21 ideas
9808 | Philosophy aims to reveal the grandeur of mathematics [Badiou] |
18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
8492 | Relations are functions with two arguments [Frege] |
21554 | Sets always exceed terms, so all the sets must exceed all the sets [Lackey] |
21553 | It seems that the ordinal number of all the ordinals must be bigger than itself [Lackey] |
9812 | In mathematics, if a problem can be formulated, it will eventually be solved [Badiou] |
9813 | Mathematics shows that thinking is not confined to the finite [Badiou] |
8487 | Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege] |
9809 | Mathematics inscribes being as such [Badiou] |
18899 | Frege takes the existence of horses to be part of their concept [Frege, by Sommers] |
9811 | It is of the essence of being to appear [Badiou] |
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] |
4972 | I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege] |
9814 | All great poetry is engaged in rivalry with mathematics [Badiou] |
8491 | The Ontological Argument fallaciously treats existence as a first-level concept [Frege] |