98 ideas
13310 | Wisdom does not lie in books, and unread people can also become wise [Seneca] |
13295 | Wise people escape necessity by willing it [Seneca] |
13317 | Philosophy aims at happiness [Seneca] |
13293 | What philosophy offers humanity is guidance [Seneca] |
13309 | That something is a necessary condition of something else doesn't mean it caused it [Seneca] |
13313 | Even philosophers have got bogged down in analysing tiny bits of language [Seneca] |
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] |
9724 | Until the 1960s the only semantics was truth-tables [Enderton] |
9707 | 'F(x)' is the unique value which F assumes for a value of x [Enderton] |
9705 | 'fld R' indicates the 'field' of all objects in the relation [Enderton] |
9704 | 'ran R' indicates the 'range' of objects being related to [Enderton] |
9703 | 'dom R' indicates the 'domain' of objects having a relation [Enderton] |
9710 | We write F:A→B to indicate that A maps into B (the output of F on A is in B) [Enderton] |
9699 | The 'powerset' of a set is all the subsets of a given set [Enderton] |
9700 | Two sets are 'disjoint' iff their intersection is empty [Enderton] |
9712 | A relation is 'symmetric' on a set if every ordered pair has the relation in both directions [Enderton] |
9713 | A relation is 'transitive' if it can be carried over from two ordered pairs to a third [Enderton] |
9701 | A 'relation' is a set of ordered pairs [Enderton] |
9702 | A 'domain' of a relation is the set of members of ordered pairs in the relation [Enderton] |
9708 | A function 'maps A into B' if the relating things are set A, and the things related to are all in B [Enderton] |
9709 | A function 'maps A onto B' if the relating things are set A, and the things related to are set B [Enderton] |
9711 | A relation is 'reflexive' on a set if every member bears the relation to itself [Enderton] |
9706 | A 'function' is a relation in which each object is related to just one other object [Enderton] |
9714 | A relation satisfies 'trichotomy' if all pairs are either relations, or contain identical objects [Enderton] |
9717 | A set is 'dominated' by another if a one-to-one function maps the first set into a subset of the second [Enderton] |
9716 | We 'partition' a set into distinct subsets, according to each relation on its objects [Enderton] |
9715 | An 'equivalence relation' is a reflexive, symmetric and transitive binary relation [Enderton] |
9722 | Inference not from content, but from the fact that it was said, is 'conversational implicature' [Enderton] |
9718 | Validity is either semantic (what preserves truth), or proof-theoretic (following procedures) [Enderton] |
9721 | A logical truth or tautology is a logical consequence of the empty set [Enderton] |
9994 | A truth assignment to the components of a wff 'satisfy' it if the wff is then True [Enderton] |
9719 | A proof theory is 'sound' if its valid inferences entail semantic validity [Enderton] |
9720 | A proof theory is 'complete' if semantically valid inferences entail proof-theoretic validity [Enderton] |
9995 | Proof in finite subsets is sufficient for proof in an infinite set [Enderton] |
9996 | Expressions are 'decidable' if inclusion in them (or not) can be proved [Enderton] |
9997 | For a reasonable language, the set of valid wff's can always be enumerated [Enderton] |
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] |
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] |
218 | Participation is not by means of similarity, so we are looking for some other method of participation [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] |
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] |
9723 | Sentences with 'if' are only conditionals if they can read as A-implies-B [Enderton] |
13297 | To the four causes Plato adds a fifth, the idea which guided the event [Seneca] |
13307 | If everything can be measured, try measuring the size of a man's soul [Seneca] |
21399 | Referring to a person, and speaking about him, are very different [Seneca] |
13325 | Trouble in life comes from copying other people, which is following convention instead of reason [Seneca] |
22239 | Humans acquired the concept of virtue from an analogy with bodily health and strength [Seneca, by Allen] |
13294 | We know death, which is like before birth; ceasing to be and never beginning are the same [Seneca] |
13299 | Living is nothing wonderful; what matters is to die well [Seneca] |
13300 | It is as silly to lament ceasing to be as to lament not having lived in the remote past [Seneca] |
13321 | Is anything sweeter than valuing yourself more when you find you are loved? [Seneca] |
13292 | Selfishness does not produce happiness; to live for yourself, live for others [Seneca] |
13303 | A man is as unhappy as he has convinced himself he is [Seneca] |
13302 | Life is like a play - it is the quality that matters, not the length [Seneca] |
13301 | We are scared of death - except when we are immersed in pleasure! [Seneca] |
13323 | The whole point of pleasure-seeking is novelty, and abandoning established ways [Seneca] |
13318 | Nature doesn't give us virtue; we must unremittingly pursue it, as a training and an art [Seneca] |
13324 | Living contrary to nature is like rowing against the stream [Seneca] |
13305 | Character is ruined by not looking back over our pasts, since the future rests on the past [Seneca] |
13312 | Excessive curiosity is a form of intemperance [Seneca] |
13308 | It's no good winning lots of fights, if you are then conquered by your own temper [Seneca] |
13315 | To govern used to mean to serve, not to rule; rulers did not test their powers over those who bestowed it [Seneca] |
222 | Only a great person can understand the essence of things, and an even greater person can teach it [Plato] |
13290 | One joy of learning is making teaching possible [Seneca] |
13322 | Both teachers and pupils should aim at one thing - the improvement of the pupil [Seneca] |
13298 | Suicide may be appropriate even when it is not urgent, if there are few reasons against it [Seneca] |
13319 | If we control our own death, no one has power over us [Seneca] |
13320 | Sometimes we have a duty not to commit suicide, for those we love [Seneca] |
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] |
13311 | Does time exist on its own? Did anything precede it? Did it pre-exist the cosmos? [Seneca] |
234 | We couldn't discuss the non-existence of the One without knowledge of it [Plato] |