105 ideas
23657 | The existence of tensed verbs shows that not all truths are necessary truths [Reid] |
23655 | An ad hominem argument is good, if it is shown that the man's principles are inconsistent [Reid] |
15716 | If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert] |
18844 | You would cripple mathematics if you denied Excluded Middle [Hilbert] |
17963 | The facts of geometry, arithmetic or statics order themselves into theories [Hilbert] |
17966 | Axioms must reveal their dependence (or not), and must be consistent [Hilbert] |
8717 | Hilbert wanted to prove the consistency of all of mathematics (which realists take for granted) [Hilbert, by Friend] |
12456 | I aim to establish certainty for mathematical methods [Hilbert] |
12461 | We believe all mathematical problems are solvable [Hilbert] |
13472 | Hilbert aimed to eliminate number from geometry [Hilbert, by Hart,WD] |
9633 | No one shall drive us out of the paradise the Cantor has created for us [Hilbert] |
12460 | We extend finite statements with ideal ones, in order to preserve our logic [Hilbert] |
12462 | Only the finite can bring certainty to the infinite [Hilbert] |
12455 | The idea of an infinite totality is an illusion [Hilbert] |
12457 | There is no continuum in reality to realise the infinitely small [Hilbert] |
17967 | To decide some questions, we must study the essence of mathematical proof itself [Hilbert] |
9546 | Euclid axioms concerns possibilities of construction, but Hilbert's assert the existence of objects [Hilbert, by Chihara] |
18742 | Hilbert's formalisation revealed implicit congruence axioms in Euclid [Hilbert, by Horsten/Pettigrew] |
18217 | Hilbert's geometry is interesting because it captures Euclid without using real numbers [Hilbert, by Field,H] |
17965 | The whole of Euclidean geometry derives from a basic equation and transformations [Hilbert] |
17964 | Number theory just needs calculation laws and rules for integers [Hilbert] |
17697 | The existence of an arbitrarily large number refutes the idea that numbers come from experience [Hilbert] |
17698 | Logic already contains some arithmetic, so the two must be developed together [Hilbert] |
10113 | The grounding of mathematics is 'in the beginning was the sign' [Hilbert] |
10115 | Hilbert substituted a syntactic for a semantic account of consistency [Hilbert, by George/Velleman] |
22293 | Hilbert said (to block paradoxes) that mathematical existence is entailed by consistency [Hilbert, by Potter] |
12459 | The subject matter of mathematics is immediate and clear concrete symbols [Hilbert] |
10116 | Hilbert aimed to prove the consistency of mathematics finitely, to show infinities won't produce contradictions [Hilbert, by George/Velleman] |
18112 | Mathematics divides in two: meaningful finitary statements, and empty idealised statements [Hilbert] |
23634 | Accepting the existence of anything presupposes the notion of existence [Reid] |
16062 | A necessary relation between fact-levels seems to be a further irreducible fact [Lynch/Glasgow] |
16061 | If some facts 'logically supervene' on some others, they just redescribe them, adding nothing [Lynch/Glasgow] |
16060 | Nonreductive materialism says upper 'levels' depend on lower, but don't 'reduce' [Lynch/Glasgow] |
16064 | The hallmark of physicalism is that each causal power has a base causal power under it [Lynch/Glasgow] |
23664 | Powers are quite distinct and simple, and so cannot be defined [Reid] |
23669 | Thinkers say that matter has intrinsic powers, but is also passive and acted upon [Reid] |
23666 | It is obvious that there could not be a power without a subject which possesses it [Reid] |
23651 | Universals are not objects of sense and cannot be imagined - but can be conceived [Reid] |
23650 | Only individuals exist [Reid] |
23649 | No one thinks two sheets possess a single whiteness, but all agree they are both white [Reid] |
23647 | Objects have an essential constitution, producing its qualities, which we are too ignorant to define [Reid] |
1350 | Continuity is needed for existence, otherwise we would say a thing existed after it ceased to exist [Reid] |
21322 | We treat slowly changing things as identical for the sake of economy in language [Reid] |
21320 | Identity is familiar to common sense, but very hard to define [Reid] |
1367 | Identity can only be affirmed of things which have a continued existence [Reid] |
11874 | Real identity admits of no degrees [Reid] |
11958 | Impossibilites are easily conceived in mathematics and geometry [Reid, by Molnar] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
23659 | If someone denies that he is thinking when he is conscious of it, we can only laugh [Reid] |
23662 | The existence of ideas is no more obvious than the existence of external objects [Reid] |
23661 | We are only aware of other beings through our senses; without that, we are alone in the universe [Reid] |
23635 | Truths are self-evident to sensible persons who understand them clearly without prejudice [Reid] |
7631 | Sensation is not committed to any external object, but perception is [Reid] |
23637 | Primary qualities are the object of mathematics [Reid] |
23638 | Secondary qualities conjure up, and are confused with, the sensations which produce them [Reid] |
23639 | It is unclear whether a toothache is in the mind or in the tooth, but the word has a single meaning [Reid] |
6492 | Reid is seen as the main direct realist of the eighteenth century [Reid, by Robinson,H] |
23633 | Many truths seem obvious, and point to universal agreement - which is what we find [Reid] |
23654 | In obscure matters the few must lead the many, but the many usually lead in common sense [Reid] |
23644 | Without memory we could have no concept of duration [Reid] |
23643 | We all trust our distinct memories (but not our distinct imaginings) [Reid] |
23660 | The theory of ideas, popular with philosophers, means past existence has to be proved [Reid] |
23641 | People dislike believing without evidence, and try to avoid it [Reid] |
23642 | If non-rational evidence reaches us, it is reason which then makes use of it [Reid] |
23549 | We treat testimony with a natural trade off of belief and caution [Reid, by Fricker,M] |
1356 | A person is a unity, and doesn't come in degrees [Reid] |
23658 | Consciousness is an indefinable and unique operation [Reid] |
23665 | Consciousness is the power of mind to know itself, and minds are grounded in powers [Reid] |
1359 | Personal identity is the basis of all rights, obligations and responsibility [Reid] |
21319 | I can hardly care about rational consequence if it wasn't me conceiving the antecedent [Reid] |
21323 | The identity of a thief is only known by similarity, but memory gives certainty in our own case [Reid] |
21321 | Memory reveals my past identity - but so does testimony of other witnesses [Reid] |
21324 | If consciousness is transferable 20 persons can be 1; forgetting implies 1 can be 20 [Reid] |
21325 | Boy same as young man, young man same as old man, old man not boy, if forgotten! [Reid] |
21327 | If a stolen horse is identified by similitude, its identity is not therefore merely similitude [Reid] |
1366 | If consciousness is personal identity, it is continually changing [Reid] |
1352 | Thoughts change continually, but the self doesn't [Reid] |
23681 | The first motion or effect cannot be produced necessarily, so the First Cause must be a free agent [Reid] |
23676 | A willed action needs reasonable understanding of what is to be done [Reid] |
23668 | Our own nature attributes free determinations to our own will [Reid] |
23680 | We are morally free, because we experience it, we are accountable, and we pursue projects [Reid] |
23652 | We must first conceive things before we can consider them [Reid] |
23656 | The structure of languages reveals a uniformity in basic human opinions [Reid] |
23630 | Only philosophers treat ideas as objects [Reid] |
23648 | First we notice and name attributes ('abstracting'); then we notice that subjects share them ('generalising') [Reid] |
23653 | If you can't distinguish the features of a complex object, your notion of it would be a muddle [Reid] |
23640 | Only mature minds can distinguish the qualities of a body [Reid] |
23629 | The ambiguity of words impedes the advancement of knowledge [Reid] |
23646 | Reference is by name, or a term-plus-circumstance, or ostensively, or by description [Reid] |
23645 | A word's meaning is the thing conceived, as fixed by linguistic experts [Reid] |
20051 | Reid said that agent causation is a unique type of causation [Reid, by Stout,R] |
23678 | A motive is merely an idea, like advice, and not a force for action [Reid] |
23663 | There are axioms of taste - such as a general consensus about a beautiful face [Reid] |
23674 | If an attempted poisoning results in benefits, we still judge the agent a poisoner [Reid] |
23675 | We shouldn't do to others what would be a wrong to us in similar circumstances [Reid] |
23672 | To be virtuous, we must care about duty [Reid] |
23673 | Every worthy man has a principle of honour, and knows what is honourable [Reid] |
23632 | Similar effects come from similar causes, and causes are only what are sufficient for the effects [Reid] |
8383 | Day and night are constantly conjoined, but they don't cause one another [Reid, by Crane] |
23677 | We all know that mere priority or constant conjunction do not have to imply causation [Reid] |
23667 | Regular events don't imply a cause, without an innate conviction of universal causation [Reid] |
23679 | The principle of the law of nature is that matter is passive, and is acted upon [Reid] |
23670 | Scientists don't know the cause of magnetism, and only discover its regulations [Reid] |
23671 | Laws are rules for effects, but these need a cause; rules of navigation don't navigate [Reid] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |