42 ideas
| 1922 | Spiritual qualities only become advantageous with the growth of wisdom [Plato] |
| 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] |
| 11259 | How can you seek knowledge of something if you don't know it? [Plato] |
| 18248 | A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro] |
| 18152 | Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock] |
| 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] |
| 12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
| 20219 | True opinions only become really valuable when they are tied down by reasons [Plato] |
| 5985 | Seeking and learning are just recollection [Plato] |
| 5986 | The slave boy learns geometry from questioning, not teaching, so it is recollection [Plato] |
| 10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
| 1923 | As a guide to action, true opinion is as good as knowledge [Plato] |
| 1919 | You don't need to learn what you know, and how do you seek for what you don't know? [Plato] |
| 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] |
| 4581 | Virtues and vices are like secondary qualities in perception, found in observers, not objects [Hume] |
| 4580 | All virtues benefit either the public, or the individual who possesses them [Hume] |
| 1913 | Is virtue taught, or achieved by practice, or a natural aptitude, or what? [Plato] |
| 1921 | If virtue is a type of knowledge then it ought to be taught [Plato] |
| 1927 | It seems that virtue is neither natural nor taught, but is a divine gift [Plato] |
| 1918 | How can you know part of virtue without knowing the whole? [Plato] |
| 1916 | Even if virtues are many and various, they must have something in common to make them virtues [Plato] |
| 4579 | The idea of a final cause is very uncertain and unphilosophical [Hume] |
| 20705 | That events could be uncaused is absurd; I only say intuition and demonstration don't show this [Hume] |