87 ideas
| 162 | Can we understand an individual soul without knowing the soul in general? [Plato] |
| 160 | The highest ability in man is the ability to discuss unity and plurality in the nature of things [Plato] |
| 166 | A speaker should be able to divide a subject, right down to the limits of divisibility [Plato] |
| 14456 | 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell] |
| 14426 | A definition by 'extension' enumerates items, and one by 'intension' gives a defining property [Russell] |
| 8468 | The sentence 'procrastination drinks quadruplicity' is meaningless, rather than false [Russell, by Orenstein] |
| 14454 | An argument 'satisfies' a function φx if φa is true [Russell] |
| 14453 | The Darapti syllogism is fallacious: All M is S, all M is P, so some S is P' - but if there is no M? [Russell] |
| 14427 | We can enumerate finite classes, but an intensional definition is needed for infinite classes [Russell] |
| 14428 | Members define a unique class, whereas defining characteristics are numerous [Russell] |
| 14440 | We may assume that there are infinite collections, as there is no logical reason against them [Russell] |
| 14447 | Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell] |
| 14443 | The British parliament has one representative selected from each constituency [Russell] |
| 14445 | Choice shows that if any two cardinals are not equal, one must be the greater [Russell] |
| 14444 | Choice is equivalent to the proposition that every class is well-ordered [Russell] |
| 14446 | We can pick all the right or left boots, but socks need Choice to insure the representative class [Russell] |
| 14459 | Reducibility: a family of functions is equivalent to a single type of function [Russell] |
| 14461 | Propositions about classes can be reduced to propositions about their defining functions [Russell] |
| 8469 | Russell's proposal was that only meaningful predicates have sets as their extensions [Russell, by Orenstein] |
| 8745 | Classes are logical fictions, and are not part of the ultimate furniture of the world [Russell] |
| 14452 | All the propositions of logic are completely general [Russell] |
| 14462 | In modern times, logic has become mathematical, and mathematics has become logical [Russell] |
| 14464 | Logic can be known a priori, without study of the actual world [Russell] |
| 12444 | Logic is concerned with the real world just as truly as zoology [Russell] |
| 10057 | Logic can only assert hypothetical existence [Russell] |
| 10450 | Russell admitted that even names could also be used as descriptions [Russell, by Bach] |
| 14458 | Asking 'Did Homer exist?' is employing an abbreviated description [Russell] |
| 14457 | Names are really descriptions, except for a few words like 'this' and 'that' [Russell] |
| 7311 | The only genuine proper names are 'this' and 'that' [Russell] |
| 14455 | 'I met a unicorn' is meaningful, and so is 'unicorn', but 'a unicorn' is not [Russell] |
| 14442 | If straight lines were like ratios they might intersect at a 'gap', and have no point in common [Russell] |
| 14438 | New numbers solve problems: negatives for subtraction, fractions for division, complex for equations [Russell] |
| 13510 | Could a number just be something which occurs in a progression? [Russell, by Hart,WD] |
| 14436 | A series can be 'Cut' in two, where the lower class has no maximum, the upper no minimum [Russell] |
| 14439 | A complex number is simply an ordered couple of real numbers [Russell] |
| 14421 | Discovering that 1 is a number was difficult [Russell] |
| 14424 | Numbers are needed for counting, so they need a meaning, and not just formal properties [Russell] |
| 14441 | The formal laws of arithmetic are the Commutative, the Associative and the Distributive [Russell] |
| 14420 | Infinity and continuity used to be philosophy, but are now mathematics [Russell] |
| 14431 | The definition of order needs a transitive relation, to leap over infinite intermediate terms [Russell] |
| 14422 | Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms [Russell] |
| 14423 | '0', 'number' and 'successor' cannot be defined by Peano's axioms [Russell] |
| 14425 | A number is something which characterises collections of the same size [Russell] |
| 14434 | What matters is the logical interrelation of mathematical terms, not their intrinsic nature [Russell] |
| 14465 | Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men' [Russell] |
| 13414 | For Russell, numbers are sets of equivalent sets [Russell, by Benacerraf] |
| 14449 | There is always something psychological about inference [Russell] |
| 14463 | Existence can only be asserted of something described, not of something named [Russell] |
| 7953 | Reasoning needs to cut nature accurately at the joints [Plato] |
| 14429 | Classes are logical fictions, made from defining characteristics [Russell] |
| 16121 | I revere anyone who can discern a single thing that encompasses many things [Plato] |
| 14430 | If a relation is symmetrical and transitive, it has to be reflexive [Russell] |
| 14432 | 'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a [Russell] |
| 153 | It takes a person to understand, by using universals, and by using reason to create a unity out of sense-impressions [Plato] |
| 154 | We would have an overpowering love of knowledge if we had a pure idea of it - as with the other Forms [Plato] |
| 14435 | The essence of individuality is beyond description, and hence irrelevant to science [Russell] |
| 12197 | Inferring q from p only needs p to be true, and 'not-p or q' to be true [Russell] |
| 14450 | All forms of implication are expressible as truth-functions [Russell] |
| 14460 | If something is true in all possible worlds then it is logically necessary [Russell] |
| 151 | True knowledge is of the reality behind sense experience [Plato] |
| 165 | If the apparent facts strongly conflict with probability, it is in everyone's interests to suppress the facts [Plato] |
| 14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
| 9296 | The soul is self-motion [Plato] |
| 23997 | Plato saw emotions and appetites as wild horses, in need of taming [Plato, by Goldie] |
| 14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
| 158 | An excellent speech seems to imply a knowledge of the truth in the mind of the speaker [Plato] |
| 159 | Only a good philosopher can be a good speaker [Plato] |
| 5946 | 'Phaedrus' pioneers the notion of philosophical rhetoric [Lawson-Tancred on Plato] |
| 155 | Beauty is the clearest and most lovely of the Forms [Plato] |
| 143 | The two ruling human principles are the natural desire for pleasure, and an acquired love of virtue [Plato] |
| 157 | Most pleasure is release from pain, and is therefore not worthwhile [Plato] |
| 144 | Reason impels us towards excellence, which teaches us self-control [Plato] |
| 156 | Bad people are never really friends with one another [Plato] |
| 148 | If the prime origin is destroyed, it will not come into being again out of anything [Plato] |
| 152 | The mind of God is fully satisfied and happy with a vision of reality and truth [Plato] |
| 21241 | Even the fool can hold 'a being than which none greater exists' in his understanding [Anselm] |
| 21243 | An existing thing is even greater if its non-existence is inconceivable [Anselm] |
| 21244 | Conceiving a greater being than God leads to absurdity [Anselm] |
| 21242 | If that than which a greater cannot be thought actually exists, that is greater than the mere idea [Anselm] |
| 1421 | A perfection must be independent and unlimited, and the necessary existence of Anselm's second proof gives this [Malcolm on Anselm] |
| 21245 | The word 'God' can be denied, but understanding shows God must exist [Anselm] |
| 21246 | Guanilo says a supremely fertile island must exist, just because we can conceive it [Anselm] |
| 21247 | Nonexistence is impossible for the greatest thinkable thing, which has no beginning or end [Anselm] |
| 1420 | Anselm's first proof fails because existence isn't a real predicate, so it can't be a perfection [Malcolm on Anselm] |
| 150 | We cannot conceive of God, so we have to think of Him as an immortal version of ourselves [Plato] |
| 149 | There isn't a single reason for positing the existence of immortal beings [Plato] |
| 146 | Soul is always in motion, so it must be self-moving and immortal [Plato] |