21 ideas
18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
15717 | Using Choice, you can cut up a small ball and make an enormous one from the pieces [Kaplan/Kaplan] |
8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
8492 | Relations are functions with two arguments [Frege] |
15712 | 1 and 0, then add for naturals, subtract for negatives, divide for rationals, take roots for irrationals [Kaplan/Kaplan] |
15711 | The rationals are everywhere - the irrationals are everywhere else [Kaplan/Kaplan] |
15714 | 'Commutative' laws say order makes no difference; 'associative' laws say groupings make no difference [Kaplan/Kaplan] |
15715 | 'Distributive' laws say if you add then multiply, or multiply then add, you get the same result [Kaplan/Kaplan] |
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] |
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] |
15713 | The first million numbers confirm that no number is greater than a million [Kaplan/Kaplan] |
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] |
1868 | The world was made as much for animals as for man [Celsus] |
8491 | The Ontological Argument fallaciously treats existence as a first-level concept [Frege] |
1867 | Christians presented Jesus as a new kind of logos to oppose that of the philosophers [Celsus] |