78 ideas
| 15447 | We shouldn't always follow where the argument leads! [Lewis on Plato] |
| Full Idea: There comes a time not to go on following where the argument leads! | |
| From: comment on Plato (The Laws [c.348 BCE], 667b) by David Lewis - Against Structural Universals 'Variant' | |
| A reaction: Lewis is a fine one to talk, since he follows argument that take him past innumerable incredulous stares of onlookers. |
| 243 | It is foolish to quarrel with the mind's own reasoning processes [Plato] |
| Full Idea: When the soul quarrels with knowledge or opinion or reason, its natural ruling principles, you have there what I call 'folly'. | |
| From: Plato (The Laws [c.348 BCE], 689b) |
| 241 | We ought to follow where the argument leads us [Plato] |
| Full Idea: We ought to follow where the argument leads us. | |
| From: Plato (The Laws [c.348 BCE], 667a) |
| 21264 | Mortals are incapable of being fully rational [Plato] |
| Full Idea: We mustn't assume that mortal eyes will ever be able to look upon reason and get to know it adequately. | |
| From: Plato (The Laws [c.348 BCE], 897d) | |
| A reaction: This is in the context of the rational control of the whole Cosmos. I presume Plato would be flabbergasted by the findings of recent physics and cosmology. Did Kant believe that he was being completely rational about ethics? |
| 251 | Truth has the supreme value, for both gods and men [Plato] |
| Full Idea: Truth heads the list of all things good, for gods and men alike. | |
| From: Plato (The Laws [c.348 BCE], 730c) |
| 18074 | Intuitionists rely on assertability instead of truth, but assertability relies on truth [Kitcher] |
| Full Idea: Though it may appear that the intuitionist is providing an account of the connectives couched in terms of assertability conditions, the notion of assertability is a derivative one, ultimately cashed out by appealing to the concept of truth. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5) | |
| A reaction: I have quite a strong conviction that Kitcher is right. All attempts to eliminate truth, as some sort of ideal at the heart of ordinary talk and of reasoning, seems to me to be doomed. |
| 6298 | Kitcher says maths is an idealisation of the world, and our operations in dealing with it [Kitcher, by Resnik] |
| Full Idea: Kitcher says maths is an 'idealising theory', like some in physics; maths idealises features of the world, and practical operations, such as segregating and matching (numbering), measuring, cutting, moving, assembling (geometry), and collecting (sets). | |
| From: report of Philip Kitcher (The Nature of Mathematical Knowledge [1984]) by Michael D. Resnik - Maths as a Science of Patterns One.4.2.2 | |
| A reaction: This seems to be an interesting line, which is trying to be fairly empirical, and avoid basing mathematics on purely a priori understanding. Nevertheless, we do not learn idealisation from experience. Resnik labels Kitcher an anti-realist. |
| 12392 | Mathematical a priorism is conceptualist, constructivist or realist [Kitcher] |
| Full Idea: Proposals for a priori mathematical knowledge have three main types: conceptualist (true in virtue of concepts), constructivist (a construct of the human mind) and realist (in virtue of mathematical facts). | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 02.3) | |
| A reaction: Realism is pure platonism. I think I currently vote for conceptualism, with the concepts deriving from the concrete world, and then being extended by fictional additions, and shifts in the notion of what 'number' means. |
| 18078 | The interest or beauty of mathematics is when it uses current knowledge to advance undestanding [Kitcher] |
| Full Idea: What makes a question interesting or gives it aesthetic appeal is its focussing of the project of advancing mathematical understanding, in light of the concepts and systems of beliefs already achieved. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 09.3) | |
| A reaction: Kitcher defends explanation (the source of understanding, presumably) in terms of unification with previous theories (the 'concepts and systems'). I always have the impression that mathematicians speak of 'beauty' when they see economy of means. |
| 12426 | The 'beauty' or 'interest' of mathematics is just explanatory power [Kitcher] |
| Full Idea: Insofar as we can honor claims about the aesthetic qualities or the interest of mathematical inquiries, we should do so by pointing to their explanatory power. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 09.4) | |
| A reaction: I think this is a good enough account for me (but probably not for my friend Carl!). Beautiful cars are particularly streamlined. Beautiful people look particularly healthy. A beautiful idea is usually wide-ranging. |
| 12395 | Real numbers stand to measurement as natural numbers stand to counting [Kitcher] |
| Full Idea: The real numbers stand to measurement as the natural numbers stand to counting. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.4) |
| 12425 | Complex numbers were only accepted when a geometrical model for them was found [Kitcher] |
| Full Idea: An important episode in the acceptance of complex numbers was the development by Wessel, Argand, and Gauss, of a geometrical model of the numbers. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 07.5) | |
| A reaction: The model was in terms of vectors and rotation. New types of number are spurned until they can be shown to integrate into a range of mathematical practice, at which point mathematicians change the meaning of 'number' (without consulting us). |
| 18071 | A one-operation is the segregation of a single object [Kitcher] |
| Full Idea: We perform a one-operation when we perform a segregative operation in which a single object is segregated. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.3) | |
| A reaction: This is part of Kitcher's empirical but constructive account of arithmetic, which I find very congenial. He avoids the word 'unit', and goes straight to the concept of 'one' (which he treats as more primitive than zero). |
| 18066 | The old view is that mathematics is useful in the world because it describes the world [Kitcher] |
| Full Idea: There is an old explanation of the utility of mathematics. Mathematics describes the structural features of our world, features which are manifested in the behaviour of all the world's inhabitants. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.1) | |
| A reaction: He only cites Russell in modern times as sympathising with this view, but Kitcher gives it some backing. I think the view is totally correct. The digression produced by Cantorian infinities has misled us. |
| 18083 | With infinitesimals, you divide by the time, then set the time to zero [Kitcher] |
| Full Idea: The method of infinitesimals is that you divide by the time, and then set the time to zero. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 10.2) |
| 18061 | Mathematical intuition is not the type platonism needs [Kitcher] |
| Full Idea: The intuitions of which mathematicians speak are not those which Platonism requires. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.3) | |
| A reaction: The point is that it is not taken to be a 'special' ability, but rather a general insight arising from knowledge of mathematics. I take that to be a good account of intuition, which I define as 'inarticulate rationality'. |
| 12420 | If mathematics comes through intuition, that is either inexplicable, or too subjective [Kitcher] |
| Full Idea: If mathematical statements are don't merely report features of transient and private mental entities, it is unclear how pure intuition generates mathematical knowledge. But if they are, they express different propositions for different people and times. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.1) | |
| A reaction: This seems to be the key dilemma which makes Kitcher reject intuition as an a priori route to mathematics. We do, though, just seem to 'see' truths sometimes, and are unable to explain how we do it. |
| 12393 | Intuition is no basis for securing a priori knowledge, because it is fallible [Kitcher] |
| Full Idea: The process of pure intuition does not measure up to the standards required of a priori warrants not because it is sensuous but because it is fallible. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 03.2) |
| 12387 | Mathematical knowledge arises from basic perception [Kitcher] |
| Full Idea: Mathematical knowledge arises from rudimentary knowledge acquired by perception. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], Intro) | |
| A reaction: This is an empiricist manifesto, which asserts his allegiance to Mill, and he gives a sophisticated account of how higher mathematics can be accounted for in this way. Well, he tries to. |
| 12412 | My constructivism is mathematics as an idealization of collecting and ordering objects [Kitcher] |
| Full Idea: The constructivist position I defend claims that mathematics is an idealized science of operations which can be performed on objects in our environment. It offers an idealized description of operations of collecting and ordering. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], Intro) | |
| A reaction: I think this is right. What is missing from Kitcher's account (and every other account I've met) is what is meant by 'idealization'. How do you go about idealising something? Hence my interest in the psychology of abstraction. |
| 18065 | We derive limited mathematics from ordinary things, and erect powerful theories on their basis [Kitcher] |
| Full Idea: I propose that a very limited amount of our mathematical knowledge can be obtained by observations and manipulations of ordinary things. Upon this small base we erect the powerful general theories of modern mathematics. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 05.2) | |
| A reaction: I agree. The three related processes that take us from the experiential base of mathematics to its lofty heights are generalisation, idealisation and abstraction. |
| 18077 | The defenders of complex numbers had to show that they could be expressed in physical terms [Kitcher] |
| Full Idea: Proponents of complex numbers had ultimately to argue that the new operations shared with the original paradigms a susceptibility to construal in physical terms. The geometrical models of complex numbers answered to this need. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 07.5) | |
| A reaction: [A nice example of the verbose ideas which this website aims to express in plain English!] The interest is not that they had to be described physically (which may pander to an uninformed audience), but that they could be so described. |
| 12423 | Analyticity avoids abstract entities, but can there be truth without reference? [Kitcher] |
| Full Idea: Philosophers who hope to avoid commitment to abstract entities by claiming that mathematical statements are analytic must show how analyticity is, or provides a species of, truth not requiring reference. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.I) | |
| A reaction: [the last part is a quotation from W.D. Hart] Kitcher notes that Frege has a better account, because he provides objects to which reference can be made. I like this idea, which seems to raise a very large question, connected to truthmakers. |
| 18069 | Arithmetic is an idealizing theory [Kitcher] |
| Full Idea: I construe arithmetic as an idealizing theory. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2) | |
| A reaction: I find 'generalising' the most helpful word, because everyone seems to understand and accept the idea. 'Idealisation' invokes 'ideals', which lots of people dislike, and lots of philosophers seem to have trouble with 'abstraction'. |
| 18068 | Arithmetic is made true by the world, but is also made true by our constructions [Kitcher] |
| Full Idea: I want to suggest both that arithmetic owes its truth to the structure of the world and that arithmetic is true in virtue of our constructive activity. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2) | |
| A reaction: Well said, but the problem seems no more mysterious to me than the fact that trees grow in the woods and we build houses out of them. I think I will declare myself to be an 'empirical constructivist' about mathematics. |
| 18070 | We develop a language for correlations, and use it to perform higher level operations [Kitcher] |
| Full Idea: The development of a language for describing our correlational activity itself enables us to perform higher level operations. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.2) | |
| A reaction: This is because all language itself (apart from proper names) is inherently general, idealised and abstracted. He sees the correlations as the nested collections expressed by set theory. |
| 18072 | Constructivism is ontological (that it is the work of an agent) and epistemological (knowable a priori) [Kitcher] |
| Full Idea: The constructivist ontological thesis is that mathematics owes its truth to the activity of an actual or ideal subject. The epistemological thesis is that we can have a priori knowledge of this activity, and so recognise its limits. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5) | |
| A reaction: The mention of an 'ideal' is Kitcher's personal view. Kitcher embraces the first view, and rejects the second. |
| 18063 | Conceptualists say we know mathematics a priori by possessing mathematical concepts [Kitcher] |
| Full Idea: Conceptualists claim that we have basic a priori knowledge of mathematical axioms in virtue of our possession of mathematical concepts. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.1) | |
| A reaction: I sympathise with this view. If concepts are reasonably clear, they will relate to one another in certain ways. How could they not? And how else would you work out those relations other than by thinking about them? |
| 18064 | If meaning makes mathematics true, you still need to say what the meanings refer to [Kitcher] |
| Full Idea: Someone who believes that basic truths of mathematics are true in virtue of meaning is not absolved from the task of saying what the referents of mathematical terms are, or ...what mathematical reality is like. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 04.6) | |
| A reaction: Nice question! He's a fan of getting at the explanatory in mathematics. |
| 18067 | Abstract objects were a bad way of explaining the structure in mathematics [Kitcher] |
| Full Idea: The original introduction of abstract objects was a bad way of doing justice to the insight that mathematics is concerned with structure. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.1) | |
| A reaction: I'm a fan of explanations in metaphysics, and hence find the concept of 'bad' explanations in metaphysics particularly intriguing. |
| 21259 | To grasp a thing we need its name, its definition, and what it really is [Plato] |
| Full Idea: There are three elements in any given thing: the first is what the object actually is, the second is the definition of this, and the third is the name. | |
| From: Plato (The Laws [c.348 BCE], 895d) | |
| A reaction: I take the importance of this to be its distinction between what it is, and the definition of what it is. Aristotle maintains this distinction, but some modern Aristotelians seem to get the confused. Plato worried a lot more about names than we do. |
| 12390 | A priori knowledge comes from available a priori warrants that produce truth [Kitcher] |
| Full Idea: X knows a priori that p iff the belief was produced with an a priori warrant, which is a process which is available to X, and this process is a warrant, and it makes p true. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.4) | |
| A reaction: [compression of a formal spelling-out] This is a modified version of Goldman's reliabilism, for a priori knowledge. It sounds a bit circular and uninformative, but it's a start. |
| 12418 | In long mathematical proofs we can't remember the original a priori basis [Kitcher] |
| Full Idea: When we follow long mathematical proofs we lose our a priori warrants for their beginnings. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 02.2) | |
| A reaction: Kitcher says Descartes complains about this problem several times in his 'Regulae'. The problem runs even deeper into all reasoning, if you become sceptical about memory. You have to remember step 1 when you do step 2. |
| 12389 | Knowledge is a priori if the experience giving you the concepts thus gives you the knowledge [Kitcher] |
| Full Idea: Knowledge is independent of experience if any experience which would enable us to acquire the concepts involved would enable us to have the knowledge. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.3) | |
| A reaction: This is the 'conceptualist' view of a priori knowledge, which Kitcher goes on to attack, preferring a 'constructivist' view. The formula here shows that we can't divorce experience entirely from a priori thought. I find conceptualism a congenial view. |
| 12416 | We have some self-knowledge a priori, such as knowledge of our own existence [Kitcher] |
| Full Idea: One can make a powerful case for supposing that some self-knowledge is a priori. At most, if not all, of our waking moments, each of us knows of herself that she exists. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.6) | |
| A reaction: This is a begrudging concession from a strong opponent to the whole notion of a priori knowledge. I suppose if you ask 'what can be known by thought alone?' then truths about thought ought to be fairly good initial candidates. |
| 12413 | A 'warrant' is a process which ensures that a true belief is knowledge [Kitcher] |
| Full Idea: A 'warrant' refers to those processes which produce belief 'in the right way': X knows that p iff p, and X believes that p, and X's belief that p was produced by a process which is a warrant for it. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 01.2) | |
| A reaction: That is, a 'warrant' is a justification which makes a belief acceptable as knowledge. Traditionally, warrants give you certainty (and are, consequently, rather hard to find). I would say, in the modern way, that warrants are agreed by social convention. |
| 20473 | If experiential can defeat a belief, then its justification depends on the defeater's absence [Kitcher, by Casullo] |
| Full Idea: According to Kitcher, if experiential evidence can defeat someone's justification for a belief, then their justification depends on the absence of that experiential evidence. | |
| From: report of Philip Kitcher (The Nature of Mathematical Knowledge [1984], p.89) by Albert Casullo - A Priori Knowledge 2.3 | |
| A reaction: Sounds implausible. There are trillions of possible defeaters for most beliefs, but to say they literally depend on trillions of absences seems a very odd way of seeing the situation |
| 21260 | Soul is what is defined by 'self-generating motion' [Plato] |
| Full Idea: The entity which we call 'soul' is precisely that which is defined by the expression 'self-generating motion'. | |
| From: Plato (The Laws [c.348 BCE], 896a) | |
| A reaction: We may suspect that he defines soul in this way for a particular context, aimed at proving the existence of a First Mover. He must think there is more to soul than the generation of movement. |
| 18075 | Idealisation trades off accuracy for simplicity, in varying degrees [Kitcher] |
| Full Idea: To idealize is to trade accuracy in describing the actual for simplicity of description, and the compromise can sometimes be struck in different ways. | |
| From: Philip Kitcher (The Nature of Mathematical Knowledge [1984], 06.5) | |
| A reaction: There is clearly rather more to idealisation than mere simplicity. A matchstick man is not an ideal man. |
| 276 | My individuality is my soul, which carries my body around [Plato] |
| Full Idea: While I am alive I have nothing to thank for my individuality except my soul, whereas my body is just the likeness that I carry around with me. | |
| From: Plato (The Laws [c.348 BCE], 959a) |
| 249 | People who value beauty above virtue insult the soul by placing the body above it [Plato] |
| Full Idea: When a man values beauty above virtue, the disrespect he shows his soul is total and fundamental, because he argues that the body is more to be honoured than the soul. | |
| From: Plato (The Laws [c.348 BCE], 727e) |
| 7667 | There are two sides to men - the pleasantly social, and the violent and creative [Diderot, by Berlin] |
| Full Idea: Diderot is among the first to preach that there are two men: the artificial man, who belongs in society and seeks to please, and the violent, bold, criminal instinct of a man who wishes to break out (and, if controlled, is responsible for works of genius. | |
| From: report of Denis Diderot (works [1769], Ch.3) by Isaiah Berlin - The Roots of Romanticism | |
| A reaction: This has an obvious ancestor in Plato's picture (esp. in 'Phaedrus') of the two conflicting sides to the psuché, which seem to be reason and emotion. In Diderot, though, the suppressed man has virtues, which Plato would deny. |
| 265 | An action is only just if it is performed by someone with a just character and outlook [Plato] |
| Full Idea: The description 'just' is applicable only to the benefit conferred or injury inflicted by someone with a just character and outlook. | |
| From: Plato (The Laws [c.348 BCE], 862b) | |
| A reaction: How should we describe the occasional administering of good justice by a generally wicked judge. Greeks focus on character, but moderns focus on actions. |
| 269 | Attempted murder is like real murder, but we should respect the luck which avoided total ruin [Plato] |
| Full Idea: An attempted murder should be treated like a successful one, but with respect shown for the luck which saved him from total ruin. | |
| From: Plato (The Laws [c.348 BCE], 877a) | |
| A reaction: The earliest reference to moral luck, I think. 'Repect' sounds vague, but it is asking judges to 'take it into consideration', which is quite practical. Attempted murderers are just as dangerous. |
| 240 | It would be strange if the gods rewarded those who experienced the most pleasure in life [Plato] |
| Full Idea: It would be strange if the gods gave the greatest rewards in heaven to those who led the most pleasant life, rather than the most just. | |
| From: Plato (The Laws [c.348 BCE], 662c) | |
| A reaction: All of philosophy is just footnotes to Plato.... See Idea 1454. |
| 264 | The conquest of pleasure is the noblest victory of all [Plato] |
| Full Idea: The conquest of pleasure is the noblest victory of all. | |
| From: Plato (The Laws [c.348 BCE], 840c) | |
| A reaction: Plato's puritanical streak. Even Aristotle doesn't agree with this. Self-control does not imply conquest of pleasure. Has a good professional wine taster conquered pleasure? |
| 4332 | Virtue is a concord of reason and emotion, with pleasure and pain trained to correct ends [Plato] |
| Full Idea: Virtue is the general concord of reason and emotion, but there is one key element, which is the correct formation of our feelings of pleasure and pain, which makes us hate what we ought to hate, and love what we ought to love. | |
| From: Plato (The Laws [c.348 BCE], 653c) | |
| A reaction: An important truth, taken up by Aristotle. To see another person humiliated gives some people pleasure and other people pain. |
| 248 | A serious desire for moral excellence is very rare indeed [Plato] |
| Full Idea: People who are anxious to attain moral excellence with all possible speed are pretty thin on the ground. | |
| From: Plato (The Laws [c.348 BCE], 718e) |
| 253 | Every crime is the result of excessive self-love [Plato] |
| Full Idea: The cause of each and every crime we commit is precisely this excessive love of ourselves. | |
| From: Plato (The Laws [c.348 BCE], 731e) |
| 263 | The only worthwhile life is one devoted to physical and moral perfection [Plato] |
| Full Idea: A life devoted to every physical perfection and every moral virtue is the only life worth the name. | |
| From: Plato (The Laws [c.348 BCE], 807c) |
| 235 | Virtue is the aim of all laws [Plato] |
| Full Idea: Virtue is the aim of the laws the legislator lays down. | |
| From: Plato (The Laws [c.348 BCE], 631a) |
| 277 | The Guardians must aim to discover the common element in the four cardinal virtues [Plato] |
| Full Idea: The guardians of the state should aim to get an exact idea of the common element in all the four virtues. | |
| From: Plato (The Laws [c.348 BCE], 965d) |
| 254 | Excessive laughter and tears must be avoided [Plato] |
| Full Idea: Excessive laughter and tears must be avoided. | |
| From: Plato (The Laws [c.348 BCE], 732c) |
| 266 | Injustice is the mastery of the soul by bad feelings, even if they do not lead to harm [Plato] |
| Full Idea: My general description of injustice is this: the mastery of the soul by anger, fear, pleasure, pain, envy and desires, whether they lead to actual damage or not. | |
| From: Plato (The Laws [c.348 BCE], 863e) |
| 242 | The best people are produced where there is no excess of wealth or poverty [Plato] |
| Full Idea: The community in which neither wealth nor poverty exists will produce the finest characters. | |
| From: Plato (The Laws [c.348 BCE], 679b) |
| 256 | Virtue and great wealth are incompatible [Plato] |
| Full Idea: Virtue and great wealth are quite incompatible. | |
| From: Plato (The Laws [c.348 BCE], 742e) |
| 245 | Totalitarian states destroy friendships and community spirit [Plato] |
| Full Idea: Excessively authoritarian government destroys all friendship and community of spirit in the state. | |
| From: Plato (The Laws [c.348 BCE], 697d) |
| 239 | Education in virtue produces citizens who are active but obedient [Plato] |
| Full Idea: Education in virtue produces a keen desire to become a perfect citizen who knows how to rule and be ruled as justice demands. | |
| From: Plato (The Laws [c.348 BCE], 643e) |
| 1402 | Friendship is impossible between master and slave, even if they are made equal [Plato] |
| Full Idea: Even if you proclaim that a master and a slave shall have equal status, friendship between them is inherently impossible. | |
| From: Plato (The Laws [c.348 BCE], 757a) |
| 262 | Men and women should qualify equally for honours on merit [Plato] |
| Full Idea: Men and women who have shown conspicuous merit should qualify for all honours without distinction of sex. | |
| From: Plato (The Laws [c.348 BCE], 802a) |
| 236 | Sound laws achieve the happiness of those who observe them [Plato] |
| Full Idea: Sound laws achieve the happiness of those who observe them. | |
| From: Plato (The Laws [c.348 BCE], 631b) |
| 259 | Justice is granting the equality which unequals deserve [Plato] |
| Full Idea: Justice consists of granting the 'equality' which unequals deserve to get. | |
| From: Plato (The Laws [c.348 BCE], 757d) | |
| A reaction: Beautifully simple, and hard to improve on. It shows the close link between equality and justice, but shows why they are not the same. The main debate about justice concerns the criteria for 'deserving'. |
| 257 | Mathematics has the widest application of any subject on the curriculum [Plato] |
| Full Idea: For domestic and public purposes, and all professional skills, no branch of a child's education has as big a range of applications as mathematics. | |
| From: Plato (The Laws [c.348 BCE], 747a) |
| 238 | Children's games should channel their pleasures into adult activity [Plato] |
| Full Idea: We should use children's games to channel their pleasures and desires towards activities in which they will have to engage when they are adult. | |
| From: Plato (The Laws [c.348 BCE], 643c) |
| 260 | Control of education is the key office of state, and should go to the best citizen [Plato] |
| Full Idea: The Minister of Education is by far the most important of all the supreme offices of the state; the best all-round citizen in the state should be appointed. | |
| From: Plato (The Laws [c.348 BCE], 765e) |
| 4331 | Education is channelling a child's feelings into the right course before it understands why [Plato] |
| Full Idea: I call 'education' the initial acquisition of virtue by the child, when the feelings of pleasure and affection, pain and hatred, are channelled in the right courses before he can understand the reason why. | |
| From: Plato (The Laws [c.348 BCE], 653b) | |
| A reaction: A precursor of Aristotle's view (Ethics 1104b11). A profound, simple and important insight. |
| 250 | The best way to educate the young is not to rebuke them, but to set a good example [Plato] |
| Full Idea: The best way to educate the younger generation (as well as yourself) is not to rebuke them but patently to practise all your life what you preach to others. | |
| From: Plato (The Laws [c.348 BCE], 729c) |
| 275 | Creation is not for you; you exist for the sake of creation [Plato] |
| Full Idea: Creation is not for your benefit; you exist for the sake of the universe. | |
| From: Plato (The Laws [c.348 BCE], 903c) |
| 273 | Movement is transmitted through everything, and it must have started with self-generated motion [Plato] |
| Full Idea: Motion is transmitted to innumerable things, and this must spring from some initial principle, which must be the change effected by self-generated motion. | |
| From: Plato (The Laws [c.348 BCE], 895a) |
| 8004 | In 'The Laws', to obey the law is to be obey god [Plato, by MacIntyre] |
| Full Idea: The divine is important in 'The Laws' because it is identified with law; to be obedient before the law is to be obedient before god. | |
| From: report of Plato (The Laws [c.348 BCE]) by Alasdair MacIntyre - A Short History of Ethics Ch.6 | |
| A reaction: Christian conservativism in a nutshell. Plato is rejecting his view in Euthyphro that piety (etc.) must precede the will of the gods. The obvious problem is bad laws, made by corrupt rulers. |
| 21261 | Self-moving soul has to be the oldest thing there is [Plato] |
| Full Idea: Soul, being the source of motion, is the most ancient thing there is. | |
| From: Plato (The Laws [c.348 BCE], 896b) | |
| A reaction: Plato seems to assume that the First Mover must still exist, which doesn't follow from anything in the argument. The First Pusher could be dead before the last domino falls. Why can't activity be the default state of everything? |
| 21258 | The only possible beginning for the endless motions of reality is something self-generated [Plato] |
| Full Idea: When the motion in reality is transmitted to thousands of things one after another, the entire sequence of their movements must surely spring from some initial principle, which can hardly be anything except the change effected by self-generated motion. | |
| From: Plato (The Laws [c.348 BCE], 895a) | |
| A reaction: This gives a domino picture of reality, with all of reality responding inertly to a first kick. Much better is to see self-generated motion in the active qualities of all matter, as seen in the sea of virtual subatomic particles at the smallest level. |
| 21257 | Self-generating motion is clearly superior to all other kinds of motion [Plato] |
| Full Idea: We can't resist the conclusion that the motion which can generate itself is infinitely superior, and all the others are inferior to it. | |
| From: Plato (The Laws [c.348 BCE], 894d) | |
| A reaction: Who said you can't get values from facts! Not that the argument depends on superiority. There could be an inferior First Mover, as a bus driver is subservient to the passengers, or (my favourite) a head teacher is inferior to the pupils. |
| 274 | Soul must be the cause of all the opposites, such as good and evil or beauty and ugliness [Plato] |
| Full Idea: Soul must be cause of good and evil, beauty and ugliness, justice and injustice, and all the opposites. | |
| From: Plato (The Laws [c.348 BCE], 896d) |
| 21263 | If all the motions of nature reflect calculations of reason, then the best kind of soul must direct it [Plato] |
| Full Idea: If the movement of the heavens and all that is in them reflects the motion and revolution and calculation of reason ...then clearly we have to admit that it is the best kind of soul that cares for the entire universe and directs it along the best path. | |
| From: Plato (The Laws [c.348 BCE], 897c) | |
| A reaction: Most of this passage reflects the cosmological argument - that without some initiating source natural events could not occur - but this slides into the design argument. So who designed mud (which is too inferior to have a Form)? |
| 278 | If astronomical movements are seen as necessary instead of by divine will, this leads to atheism [Plato] |
| Full Idea: If a man studying astronomy sees events apparently happening by necessity rather than being directed by the intention of a benevolent will, he will turn into an atheist. | |
| From: Plato (The Laws [c.348 BCE], 967a) |
| 21265 | The heavens must be full of gods, controlling nature either externally or from within [Plato] |
| Full Idea: A soul or souls have been shown to be cause of all the phenomena, and whether it is by their living presence in matter that they direct all the heavens, or by some other means, we insist that these souls are gods. So 'everything is full of gods'. | |
| From: Plato (The Laws [c.348 BCE], 899b) | |
| A reaction: This seems to have little to do with the pagan gods on Olympus. It is also notably not monotheistic. It is somewhere between animism and panpsychism. Does he think the rivers and woods contain gods? Probably not. Just the orderly heavens. |
| 21262 | There must be at least two souls controlling the cosmos, one doing good, the other the opposite [Plato] |
| Full Idea: There must be more than one soul (not fewer than two) controlling movement and the heavens: that which does good, and that which has the opposite capacity. | |
| From: Plato (The Laws [c.348 BCE], 896e) | |
| A reaction: [Wording compressed - as often with the dialogues] This idea of controlling opposites is found in Empedocles. Presumably this good soul defers to the Form of the Good, as implied by the Euthyphro Question. |