82 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] |
10354 | Correspondence could be with other beliefs, rather than external facts [Kusch] |
21752 | Prior to Gödel we thought truth in mathematics consisted in provability [Gödel, by Quine] |
10353 | Tarskians distinguish truth from falsehood by relations between members of sets [Kusch] |
17835 | Gödel show that the incompleteness of set theory was a necessity [Gödel, by Hallett,M] |
17886 | The limitations of axiomatisation were revealed by the incompleteness theorems [Gödel, by Koellner] |
10071 | Second Incompleteness: nice theories can't prove their own consistency [Gödel, by Smith,P] |
19123 | If soundness can't be proved internally, 'reflection principles' can be added to assert soundness [Gödel, by Halbach/Leigh] |
10621 | Gödel's First Theorem sabotages logicism, and the Second sabotages Hilbert's Programme [Smith,P on Gödel] |
17888 | The undecidable sentence can be decided at a 'higher' level in the system [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] |
10132 | There can be no single consistent theory from which all mathematical truths can be derived [Gödel, by George/Velleman] |
3198 | Gödel showed that arithmetic is either incomplete or inconsistent [Gödel, by Rey] |
10072 | First Incompleteness: arithmetic must always be incomplete [Gödel, by Smith,P] |
9590 | Arithmetical truth cannot be fully and formally derived from axioms and inference rules [Gödel, by Nagel/Newman] |
11069 | Gödel's Second says that semantic consequence outruns provability [Gödel, by Hanna] |
10118 | First Incompleteness: a decent consistent system is syntactically incomplete [Gödel, by George/Velleman] |
10122 | Second Incompleteness: a decent consistent system can't prove its own consistency [Gödel, by George/Velleman] |
10611 | There is a sentence which a theory can show is true iff it is unprovable [Gödel, by Smith,P] |
10867 | 'This system can't prove this statement' makes it unprovable either way [Gödel, by Clegg] |
16150 | One is, so numbers exist, so endless numbers exist, and each one must partake of being [Plato] |
8747 | Realists are happy with impredicative definitions, which describe entities in terms of other existing entities [Gödel, 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] |
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] |
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] |
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] |
215 | If things partake of ideas, this implies either that everything thinks, or that everything actually is thought [Plato] |
212 | The whole idea of each Form must be found in each thing which participates in it [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] |
10337 | We can have knowledge without belief, if others credit us with knowledge [Kusch] |
10357 | Methodological Solipsism assumes all ideas could be derived from one mind [Kusch] |
10339 | Foundations seem utterly private, even from oneself at a later time [Kusch] |
10331 | Testimony is reliable if it coheres with evidence for a belief, and with other beliefs [Kusch] |
10338 | The coherentist restricts the space of reasons to the realm of beliefs [Kusch] |
10340 | Individualistic coherentism lacks access to all of my beliefs, or critical judgement of my assessment [Kusch] |
10345 | Individual coherentism cannot generate the necessary normativity [Kusch] |
10350 | Cultures decide causal routes, and they can be critically assessed [Kusch] |
10343 | Process reliabilism has been called 'virtue epistemology', resting on perception, memory, reason [Kusch] |
10341 | Justification depends on the audience and one's social role [Kusch] |
10334 | Testimony is an area in which epistemology meets ethics [Kusch] |
10336 | Powerless people are assumed to be unreliable, even about their own lives [Kusch] |
10324 | Testimony does not just transmit knowledge between individuals - it actually generates knowledge [Kusch] |
10327 | Some want to reduce testimony to foundations of perceptions, memories and inferences [Kusch] |
10329 | Testimony won't reduce to perception, if perception depends on social concepts and categories [Kusch] |
10330 | A foundation is what is intelligible, hence from a rational source, and tending towards truth [Kusch] |
10325 | Vindicating testimony is an expression of individualism [Kusch] |
10335 | Myths about lonely genius are based on epistemological individualism [Kusch] |
10323 | Communitarian Epistemology says 'knowledge' is a social status granted to groups of people [Kusch] |
10348 | Private justification is justification to imagined other people [Kusch] |
10349 | To be considered 'an individual' is performed by a society [Kusch] |
3192 | Basic logic can be done by syntax, with no semantics [Gödel, by Rey] |
10344 | Our experience may be conceptual, but surely not the world itself? [Kusch] |
10358 | Often socialising people is the only way to persuade them [Kusch] |
10333 | Communitarianism in epistemology sees the community as the primary knower [Kusch] |
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] |
10351 | Natural kinds are social institutions [Kusch] |
10332 | Omniscience is incoherent, since knowledge is a social concept [Kusch] |
234 | We couldn't discuss the non-existence of the One without knowledge of it [Plato] |