74 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] |
15924 | Predicative definitions are acceptable in mathematics if they distinguish objects, rather than creating them? [Zermelo, by Lavine] |
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] |
17608 | We take set theory as given, and retain everything valuable, while avoiding contradictions [Zermelo] |
17607 | Set theory investigates number, order and function, showing logical foundations for mathematics [Zermelo] |
10870 | ZFC: Existence, Extension, Specification, Pairing, Unions, Powers, Infinity, Choice [Zermelo, by Clegg] |
13012 | Zermelo published his axioms in 1908, to secure a controversial proof [Zermelo, by Maddy] |
17609 | Set theory can be reduced to a few definitions and seven independent axioms [Zermelo] |
9565 | Zermelo made 'set' and 'member' undefined axioms [Zermelo, by Chihara] |
3339 | For Zermelo's set theory the empty set is zero and the successor of each number is its unit set [Zermelo, by Blackburn] |
17832 | Zermelo showed that the ZF axioms in 1930 were non-categorical [Zermelo, by Hallett,M] |
13017 | Zermelo introduced Pairing in 1930, and it seems fairly obvious [Zermelo, by Maddy] |
13028 | Replacement was added when some advanced theorems seemed to need it [Zermelo, by Maddy] |
13015 | Zermelo used Foundation to block paradox, but then decided that only Separation was needed [Zermelo, by Maddy] |
13020 | The Axiom of Separation requires set generation up to one step back from contradiction [Zermelo, by Maddy] |
13486 | Not every predicate has an extension, but Separation picks the members that satisfy a predicate [Zermelo, by Hart,WD] |
17626 | The antinomy of endless advance and of completion is resolved in well-ordered transfinite numbers [Zermelo] |
13487 | In ZF, the Burali-Forti Paradox proves that there is no set of all ordinals [Zermelo, by Hart,WD] |
15897 | Zermelo realised that Choice would facilitate the sort of 'counting' Cantor needed [Zermelo, by Lavine] |
18178 | For Zermelo the successor of n is {n} (rather than n U {n}) [Zermelo, by Maddy] |
13027 | Zermelo believed, and Von Neumann seemed to confirm, that numbers are sets [Zermelo, by Maddy] |
9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
10502 | We can rise by degrees through abstraction, with higher levels representing more things [Arnauld,A/Nicole,P] |
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] |
18258 | We can only know the exterior world via our ideas [Arnauld,A/Nicole,P] |
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] |
16784 | Forms make things distinct and explain the properties, by pure form, or arrangement of parts [Arnauld,A/Nicole,P] |
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] |
10499 | We know by abstraction because we only understand composite things a part at a time [Arnauld,A/Nicole,P] |
10501 | A triangle diagram is about all triangles, if some features are ignored [Arnauld,A/Nicole,P] |
10500 | No one denies that a line has width, but we can just attend to its length [Arnauld,A/Nicole,P] |
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] |
17613 | We should judge principles by the science, not science by some fixed principles [Zermelo] |
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] |
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] |