54 ideas
21955 | My dogmatic slumber was first interrupted by David Hume [Kant] |
16931 | Metaphysics is generating a priori knowledge by intuition and concepts, leading to the synthetic [Kant] |
9542 | The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell] |
21720 | Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead] |
10044 | Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro] |
18208 | We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead] |
8204 | Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead] |
9359 | Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead] |
21707 | Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B] |
10036 | In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel] |
16918 | Mathematics cannot proceed just by the analysis of concepts [Kant] |
16930 | Geometry is not analytic, because a line's being 'straight' is a quality [Kant] |
16919 | Geometry rests on our intuition of space [Kant] |
16920 | Numbers are formed by addition of units in time [Kant] |
18248 | A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro] |
16929 | 7+5 = 12 is not analytic, because no analysis of 7+5 will reveal the concept of 12 [Kant] |
18152 | Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock] |
16910 | Mathematics can only start from an a priori intuition which is not empirical but pure [Kant] |
16917 | All necessary mathematical judgements are based on intuitions of space and time [Kant] |
16928 | Mathematics cannot be empirical because it is necessary, and that has to be a priori [Kant] |
10025 | Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes] |
8683 | Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend] |
10037 | 'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead] |
10093 | The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman] |
8691 | The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead] |
10305 | In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead] |
8684 | Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend] |
8746 | To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro] |
11833 | The substance, once the predicates are removed, remains unknown to us [Kant] |
12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
21957 | 'Transcendental' concerns how we know, rather than what we know [Kant] |
16923 | I admit there are bodies outside us [Kant] |
21441 | 'Transcendental' is not beyond experience, but a prerequisite of experience [Kant] |
16916 | A priori synthetic knowledge is only of appearances, not of things in themselves [Kant] |
16915 | A priori intuitions can only concern the objects of our senses [Kant] |
16914 | A priori intuition of objects is only possible by containing the form of my sensibility [Kant] |
21447 | I can make no sense of the red experience being similar to the quality in the object [Kant] |
16924 | I count the primary features of things (as well as the secondary ones) as mere appearances [Kant] |
16913 | I can't intuit a present thing in itself, because the properties can't enter my representations [Kant] |
16925 | Appearance gives truth, as long as it is only used within experience [Kant] |
16911 | Intuition is a representation that depends on the presence of the object [Kant] |
10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
21725 | The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B] |
23474 | A judgement is a complex entity, of mind and various objects [Russell/Whitehead] |
23455 | The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead] |
23480 | The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead] |
18275 | Only the act of judging completes the meaning of a statement [Russell/Whitehead] |
16912 | Some concepts can be made a priori, which are general thoughts of objects, like quantity or cause [Kant] |
23453 | Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead] |
16926 | Analytic judgements say clearly what was in the concept of the subject [Kant] |
16927 | Analytic judgement rests on contradiction, since the predicate cannot be denied of the subject [Kant] |
468 | Musical performance can reveal a range of virtues [Damon of Ath.] |
16922 | Space must have three dimensions, because only three lines can meet at right angles [Kant] |
16921 | If all empirical sensation of bodies is removed, space and time are still left [Kant] |