40 ideas
| 23250 | Desired responsible actions result either from rational or from irrational desire [Aristotle] |
| 5847 | It is the role of dialectic to survey syllogisms [Aristotle] |
| 14231 | We should always apply someone's theory of meaning to their own utterances [Liggins] |
| 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] |
| 14232 | We normally formalise 'There are Fs' with singular quantification and predication, but this may be wrong [Liggins] |
| 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] |
| 14233 | Nihilists needn't deny parts - they can just say that some of the xs are among the ys [Liggins] |
| 5862 | A single counterexample is enough to prove that a truth is not necessary [Aristotle] |
| 5854 | Nobody fears a disease which nobody has yet caught [Aristotle] |
| 5849 | Rhetoric is a political offshoot of dialectic and ethics [Aristotle] |
| 5851 | Pentathletes look the most beautiful, because they combine speed and strength [Aristotle] |
| 5858 | Men are physically prime at thirty-five, and mentally prime at forty-nine [Aristotle] |
| 5855 | We all feel universal right and wrong, independent of any community or contracts [Aristotle] |
| 5850 | Happiness is composed of a catalogue of internal and external benefits [Aristotle] |
| 5856 | Self-interest is a relative good, but nobility an absolute good [Aristotle] |
| 5853 | The best virtues are the most useful to others [Aristotle] |
| 5848 | All good things can be misused, except virtue [Aristotle] |
| 5857 | The young feel pity from philanthropy, but the old from self-concern [Aristotle] |
| 5859 | Rich people are mindlessly happy [Aristotle] |
| 5852 | The four constitutions are democracy (freedom), oligarchy (wealth), aristocracy (custom), tyranny (security) [Aristotle] |
| 1660 | It is noble to avenge oneself on one's enemies, and not come to terms with them [Aristotle] |
| 5861 | People assume events cause what follows them [Aristotle] |