29 ideas
10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
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] |
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] |
15435 | If you think universals are immanent, you must believe them to be sparse, and not every related predicate [Lewis] |
15451 | I assume there could be natural properties that are not instantiated in our world [Lewis] |
15433 | Tropes are particular properties, which cannot recur, but can be exact duplicates [Lewis] |
15436 | Universals are meant to give an account of resemblance [Lewis] |
15438 | We can add a primitive natural/unnatural distinction to class nominalism [Lewis] |
15448 | The 'magical' view of structural universals says they are atoms, even though they have parts [Lewis] |
15449 | If 'methane' is an atomic structural universal, it has nothing to connect it to its carbon universals [Lewis] |
15439 | The 'pictorial' view of structural universals says they are wholes made of universals as parts [Lewis] |
15441 | The structural universal 'methane' needs the universal 'hydrogen' four times over [Lewis] |
15445 | Butane and Isobutane have the same atoms, but different structures [Lewis] |
15434 | Structural universals have a necessary connection to the universals forming its parts [Lewis] |
15437 | We can't get rid of structural universals if there are no simple universals [Lewis] |
15446 | Composition is not just making new things from old; there are too many counterexamples [Lewis] |
15440 | A whole is distinct from its parts, but is not a further addition in ontology [Lewis] |
15444 | Different things (a toy house and toy car) can be made of the same parts at different times [Lewis] |
14365 | Scientific understanding is always the grasping of a correct explanation [Strevens] |
14368 | We may 'understand that' the cat is on the mat, but not at all 'understand why' it is there [Strevens] |
14369 | Understanding is a precondition, comes in degrees, is active, and holistic - unlike explanation [Strevens] |
15450 | Maybe abstraction is just mereological subtraction [Lewis] |
15443 | Mathematicians abstract by equivalence classes, but that doesn't turn a many into one [Lewis] |