51 ideas
| 5333 | Philosophy needs wisdom about who we are, as well as how we ought to be [Flanagan] |
| 5334 | We resist science partly because it can't provide ethical wisdom [Flanagan] |
| 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] |
| 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] |
| 5340 | Explanation does not entail prediction [Flanagan] |
| 5346 | In the 17th century a collisionlike view of causation made mental causation implausible [Flanagan] |
| 21833 | Research suggest that we overrate conscious experience [Flanagan] |
| 5341 | Only you can have your subjective experiences because only you are hooked up to your nervous system [Flanagan] |
| 5351 | We only have a sense of our self as continuous, not as exactly the same [Flanagan] |
| 5353 | The self is an abstraction which magnifies important aspects of autobiography [Flanagan] |
| 5354 | We are not born with a self; we develop a self through living [Flanagan] |
| 5349 | For Buddhists a fixed self is a morally dangerous illusion [Flanagan] |
| 5338 | Normal free will claims control of what I do, but a stronger view claims control of thought and feeling [Flanagan] |
| 5344 | Free will is held to give us a whole list of desirable capacities for living [Flanagan] |
| 5332 | People believe they have free will that circumvents natural law, but only an incorporeal mind could do this [Flanagan] |
| 5345 | We only think of ourselves as having free will because we first thought of God that way [Flanagan] |
| 5343 | People largely came to believe in dualism because it made human agents free [Flanagan] |
| 7435 | Dispositions are second-order properties, the property of having some property [Jackson/Pargetter/Prior, by Armstrong] |
| 5347 | Behaviourism notoriously has nothing to say about mental causation [Flanagan] |
| 5339 | Cars and bodies obey principles of causation, without us knowing any 'strict laws' about them [Flanagan] |
| 21834 | Sensations may be identical to brain events, but complex mental events don't seem to be [Flanagan] |
| 5342 | Physicalism doesn't deny that the essence of an experience is more than its neural realiser [Flanagan] |
| 5335 | Emotions are usually very apt, rather than being non-rational and fickle [Flanagan] |
| 5348 | Intellectualism admires the 'principled actor', non-intellectualism admires the 'good character' [Flanagan] |
| 5355 | Cognitivists think morals are discovered by reason [Flanagan] |
| 21837 | Morality is normative because it identifies best practices among the normal practices [Flanagan] |
| 5336 | Ethics is the science of the conditions that lead to human flourishing [Flanagan] |
| 21830 | For Darwinians, altruism is either contracts or genetics [Flanagan] |
| 21835 | We need Eudaimonics - the empirical study of how we should flourish [Flanagan] |
| 21831 | Alienation is not finding what one wants, or being unable to achieve it [Flanagan] |
| 5350 | The Hindu doctrine of reincarnation only appeared in the eighth century CE [Flanagan] |
| 21832 | Buddhists reject God and the self, and accept suffering as key, and liberation through wisdom [Flanagan] |
| 5352 | The idea of the soul gets some support from the scientific belief in essential 'natural kinds' [Flanagan] |