53 ideas
| 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] |
| 6007 | If you know your father, but don't recognise your father veiled, you know and don't know the same person [Eubulides, by Dancy,R] |
| 6006 | If you say truly that you are lying, you are lying [Eubulides, by Dancy,R] |
| 6008 | Removing one grain doesn't destroy a heap, so a heap can't be destroyed [Eubulides, by Dancy,R] |
| 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] |
| 4363 | The word 'person' is useless in ethics, because what counts as a good or bad self-conscious being? [Hursthouse] |
| 4355 | There may be inverse akrasia, where the agent's action is better than their judgement recommends [Hursthouse] |
| 4325 | Must all actions be caused in part by a desire, or can a belief on its own be sufficient? [Hursthouse] |
| 4351 | It is a fantasy that only through the study of philosophy can one become virtuous [Hursthouse] |
| 4340 | You are not a dishonest person if a tragic dilemma forces you to do something dishonest [Hursthouse] |
| 4329 | After a moral dilemma is resolved there is still a 'remainder', requiring (say) regret [Hursthouse] |
| 4330 | Deontologists resolve moral dilemmas by saying the rule conflict is merely apparent [Hursthouse] |
| 4341 | Involuntary actions performed in tragic dilemmas are bad because they mar a good life [Hursthouse] |
| 4358 | Virtue may be neither sufficient nor necessary for eudaimonia [Hursthouse] |
| 4337 | Teenagers are often quite wise about ideals, but rather stupid about consequences [Hursthouse] |
| 4324 | Animals and plants can 'flourish', but only rational beings can have eudaimonia [Hursthouse] |
| 4359 | When it comes to bringing up children, most of us think that the virtues are the best bet [Hursthouse] |
| 4336 | Any strict ranking of virtues or rules gets abandoned when faced with particular cases [Hursthouse] |
| 4334 | Virtue ethics is open to the objection that it fails to show priority among the virtues [Hursthouse] |
| 4361 | Good animals can survive, breed, feel characteristic pleasure and pain, and contribute to the group [Hursthouse] |
| 4349 | Virtuous people may not be fully clear about their reasons for action [Hursthouse] |
| 4352 | Performing an act simply because it is virtuous is sufficient to be 'morally motivated' or 'dutiful' [Hursthouse] |
| 4353 | If moral motivation is an all-or-nothing sense of duty, how can children act morally? [Hursthouse] |
| 4346 | The emotions of sympathy, compassion and love are no guarantee of right action or acting well [Hursthouse] |
| 4339 | According to virtue ethics, two agents may respond differently, and yet both be right [Hursthouse] |
| 4354 | Maybe in a deeply poisoned character none of their milder character traits could ever be a virtue [Hursthouse] |
| 4364 | Being unusually virtuous in some areas may entail being less virtuous in others [Hursthouse] |
| 4356 | We are puzzled by a person who can show an exceptional virtue and also behave very badly [Hursthouse] |
| 4327 | Deontologists do consider consequences, because they reveal when a rule might apply [Hursthouse] |
| 4335 | 'Codifiable' morality give rules for decisions which don't require wisdom [Hursthouse] |
| 4328 | Preference utilitarianism aims to be completely value-free, or empirical [Hursthouse] |
| 4343 | We are torn between utilitarian and deontological views of lying, depending on the examples [Hursthouse] |
| 4338 | Deontologists usually accuse utilitarians of oversimplifying hard cases [Hursthouse] |
| 4365 | We are distinct from other animals in behaving rationally - pursuing something as good, for reasons [Hursthouse] |
| 4350 | If people are virtuous in obedience to God, would they become wicked if they lost their faith? [Hursthouse] |