25 ideas
10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
16477 | Asserting not-p is saying p is false [Russell] |
16484 | There are four experiences that lead us to talk of 'some' things [Russell] |
21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
16486 | The physical world doesn't need logic, but the mental world does [Russell] |
10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
2947 | Questions wouldn't lead anywhere without the law of excluded middle [Russell] |
16480 | A disjunction expresses indecision [Russell] |
16479 | 'Or' expresses hesitation, in a dog at a crossroads, or birds risking grabbing crumbs [Russell] |
16481 | 'Or' expresses a mental state, not something about the world [Russell] |
16487 | Maybe the 'or' used to describe mental states is not the 'or' of logic [Russell] |
16483 | Disjunction may also arise in practice if there is imperfect memory. [Russell] |
10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
16475 | A 'heterological' predicate can't be predicated of itself; so is 'heterological' heterological? Yes=no! [Russell] |
10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
16482 | All our knowledge (if verbal) is general, because all sentences contain general words [Russell] |
4758 | Naďve realism leads to physics, but physics then shows that naďve realism is false [Russell] |
16476 | For simple words, a single experience can show that they are true [Russell] |
16485 | Perception can't prove universal generalisations, so abandon them, or abandon empiricism? [Russell] |
16478 | A mother cat is paralysed if equidistant between two needy kittens [Russell] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |