49 ideas
1798 | He studied philosophy by suspending his judgement on everything [Pyrrho, by Diog. Laertius] |
1800 | Sceptics say reason is only an instrument, because reason can only be attacked with reason [Pyrrho, by Diog. Laertius] |
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] |
6595 | If we need a criterion of truth, we need to know whether it is the correct criterion [Pyrrho, by Fogelin] |
6593 | The Pyrrhonians attacked the dogmas of professors, not ordinary people [Pyrrho, by Fogelin] |
6592 | Academics said that Pyrrhonians were guilty of 'negative dogmatism' [Pyrrho, by Fogelin] |
1808 | Perception of things depends on their size or quantity (Mode 8) [Pyrrho, by Diog. Laertius] |
1802 | Individuals vary in responses and feelings (Mode 2) [Pyrrho, by Diog. Laertius] |
1807 | Perception varies with viewing distance and angle (Mode 7) [Pyrrho, by Diog. Laertius] |
1801 | Animals vary in their feelings and judgements (Mode 1) [Pyrrho, by Diog. Laertius] |
1803 | Objects vary according to which sense perceives them (Mode 3) [Pyrrho, by Diog. Laertius] |
1806 | Perception of objects depends on surrounding conditions (Mode 6) [Pyrrho, by Diog. Laertius] |
1804 | Perception varies with madness or disease (Mode 4) [Pyrrho, by Diog. Laertius] |
1810 | Perception and judgement depend on comparison (Mode 10) [Pyrrho, by Diog. Laertius] |
1805 | Judgements vary according to local culture and law (Mode 5) [Pyrrho, by Diog. Laertius] |
1809 | Perception is affected by expectations (Mode 9) [Pyrrho, by Diog. Laertius] |
5901 | Is 'productive of happiness' the definition of 'right', or the cause of it? [Ross on Bentham] |
5271 | Prejudice apart, push-pin has equal value with music and poetry [Bentham] |
5934 | Of Bentham's 'dimensions' of pleasure, only intensity and duration matter [Ross on Bentham] |
3777 | Pleasure and pain control all human desires and duties [Bentham] |
3554 | Bentham thinks happiness is feeling good, but why use morality to achieve that? [Annas on Bentham] |
3781 | The value of pleasures and pains is their force [Bentham] |
20977 | Natural rights are nonsense, and unspecified natural rights is nonsense on stilts [Bentham] |
3778 | The community's interest is a sum of individual interests [Bentham] |
21003 | Only laws can produce real rights; rights from 'law of nature' are imaginary [Bentham] |
20280 | Large mature animals are more rational than babies. But all that really matters is - can they suffer? [Bentham] |
3779 | Unnatural, when it means anything, means infrequent [Bentham] |
3062 | There are no causes, because they are relative, and alike things can't cause one another [Pyrrho, by Diog. Laertius] |
3063 | Motion can't move where it is, and can't move where it isn't, so it can't exist [Pyrrho, by Diog. Laertius] |
3780 | We must judge a thing morally to know if it conforms to God's will [Bentham] |