46 ideas
| 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] |
| 10041 | Impredicative Definitions refer to the totality to which the object itself belongs [Gödel] |
| 21716 | In simple type theory the axiom of Separation is better than Reducibility [Gödel, by Linsky,B] |
| 10035 | Mathematical Logic is a non-numerical branch of mathematics, and the supreme science [Gödel] |
| 10042 | Reference to a totality need not refer to a conjunction of all its elements [Gödel] |
| 10038 | A logical system needs a syntactical survey of all possible expressions [Gödel] |
| 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] |
| 10046 | The generalized Continuum Hypothesis asserts a discontinuity in cardinal numbers [Gödel] |
| 10039 | Some arithmetical problems require assumptions which transcend arithmetic [Gödel] |
| 16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
| 10043 | Mathematical objects are as essential as physical objects are for perception [Gödel] |
| 10045 | Impredicative definitions are admitted into ordinary mathematics [Gödel] |
| 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] |
| 223 | If you deny that each thing always stays the same, you destroy the possibility of discussion [Plato] |
| 227 | You must always mean the same thing when you utter the same name [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] |
| 228 | Greatness and smallness must exist, to be opposed to one another, and come into being in things [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] |
| 16151 | Plato moves from Forms to a theory of genera and principles in his later work [Plato, by Frede,M] |
| 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] |
| 212 | The whole idea of each Form must be found in each thing which participates in it [Plato] |
| 216 | If things are made alike by participating in something, that thing will be the absolute idea [Plato] |
| 218 | Participation is not by means of similarity, so we are looking for some other method of participation [Plato] |
| 214 | If absolute greatness and great things are seen as the same, another thing appears which makes them seem great [Plato] |
| 217 | Nothing can be like an absolute idea, because a third idea intervenes to make them alike (leading to a regress) [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] |
| 490 | Everything happens by reason and necessity [Leucippus] |
| 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] |
| 231 | Everything partakes of the One in some way [Plato] |
| 2062 | The only movement possible for the One is in space or in alteration [Plato] |
| 233 | Some things do not partake of the One [Plato] |
| 234 | We couldn't discuss the non-existence of the One without knowledge of it [Plato] |