84 ideas
7623 | For ancient Greeks being wise was an ethical value [Putnam] |
224 | When questions are doubtful we should concentrate not on objects but on ideas of the intellect [Plato] |
232 | Opposites are as unlike as possible [Plato] |
8937 | Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic [Hegel on Plato] |
4714 | Putnam's epistemic notion of truth replaces the realism of correspondence with ontological relativism [Putnam, by O'Grady] |
7617 | Before Kant, all philosophers had a correspondence theory of truth [Putnam] |
4716 | The correspondence theory is wrong, because there is no one correspondence between reality and fact [Putnam, by O'Grady] |
7616 | Truth is an idealisation of rational acceptability [Putnam] |
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] |
14203 | Intension is not meaning, as 'cube' and 'square-faced polyhedron' are intensionally the same [Putnam] |
14207 | If cats equal cherries, model theory allows reinterpretation of the whole language preserving truth [Putnam] |
13986 | Plato found antinomies in ideas, Kant in space and time, and Bradley in relations [Plato, by Ryle] |
14150 | Plato's 'Parmenides' is perhaps the best collection of antinomies ever made [Russell on 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] |
16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
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] |
229 | The one was and is and will be and was becoming and is becoming and will become [Plato] |
21821 | Plato's Parmenides has a three-part theory, of Primal One, a One-Many, and a One-and-Many [Plato, by Plotinus] |
221 | Absolute ideas, such as the Good and the Beautiful, cannot be known by us [Plato] |
14214 | If we try to cure the abundance of theories with causal links, this is 'just more theory' [Putnam, by Lewis] |
14205 | The sentence 'A cat is on a mat' remains always true when 'cat' means cherry and 'mat' means tree [Putnam] |
7610 | A fact is simply what it is rational to accept [Putnam] |
7618 | Very nominalistic philosophers deny properties, though scientists accept them [Putnam] |
227 | You must always mean the same thing when you utter the same name [Plato] |
223 | If you deny that each thing always stays the same, you destroy the possibility of discussion [Plato] |
210 | It would be absurd to think there were abstract Forms for vile things like hair, mud and dirt [Plato] |
220 | The concept of a master includes the concept of a slave [Plato] |
211 | If admirable things have Forms, maybe everything else does as well [Plato] |
219 | If absolute ideas existed in us, they would cease to be absolute [Plato] |
228 | Greatness and smallness must exist, to be opposed to one another, and come into being in things [Plato] |
16151 | Plato moves from Forms to a theory of genera and principles in his later work [Plato, by Frede,M] |
218 | Participation is not by means of similarity, so we are looking for some other method of participation [Plato] |
212 | The whole idea of each Form must be found in each thing which participates in it [Plato] |
215 | If things partake of ideas, this implies either that everything thinks, or that everything actually is thought [Plato] |
213 | Each idea is in all its participants at once, just as daytime is a unity but in many separate places at once [Plato] |
216 | If things are made alike by participating in something, that thing will be the absolute idea [Plato] |
217 | Nothing can be like an absolute idea, because a third idea intervenes to make them alike (leading to a regress) [Plato] |
214 | If absolute greatness and great things are seen as the same, another thing appears which makes them seem great [Plato] |
15851 | Parts must belong to a created thing with a distinct form [Plato] |
15846 | In Parmenides, if composition is identity, a whole is nothing more than its parts [Plato, by Harte,V] |
15849 | Plato says only a one has parts, and a many does not [Plato, by Harte,V] |
15850 | Anything which has parts must be one thing, and parts are of a one, not of a many [Plato] |
13259 | It seems that the One must be composed of parts, which contradicts its being one [Plato] |
15847 | Two things relate either as same or different, or part of a whole, or the whole of the part [Plato] |
12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
4718 | If necessity is always relative to a description in a language, then there is only 'de dicto' necessity [Putnam, by O'Grady] |
10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
7620 | Some kind of objective 'rightness' is a presupposition of thought itself [Putnam] |
14204 | Naďve operationalism would have meanings change every time the tests change [Putnam] |
7611 | Rationality is one part of our conception of human flourishing [Putnam] |
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] |
14200 | 'Water' on Twin Earth doesn't refer to water, but no mental difference can account for this [Putnam] |
7612 | Reference is social not individual, because we defer to experts when referring to elm trees [Putnam] |
7613 | Concepts are (at least in part) abilities and not occurrences [Putnam] |
14202 | Neither individual nor community mental states fix reference [Putnam] |
14201 | Maybe the total mental state of a language community fixes the reference of a term [Putnam] |
23453 | Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead] |
14206 | There are infinitely many interpretations of a sentence which can all seem to be 'correct' [Putnam] |
7624 | The word 'inconsiderate' nicely shows the blurring of facts and values [Putnam] |
222 | Only a great person can understand the essence of things, and an even greater person can teach it [Plato] |
225 | The unlimited has no shape and is endless [Plato] |
233 | Some things do not partake of the One [Plato] |
2062 | The only movement possible for the One is in space or in alteration [Plato] |
231 | Everything partakes of the One in some way [Plato] |
234 | We couldn't discuss the non-existence of the One without knowledge of it [Plato] |