32 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.375 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.375 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? |
| 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.375 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. |
| 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.375 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. |
| 14240 | The empty set is something, not nothing! [Oliver/Smiley] |
| Full Idea: Some authors need to be told loud and clear: if there is an empty set, it is something, not nothing. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) | |
| A reaction: I'm inclined to think of a null set as a pair of brackets, so maybe that puts it into a metalanguage. |
| 14239 | The empty set is usually derived from Separation, but it also seems to need Infinity [Oliver/Smiley] |
| Full Idea: The empty set is usually derived via Zermelo's axiom of separation. But the axiom of separation is conditional: it requires the existence of a set in order to generate others as subsets of it. The original set has to come from the axiom of infinity. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) | |
| A reaction: They charge that this leads to circularity, as Infinity depends on the empty set. |
| 14241 | We don't need the empty set to express non-existence, as there are other ways to do that [Oliver/Smiley] |
| Full Idea: The empty set is said to be useful to express non-existence, but saying 'there are no Us', or ¬∃xUx are no less concise, and certainly less roundabout. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) |
| 14242 | Maybe we can treat the empty set symbol as just meaning an empty term [Oliver/Smiley] |
| Full Idea: Suppose we introduce Ω not as a term standing for a supposed empty set, but as a paradigm of an empty term, not standing for anything. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 1.2) | |
| A reaction: This proposal, which they go on to explore, seems to mean that Ω (i.e. the traditional empty set symbol) is no longer part of set theory but is part of semantics. |
| 14243 | The unit set may be needed to express intersections that leave a single member [Oliver/Smiley] |
| Full Idea: Thomason says with no unit sets we couldn't call {1,2}∩{2,3} a set - but so what? Why shouldn't the intersection be the number 2? However, we then have to distinguish three different cases of intersection (common subset or member, or disjoint). | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 2.2) |
| 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.375 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. |
| 13777 | A name is a sort of tool [Plato] |
| Full Idea: A name is a sort of tool. | |
| From: Plato (Cratylus [c.375 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.375 BCE], 436c) | |
| A reaction: Lovely. This is Gareth Evans's 'Madagascar' example. See Idea 9041. |
| 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.375 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. |
| 14234 | If you only refer to objects one at a time, you need sets in order to refer to a plurality [Oliver/Smiley] |
| Full Idea: A 'singularist', who refers to objects one at a time, must resort to the language of sets in order to replace plural reference to members ('Henry VIII's wives') by singular reference to a set ('the set of Henry VIII's wives'). | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro) | |
| A reaction: A simple and illuminating point about the motivation for plural reference. Null sets and singletons give me the creeps, so I would personally prefer to avoid set theory when dealing with ontology. |
| 14237 | We can use plural language to refer to the set theory domain, to avoid calling it a 'set' [Oliver/Smiley] |
| Full Idea: Plurals earn their keep in set theory, to answer Skolem's remark that 'in order to treat of 'sets', we must begin with 'domains' that are constituted in a certain way'. We can speak in the plural of 'the objects', not a 'domain' of objects. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], Intro) | |
| A reaction: [Skolem 1922:291 in van Heijenoort] Zermelo has said that the domain cannot be a set, because every set belongs to it. |
| 14245 | Logical truths are true no matter what exists - but predicate calculus insists that something exists [Oliver/Smiley] |
| Full Idea: Logical truths should be true no matter what exists, so true even if nothing exists. The classical predicate calculus, however, makes it logically true that something exists. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.1) |
| 14246 | If mathematics purely concerned mathematical objects, there would be no applied mathematics [Oliver/Smiley] |
| Full Idea: If mathematics was purely concerned with mathematical objects, there would be no room for applied mathematics. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.1) | |
| A reaction: Love it! Of course, they are using 'objects' in the rather Fregean sense of genuine abstract entities. I don't see why fictionalism shouldn't allow maths to be wholly 'pure', although we have invented fictions which actually have application. |
| 14247 | Sets might either represent the numbers, or be the numbers, or replace the numbers [Oliver/Smiley] |
| Full Idea: Identifying numbers with sets may mean one of three quite different things: 1) the sets represent the numbers, or ii) they are the numbers, or iii) they replace the numbers. | |
| From: Oliver,A/Smiley,T (What are Sets and What are they For? [2006], 5.2) | |
| A reaction: Option one sounds the most plausible to me. I will take numbers to be patterns embedded in nature, and sets are one way of presenting them in shorthand form, in order to bring out what is repeated. |
| 19400 | Possibles demand existence, so as many of them as possible must actually exist [Leibniz] |
| Full Idea: From the conflict of all the possibles demanding existence, this at once follows, that there exists that series of things by which as many of them as possible exist. | |
| From: Gottfried Leibniz (Exigency to Exist in Essences [1690], p.91) | |
| A reaction: I'm in tune with a lot of Leibniz, but my head swims with this one. He seems to be a Lewisian about possible worlds - that they are concrete existing entities (with appetites!). Could Lewis include Leibniz's idea in his system? |
| 19401 | God's sufficient reason for choosing reality is in the fitness or perfection of possibilities [Leibniz] |
| Full Idea: The sufficient reason for God's choice can be found only in the fitness (convenance) or in the degree of perfection that the several worlds possess. | |
| From: Gottfried Leibniz (Exigency to Exist in Essences [1690], p.92) | |
| A reaction: The 'fitness' of a world and its 'perfection' seem very different things. A piece of a jigsaw can have wonderful fitness, without perfection. Occasionally you get that sinking feeling with metaphysicians that they just make it up. |
| 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.375 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.375 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.375 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.375 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.375 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.375 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. |
| 19402 | The actual universe is the richest composite of what is possible [Leibniz] |
| Full Idea: The actual universe is the collection of the possibles which forms the richest composite. | |
| From: Gottfried Leibniz (Exigency to Exist in Essences [1690], p.92) | |
| A reaction: 'Richest' for Leibniz means a maximum combination of existence, order and variety. It's rather like picking the best starting team from a squad of footballers. |
| 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.375 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? |
| 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.375 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.375 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. |
| 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.375 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.375 BCE], 406c) |