45 ideas
| 21970 | Philosophy attains its goal if one person feels perfect accord between their system and experience [Fichte] |
| 6912 | For Fichte there is no God outside the ego, and 'our religion is reason' [Fichte, by Feuerbach] |
| 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] |
| 17453 | The meaning of a number isn't just the numerals leading up to it [Heck] |
| 17457 | A basic grasp of cardinal numbers needs an understanding of equinumerosity [Heck] |
| 18248 | A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro] |
| 17448 | In counting, numerals are used, not mentioned (as objects that have to correlated) [Heck] |
| 17456 | Counting is the assignment of successively larger cardinal numbers to collections [Heck] |
| 17455 | Is counting basically mindless, and independent of the cardinality involved? [Heck] |
| 17450 | Understanding 'just as many' needn't involve grasping one-one correspondence [Heck] |
| 17451 | We can know 'just as many' without the concepts of equinumerosity or numbers [Heck] |
| 17459 | Frege's Theorem explains why the numbers satisfy the Peano axioms [Heck] |
| 18152 | Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock] |
| 17454 | Children can use numbers, without a concept of them as countable objects [Heck] |
| 8683 | Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend] |
| 10025 | Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes] |
| 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] |
| 17458 | Equinumerosity is not the same concept as one-one correspondence [Heck] |
| 17449 | We can understand cardinality without the idea of one-one correspondence [Heck] |
| 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] |
| 12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
| 21973 | Fichte believed in things-in-themselves [Fichte, by Moore,AW] |
| 21914 | We can deduce experience from self-consciousness, without the thing-in-itself [Fichte] |
| 20951 | The absolute I divides into consciousness, and a world which is not-I [Fichte, by Bowie] |
| 21964 | Reason arises from freedom, so philosophy starts from the self, and not from the laws of nature [Fichte] |
| 21968 | Abandon the thing-in-itself; things only exist in relation to our thinking [Fichte] |
| 10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
| 21965 | Spinoza could not actually believe his determinism, because living requires free will [Fichte] |
| 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] |
| 23453 | Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead] |