68 ideas
22659 | It is wisdom to believe what you desire, because belief is needed to achieve it [James] |
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] |
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] |
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] |
10859 | A set is 'well-ordered' if every subset has a first element [Clegg] |
10857 | Set theory made a closer study of infinity possible [Clegg] |
10864 | Any set can always generate a larger set - its powerset, of subsets [Clegg] |
10872 | Extensionality: Two sets are equal if and only if they have the same elements [Clegg] |
10875 | Pairing: For any two sets there exists a set to which they both belong [Clegg] |
10876 | Unions: There is a set of all the elements which belong to at least one set in a collection [Clegg] |
10878 | Infinity: There exists a set of the empty set and the successor of each element [Clegg] |
10877 | Powers: All the subsets of a given set form their own new powerset [Clegg] |
10879 | Choice: For every set a mechanism will choose one member of any non-empty subset [Clegg] |
10871 | Axiom of Existence: there exists at least one set [Clegg] |
10874 | Specification: a condition applied to a set will always produce a new set [Clegg] |
10880 | Mathematics can be 'pure' (unapplied), 'real' (physically grounded); or 'applied' (just applicable) [Clegg] |
10861 | Beyond infinity cardinals and ordinals can come apart [Clegg] |
10860 | An ordinal number is defined by the set that comes before it [Clegg] |
10854 | Transcendental numbers can't be fitted to finite equations [Clegg] |
10858 | By adding an axis of imaginary numbers, we get the useful 'number plane' instead of number line [Clegg] |
10853 | Either lack of zero made early mathematics geometrical, or the geometrical approach made zero meaningless [Clegg] |
10866 | Cantor's account of infinities has the shaky foundation of irrational numbers [Clegg] |
10869 | The Continuum Hypothesis is independent of the axioms of set theory [Clegg] |
10862 | The 'continuum hypothesis' says aleph-one is the cardinality of the reals [Clegg] |
22641 | Realities just are, and beliefs are true of them [James] |
22649 | Classification can only ever be for a particular purpose [James] |
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] |
18974 | Truth is a species of good, being whatever proves itself good in the way of belief [James] |
18989 | Pragmatism accepts any hypothesis which has useful consequences [James] |
22640 | We find satisfaction in consistency of all of our beliefs, perceptions and mental connections [James] |
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] |
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] |
22660 | Evolution suggests prevailing or survival as a new criterion of right and wrong [James] |
3031 | The greatest good is not the achievement of desire, but to desire what is proper [Menedemus, by Diog. Laertius] |
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] |
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] |