72 ideas
| 15447 | We shouldn't always follow where the argument leads! [Lewis on Plato] |
| 243 | It is foolish to quarrel with the mind's own reasoning processes [Plato] |
| 241 | We ought to follow where the argument leads us [Plato] |
| 21264 | Mortals are incapable of being fully rational [Plato] |
| 251 | Truth has the supreme value, for both gods and men [Plato] |
| 9542 | The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell] |
| 21720 | Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead] |
| 10044 | Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro] |
| 18208 | We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead] |
| 8204 | Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead] |
| 9359 | Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead] |
| 21707 | Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B] |
| 10036 | In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel] |
| 18248 | A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro] |
| 18152 | Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock] |
| 8683 | Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend] |
| 10025 | Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes] |
| 10037 | 'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead] |
| 10093 | The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman] |
| 8691 | The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead] |
| 10305 | In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead] |
| 8684 | Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend] |
| 8746 | To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro] |
| 6019 | If someone squashed a horse to make a dog, something new would now exist [Mnesarchus] |
| 21259 | To grasp a thing we need its name, its definition, and what it really is [Plato] |
| 12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
| 10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
| 21260 | Soul is what is defined by 'self-generating motion' [Plato] |
| 276 | My individuality is my soul, which carries my body around [Plato] |
| 21725 | The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B] |
| 23474 | A judgement is a complex entity, of mind and various objects [Russell/Whitehead] |
| 23455 | The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead] |
| 23480 | The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead] |
| 18275 | Only the act of judging completes the meaning of a statement [Russell/Whitehead] |
| 23453 | Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead] |
| 249 | People who value beauty above virtue insult the soul by placing the body above it [Plato] |
| 265 | An action is only just if it is performed by someone with a just character and outlook [Plato] |
| 269 | Attempted murder is like real murder, but we should respect the luck which avoided total ruin [Plato] |
| 240 | It would be strange if the gods rewarded those who experienced the most pleasure in life [Plato] |
| 264 | The conquest of pleasure is the noblest victory of all [Plato] |
| 253 | Every crime is the result of excessive self-love [Plato] |
| 263 | The only worthwhile life is one devoted to physical and moral perfection [Plato] |
| 4332 | Virtue is a concord of reason and emotion, with pleasure and pain trained to correct ends [Plato] |
| 248 | A serious desire for moral excellence is very rare indeed [Plato] |
| 235 | Virtue is the aim of all laws [Plato] |
| 277 | The Guardians must aim to discover the common element in the four cardinal virtues [Plato] |
| 254 | Excessive laughter and tears must be avoided [Plato] |
| 266 | Injustice is the mastery of the soul by bad feelings, even if they do not lead to harm [Plato] |
| 256 | Virtue and great wealth are incompatible [Plato] |
| 242 | The best people are produced where there is no excess of wealth or poverty [Plato] |
| 245 | Totalitarian states destroy friendships and community spirit [Plato] |
| 239 | Education in virtue produces citizens who are active but obedient [Plato] |
| 262 | Men and women should qualify equally for honours on merit [Plato] |
| 1402 | Friendship is impossible between master and slave, even if they are made equal [Plato] |
| 236 | Sound laws achieve the happiness of those who observe them [Plato] |
| 259 | Justice is granting the equality which unequals deserve [Plato] |
| 238 | Children's games should channel their pleasures into adult activity [Plato] |
| 260 | Control of education is the key office of state, and should go to the best citizen [Plato] |
| 257 | Mathematics has the widest application of any subject on the curriculum [Plato] |
| 4331 | Education is channelling a child's feelings into the right course before it understands why [Plato] |
| 250 | The best way to educate the young is not to rebuke them, but to set a good example [Plato] |
| 275 | Creation is not for you; you exist for the sake of creation [Plato] |
| 273 | Movement is transmitted through everything, and it must have started with self-generated motion [Plato] |
| 8004 | In 'The Laws', to obey the law is to be obey god [Plato, by MacIntyre] |
| 21257 | Self-generating motion is clearly superior to all other kinds of motion [Plato] |
| 21258 | The only possible beginning for the endless motions of reality is something self-generated [Plato] |
| 21261 | Self-moving soul has to be the oldest thing there is [Plato] |
| 274 | Soul must be the cause of all the opposites, such as good and evil or beauty and ugliness [Plato] |
| 21263 | If all the motions of nature reflect calculations of reason, then the best kind of soul must direct it [Plato] |
| 278 | If astronomical movements are seen as necessary instead of by divine will, this leads to atheism [Plato] |
| 21265 | The heavens must be full of gods, controlling nature either externally or from within [Plato] |
| 21262 | There must be at least two souls controlling the cosmos, one doing good, the other the opposite [Plato] |