29 ideas
22820 | Early Romantics sought a plurality of systems, in a quest for freedom [Hösle] |
10571 | Concern for rigour can get in the way of understanding phenomena [Fine,K] |
18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
10565 | There is no stage at which we can take all the sets to have been generated [Fine,K] |
10564 | We might combine the axioms of set theory with the axioms of mereology [Fine,K] |
8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
8492 | Relations are functions with two arguments [Frege] |
10569 | If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K] |
10570 | Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K] |
10573 | Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K] |
10575 | Why should a Dedekind cut correspond to a number? [Fine,K] |
10574 | Unless we know whether 0 is identical with the null set, we create confusions [Fine,K] |
10560 | Set-theoretic imperialists think sets can represent every mathematical object [Fine,K] |
8487 | Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege] |
10568 | Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K] |
18899 | Frege takes the existence of horses to be part of their concept [Frege, by Sommers] |
10563 | A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K] |
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] |
10561 | Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K] |
10562 | We can combine ZF sets with abstracts as urelements [Fine,K] |
10567 | We can create objects from conditions, rather than from concepts [Fine,K] |
4972 | I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege] |
22819 | In the 18th century history came to be seen as progressive, rather than cyclical [Hösle] |
8491 | The Ontological Argument fallaciously treats existence as a first-level concept [Frege] |