68 ideas
| 224 | When questions are doubtful we should concentrate not on objects but on ideas of the intellect [Plato] |
| 12596 | Reasoning aims at increasing explanatory coherence [Harman] |
| 12599 | Reason conservatively: stick to your beliefs, and prefer reasoning that preserves most of them [Harman] |
| 232 | Opposites are as unlike as possible [Plato] |
| 8937 | Plato's 'Parmenides' is the greatest artistic achievement of the ancient dialectic [Hegel on Plato] |
| 10775 | The axiom of choice now seems acceptable and obvious (if it is meaningful) [Tharp] |
| 12595 | We have a theory of logic (implication and inconsistency), but not of inference or reasoning [Harman] |
| 10766 | Logic is either for demonstration, or for characterizing structures [Tharp] |
| 10767 | Elementary logic is complete, but cannot capture mathematics [Tharp] |
| 10769 | Second-order logic isn't provable, but will express set-theory and classic problems [Tharp] |
| 10762 | In sentential logic there is a simple proof that all truth functions can be reduced to 'not' and 'and' [Tharp] |
| 12597 | I might accept P and Q as likely, but reject P-and-Q as unlikely [Harman] |
| 10776 | The main quantifiers extend 'and' and 'or' to infinite domains [Tharp] |
| 10774 | There are at least five unorthodox quantifiers that could be used [Tharp] |
| 10773 | The Löwenheim-Skolem property is a limitation (e.g. can't say there are uncountably many reals) [Tharp] |
| 10777 | Skolem mistakenly inferred that Cantor's conceptions were illusory [Tharp] |
| 10765 | Soundness would seem to be an essential requirement of a proof procedure [Tharp] |
| 10763 | Completeness and compactness together give axiomatizability [Tharp] |
| 10770 | If completeness fails there is no algorithm to list the valid formulas [Tharp] |
| 10771 | Compactness is important for major theories which have infinitely many axioms [Tharp] |
| 10772 | Compactness blocks infinite expansion, and admits non-standard models [Tharp] |
| 10764 | A complete logic has an effective enumeration of the valid formulas [Tharp] |
| 10768 | Effective enumeration might be proved but not specified, so it won't guarantee knowledge [Tharp] |
| 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] |
| 16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
| 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] |
| 12598 | Reality is the overlap of true complete theories [Harman] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 12602 | There is no natural border between inner and outer [Harman] |
| 12603 | We can only describe mental attitudes in relation to the external world [Harman] |
| 12601 | The way things look is a relational matter, not an intrinsic matter [Harman] |
| 12592 | Concepts in thought have content, but not meaning, which requires communication [Harman] |
| 12590 | Take meaning to be use in calculation with concepts, rather than in communication [Harman] |
| 12593 | The use theory attaches meanings to words, not to sentences [Harman] |
| 12588 | Meaning from use of thoughts, constructed from concepts, which have a role relating to reality [Harman] |
| 12589 | Some regard conceptual role semantics as an entirely internal matter [Harman] |
| 12600 | The content of thought is relations, between mental states, things in the world, and contexts [Harman] |
| 12594 | If one proposition negates the other, which is the negative one? [Harman] |
| 12591 | Mastery of a language requires thinking, and not just communication [Harman] |
| 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] |