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14456 | 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity |

14426 | A definition by 'extension' enumerates items, and one by 'intension' gives a defining property |

8468 | The sentence 'procrastination drinks quadruplicity' is meaningless, rather than false |

14454 | An argument 'satisfies' a function φx if φa is true |

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? |

14427 | We can enumerate finite classes, but an intensional definition is needed for infinite classes |

14428 | Members define a unique class, whereas defining characteristics are numerous |

14440 | We may assume that there are infinite collections, as there is no logical reason against them |

14447 | Infinity says 'for any inductive cardinal, there is a class having that many terms' |

14443 | The British parliament has one representative selected from each constituency |

14444 | Choice is equivalent to the proposition that every class is well-ordered |

14445 | Choice shows that if any two cardinals are not equal, one must be the greater |

14446 | We can pick all the right or left boots, but socks need Choice to insure the representative class |

14459 | Reducibility: a family of functions is equivalent to a single type of function |

14461 | Propositions about classes can be reduced to propositions about their defining functions |

8469 | Russell's proposal was that only meaningful predicates have sets as their extensions |

8745 | Classes are logical fictions, and are not part of the ultimate furniture of the world |

14452 | All the propositions of logic are completely general |

14462 | In modern times, logic has become mathematical, and mathematics has become logical |

12444 | Logic is concerned with the real world just as truly as zoology |

10057 | Logic can only assert hypothetical existence |

14464 | Logic can be known a priori, without study of the actual world |

10450 | Russell admitted that even names could also be used as descriptions |

14458 | Asking 'Did Homer exist?' is employing an abbreviated description |

14457 | Names are really descriptions, except for a few words like 'this' and 'that' |

7311 | The only genuine proper names are 'this' and 'that' |

14455 | 'I met a unicorn' is meaningful, and so is 'unicorn', but 'a unicorn' is not |

14438 | New numbers solve problems: negatives for subtraction, fractions for division, complex for equations |

13510 | Could a number just be something which occurs in a progression? |

14436 | A series can be 'Cut' in two, where the lower class has no maximum, the upper no minimum |

14437 | Dedekind's axiom that his Cut must be filled has the advantages of theft over honest toil |

14439 | A complex number is simply an ordered couple of real numbers |

14421 | Discovering that 1 is a number was difficult |

14424 | Numbers are needed for counting, so they need a meaning, and not just formal properties |

14441 | The formal laws of arithmetic are the Commutative, the Associative and the Distributive |

14420 | Infinity and continuity used to be philosophy, but are now mathematics |

14442 | If straight lines were like ratios they might intersect at a 'gap', and have no point in common |

14431 | The definition of order needs a transitive relation, to leap over infinite intermediate terms |

14423 | '0', 'number' and 'successor' cannot be defined by Peano's axioms |

14422 | Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms |

14425 | A number is something which characterises collections of the same size |

14434 | What matters is the logical interrelation of mathematical terms, not their intrinsic nature |

14465 | Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men' |

13414 | For Russell, numbers are sets of equivalent sets |

14449 | There is always something psychological about inference |

14463 | Existence can only be asserted of something described, not of something named |

14429 | Classes are logical fictions, made from defining characteristics |

14432 | 'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a |

14430 | If a relation is symmetrical and transitive, it has to be reflexive |

14435 | The essence of individuality is beyond description, and hence irrelevant to science |

12197 | Inferring q from p only needs p to be true, and 'not-p or q' to be true |

14450 | All forms of implication are expressible as truth-functions |

14460 | If something is true in all possible worlds then it is logically necessary |

14433 | Mathematically expressed propositions are true of the world, but how to interpret them? |

14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts |