledge-First Epistemology? [2014], p.12) | |
| A reaction: [They cite Kent Bach 1985] Presumably the only thing that really justifies a belief is the truth, or the actual facts. You could then say 'p is a justified belief, though no one actually believes it'. E.g. the number of stars is odd. |
| 19539 | If knowledge is unanalysable, that makes justification more important [Dougherty/Rysiew] |
| Full Idea: If knowledge is indeed unanalyzable, that could be seen as a liberation of justification to assume importance in its own right. | |
| From: Dougherty,T/Rysiew,P (What is Knowledge-First Epistemology? [2014], p.11) | |
| A reaction: [They cite Kvanvig 2003:192 and Greco 2010:9-] See Scruton's Idea 3897. I suspect that we should just give up discussing 'knowledge', which is a woolly and uninformative term, and focus on where the real epistemological action is. |
| 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. |
| 19538 | Entailment is modelled in formal semantics as set inclusion (where 'mammals' contains 'cats') [Dougherty/Rysiew] |
| Full Idea: Entailment is modelled in formal semantics as set inclusion. 'Cat' entails 'mammal' because the cats are a subset of the mammals. | |
| From: Dougherty,T/Rysiew,P (What is Knowledge-First Epistemology? [2014], p.10) | |
| A reaction: I would have thought that this was only one type of entailment. 'Travelling to Iceland entails flying'. Travelling includes flying, the reverse of cats/mammals, to a very complex set-theoretic account is needed. Interesting. |
| 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) |
| 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) |
| 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) |