100 ideas
22659 | It is wisdom to believe what you desire, because belief is needed to achieve it [James] |
4697 | There has been a distinct 'Social Turn' in recent philosophy, like the earlier 'Linguistic Turn' [O'Grady] |
22657 | All good philosophers start from a dumb conviction about which truths can be revealed [James] |
22647 | A complete system is just a classification of the whole world's ingredients [James] |
4731 | Good reasoning will avoid contradiction, enhance coherence, not ignore evidence, and maximise evidence [O'Grady] |
22648 | A single explanation must have a single point of view [James] |
22642 | Man has an intense natural interest in the consistency of his own thinking [James] |
22644 | Our greatest pleasure is the economy of reducing chaotic facts to one single fact [James] |
4735 | Just as maps must simplify their subject matter, so thought has to be reductionist about reality [O'Grady] |
4703 | The epistemic theory of truth presents it as 'that which is licensed by our best theory of reality' [O'Grady] |
4701 | To say a relative truth is inexpressible in other frameworks is 'weak', while saying it is false is 'strong' [O'Grady] |
6710 | You can only define a statement that something is 'true' by referring to its functional possibilities [James] |
18986 | Truth is just a name for verification-processes [James] |
18983 | In many cases there is no obvious way in which ideas can agree with their object [James] |
18972 | Ideas are true in so far as they co-ordinate our experiences [James] |
18973 | New opinions count as 'true' if they are assimilated to an individual's current beliefs [James] |
18984 | True ideas are those we can assimilate, validate, corroborate and verify (and false otherwise) [James] |
22305 | If the hypothesis of God is widely successful, it is true [James] |
15716 | If axioms and their implications have no contradictions, they pass my criterion of truth and existence [Hilbert] |
4705 | Logical relativism appears if we allow more than one legitimate logical system [O'Grady] |
4700 | A third value for truth might be "indeterminate", or a point on a scale between 'true' and 'false' [O'Grady] |
18844 | You would cripple mathematics if you denied Excluded Middle [Hilbert] |
4704 | Wittgenstein reduced Russell's five primitive logical symbols to a mere one [O'Grady] |
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] |
4711 | Anti-realists say our theories (such as wave-particle duality) give reality incompatible properties [O'Grady] |
4698 | What counts as a fact partly depends on the availability of human concepts to describe them [O'Grady] |
22641 | Realities just are, and beliefs are true of them [James] |
22649 | Classification can only ever be for a particular purpose [James] |
4715 | We may say that objects have intrinsic identity conditions, but still allow multiple accounts of them [O'Grady] |
18987 | A 'thing' is simply carved out of reality for human purposes [James] |
18981 | 'Substance' is just a word for groupings and structures in experience [James] |
4719 | Maybe developments in logic and geometry have shown that the a priori may be relative [O'Grady] |
18974 | Truth is a species of good, being whatever proves itself good in the way of belief [James] |
9636 | My theory aims at the certitude of mathematical methods [Hilbert] |
4720 | Sense-data are only safe from scepticism if they are primitive and unconceptualised [O'Grady] |
18989 | Pragmatism accepts any hypothesis which has useful consequences [James] |
4722 | Modern epistemology centres on debates about foundations, and about external justification [O'Grady] |
4724 | Internalists say the reasons for belief must be available to the subject, and externalists deny this [O'Grady] |
4723 | Coherence involves support from explanation and evidence, and also probability and confirmation [O'Grady] |
22640 | We find satisfaction in consistency of all of our beliefs, perceptions and mental connections [James] |
4709 | Ontological relativists are anti-realists, who deny that our theories carve nature at the joints [O'Grady] |
4725 | Contextualism says that knowledge is relative to its context; 'empty' depends on your interests [O'Grady] |
22655 | Scientific genius extracts more than other people from the same evidence [James] |
22658 | Experimenters assume the theory is true, and stick to it as long as result don't disappoint [James] |
18971 | Theories are practical tools for progress, not answers to enigmas [James] |
18985 | True thoughts are just valuable instruments of action [James] |
18982 | Pragmatism says all theories are instrumental - that is, mental modes of adaptation to reality [James] |
4732 | One may understand a realm of ideas, but be unable to judge their rationality or truth [O'Grady] |
22654 | We can't know if the laws of nature are stable, but we must postulate it or assume it [James] |
22656 | Trying to assess probabilities by mere calculation is absurd and impossible [James] |
22646 | We have a passion for knowing the parts of something, rather than the whole [James] |
22652 | The mind has evolved entirely for practical interests, seen in our reflex actions [James] |
22651 | Dogs' curiosity only concerns what will happen next [James] |
9286 | Consciousness is not a stuff, but is explained by the relations between experiences [James] |
9285 | 'Consciousness' is a nonentity, a mere echo of the disappearing 'soul' [James] |
23981 | Rage is inconceivable without bodily responses; so there are no disembodied emotions [James] |
22650 | How can the ground of rationality be itself rational? [James] |
22643 | It seems that we feel rational when we detect no irrationality [James] |
18975 | We return to experience with concepts, where they show us differences [James] |
4710 | Verificationism was attacked by the deniers of the analytic-synthetic distinction, needed for 'facts' [O'Grady] |
4717 | If we abandon the analytic-synthetic distinction, scepticism about meaning may be inevitable [O'Grady] |
4706 | Early Quine says all beliefs could be otherwise, but later he said we would assume mistranslation [O'Grady] |
4734 | Cryptographers can recognise that something is a language, without translating it [O'Grady] |
22660 | Evolution suggests prevailing or survival as a new criterion of right and wrong [James] |
6570 | Imagine millions made happy on condition that one person suffers endless lonely torture [James] |
22645 | Understanding by means of causes is useless if they are not reduced to a minimum number [James] |
17968 | By digging deeper into the axioms we approach the essence of sciences, and unity of knowedge [Hilbert] |
18980 | If there is a 'greatest knower', it doesn't follow that they know absolutely everything [James] |
18978 | It is hard to grasp a cosmic mind which produces such a mixture of goods and evils [James] |
18991 | If the God hypothesis works well, then it is true [James] |
18977 | The wonderful design of a woodpecker looks diabolical to its victims [James] |
18979 | Things with parts always have some structure, so they always appear to be designed [James] |
18976 | Private experience is the main evidence for God [James] |
22653 | Early Christianity says God recognises the neglected weak and tender impulses [James] |
18990 | Nirvana means safety from sense experience, and hindus and buddhists are just afraid of life [James] |
4727 | The chief problem for fideists is other fideists who hold contrary ideas [O'Grady] |