44 ideas
18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
9572 | Realists about sets say there exists a null set in the real world, with no members [Chihara] |
9550 | We only know relational facts about the empty set, but nothing intrinsic [Chihara] |
9562 | In simple type theory there is a hierarchy of null sets [Chihara] |
9573 | The null set is a structural position which has no other position in membership relation [Chihara] |
9551 | What is special about Bill Clinton's unit set, in comparison with all the others? [Chihara] |
9549 | The set theorist cannot tell us what 'membership' is [Chihara] |
9571 | ZFU refers to the physical world, when it talks of 'urelements' [Chihara] |
9563 | A pack of wolves doesn't cease when one member dies [Chihara] |
8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
8492 | Relations are functions with two arguments [Frege] |
9561 | The mathematics of relations is entirely covered by ordered pairs [Chihara] |
9552 | Sentences are consistent if they can all be true; for Frege it is that no contradiction can be deduced [Chihara] |
9553 | Analytic geometry gave space a mathematical structure, which could then have axioms [Chihara] |
10192 | We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride] |
8487 | Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege] |
18899 | Frege takes the existence of horses to be part of their concept [Frege, by Sommers] |
9559 | If a successful theory confirms mathematics, presumably a failed theory disconfirms it? [Chihara] |
9566 | No scientific explanation would collapse if mathematical objects were shown not to exist [Chihara] |
4028 | Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege] |
8489 | The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege] |
9947 | Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman] |
10319 | An assertion about the concept 'horse' must indirectly speak of an object [Frege, by Hale] |
8488 | A concept is a function whose value is always a truth-value [Frege] |
9948 | Unlike objects, concepts are inherently incomplete [Frege, by George/Velleman] |
9568 | I prefer the open sentences of a Constructibility Theory, to Platonist ideas of 'equivalence classes' [Chihara] |
9547 | Mathematical entities are causally inert, so the causal theory of reference won't work for them [Chihara] |
4972 | I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege] |
21059 | General rules of action also need a judgement about when to apply them [Kant] |
21061 | Duty does not aim at an end, but gives rise to universal happiness as aim of the will [Kant] |
21060 | It can't be a duty to strive after the impossible [Kant] |
21062 | The will's motive is the absolute law itself, and moral feeling is receptivity to law [Kant] |
21071 | There can be no restraints on freedom if reason does not reveal some basic rights [Kant] |
21063 | Personal contracts are for some end, but a civil state contract involves a duty to share [Kant] |
21068 | There must be a unanimous contract that citizens accept majority decisions [Kant] |
21069 | A contract is theoretical, but it can guide rulers to make laws which the whole people will accept [Kant] |
21070 | A law is unjust if the whole people could not possibly agree to it [Kant] |
21067 | A citizen must control his own life, and possess property or an important skill [Kant] |
21064 | A lawful civil state must embody freedom, equality and independence for its members [Kant] |
21066 | Citizens can rise to any rank that talent, effort and luck can achieve [Kant] |
21065 | You can't make a contract renouncing your right to make contracts! [Kant] |
21072 | The people (who have to fight) and not the head of state should declare a war [Kant] |
9574 | 'Gunk' is an individual possessing no parts that are atoms [Chihara] |
8491 | The Ontological Argument fallaciously treats existence as a first-level concept [Frege] |