49 ideas
17621 | What matters in mathematics is its objectivity, not the existence of the objects [Dummett] |
192 | Only one thing can be contrary to something [Plato] |
18806 | Frege thought traditional categories had psychological and linguistic impurities [Frege, by Rumfitt] |
10537 | The ordered pairs <x,y> can be reduced to the class of sets of the form {{x},{x,y}} [Dummett] |
10542 | To associate a cardinal with each set, we need the Axiom of Choice to find a representative [Dummett] |
8490 | First-level functions have objects as arguments; second-level functions take functions as arguments [Frege] |
8492 | Relations are functions with two arguments [Frege] |
10554 | Intuitionists find the Incompleteness Theorem unsurprising, since proof is intuitive, not formal [Dummett] |
8487 | Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege] |
10552 | Intuitionism says that totality of numbers is only potential, but is still determinate [Dummett] |
18899 | Frege takes the existence of horses to be part of their concept [Frege, by Sommers] |
10515 | Ostension is possible for concreta; abstracta can only be referred to via other objects [Dummett, by Hale] |
10544 | The concrete/abstract distinction seems crude: in which category is the Mistral? [Dummett] |
10546 | We don't need a sharp concrete/abstract distinction [Dummett] |
10540 | We can't say that light is concrete but radio waves abstract [Dummett] |
10548 | The context principle for names rules out a special philosophical sense for 'existence' [Dummett] |
10281 | The objects we recognise the world as containing depends on the structure of our language [Dummett] |
4028 | Frege allows either too few properties (as extensions) or too many (as predicates) [Mellor/Oliver on Frege] |
10532 | We can understand universals by studying predication [Dummett] |
190 | If asked whether justice itself is just or unjust, you would have to say that it is just [Plato] |
10534 | 'Nominalism' used to mean denial of universals, but now means denial of abstract objects [Dummett] |
10541 | Concrete objects such as sounds and smells may not be possible objects of ostension [Dummett] |
10545 | Abstract objects may not cause changes, but they can be the subject of change [Dummett] |
10555 | If we can intuitively apprehend abstract objects, this makes them observable and causally active [Dummett] |
10543 | Abstract objects must have names that fall within the range of some functional expression [Dummett] |
10320 | If a genuine singular term needs a criterion of identity, we must exclude abstract nouns [Dummett, by Hale] |
10547 | Abstract objects can never be confronted, and need verbal phrases for reference [Dummett] |
8489 | The concept 'object' is too simple for analysis; unlike a function, it is an expression with no empty place [Frege] |
10531 | There is a modern philosophical notion of 'object', first introduced by Frege [Dummett] |
20185 | The most important things in life are wisdom and knowledge [Plato] |
20184 | The only real evil is loss of knowledge [Plato] |
191 | Everything resembles everything else up to a point [Plato] |
9947 | Concepts are the ontological counterparts of predicative expressions [Frege, by George/Velleman] |
19168 | Concepts only have a 'functional character', because they map to truth values, not objects [Dummett, by Davidson] |
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] |
10549 | Since abstract objects cannot be picked out, we must rely on identity statements [Dummett] |
10516 | A realistic view of reference is possible for concrete objects, but not for abstract objects [Dummett, by Hale] |
4972 | I may regard a thought about Phosphorus as true, and the same thought about Hesperus as false [Frege] |
203 | Courage is knowing what should or shouldn't be feared [Plato] |
202 | No one willingly and knowingly embraces evil [Plato] |
193 | Some things are good even though they are not beneficial to men [Plato] |
197 | Some pleasures are not good, and some pains are not evil [Plato] |
200 | People tend only to disapprove of pleasure if it leads to pain, or prevents future pleasure [Plato] |
188 | Socrates did not believe that virtue could be taught [Plato] |
204 | Socrates is contradicting himself in claiming virtue can't be taught, but that it is knowledge [Plato] |
189 | If we punish wrong-doers, it shows that we believe virtue can be taught [Plato] |
8491 | The Ontological Argument fallaciously treats existence as a first-level concept [Frege] |