42 ideas
| 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] |
| 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] |
| 10860 | An ordinal number is defined by the set that comes before it [Clegg] |
| 10861 | Beyond infinity cardinals and ordinals can come apart [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] |
| 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] |
| 18971 | Theories are practical tools for progress, not answers to enigmas [James] |
| 18982 | Pragmatism says all theories are instrumental - that is, mental modes of adaptation to reality [James] |
| 18985 | True thoughts are just valuable instruments of action [James] |
| 18975 | We return to experience with concepts, where they show us differences [James] |
| 13304 | Learned men gain more in one day than others do in a lifetime [Posidonius] |
| 20820 | Time is an interval of motion, or the measure of speed [Posidonius, by Stobaeus] |
| 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] |
| 18990 | Nirvana means safety from sense experience, and hindus and buddhists are just afraid of life [James] |