60 ideas
| 23966 | The personal view can still be objective, so I call sciences 'impersonal', rather than objective [Goldie] |
| 13451 | The two best understood conceptions of set are the Iterative and the Limitation of Size [Rayo/Uzquiano] |
| 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] |
| 13452 | Some set theories give up Separation in exchange for a universal set [Rayo/Uzquiano] |
| 13449 | We could have unrestricted quantification without having an all-inclusive domain [Rayo/Uzquiano] |
| 13450 | Absolute generality is impossible, if there are indefinitely extensible concepts like sets and ordinals [Rayo/Uzquiano] |
| 13453 | Perhaps second-order quantifications cover concepts of objects, rather than plain objects [Rayo/Uzquiano] |
| 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] |
| 24005 | We know other's emotions by explanation, contagion, empathy, imagination, or sympathy [Goldie] |
| 24006 | Empathy and imagining don't ensure sympathy, and sympathy doesn't need them [Goldie] |
| 23973 | Unlike moods, emotions have specific objects, though the difference is a matter of degree [Goldie] |
| 23974 | Emotional intentionality as belief and desire misses out the necessity of feelings [Goldie] |
| 23972 | A long lasting and evolving emotion is still seen as a single emotion, such as love [Goldie] |
| 23978 | 'Having an emotion' differs from 'being emotional' [Goldie] |
| 23992 | Some Aborigines have fifteen different words for types of fear [Goldie] |
| 23979 | Emotional responses can reveal to us our values, which might otherwise remain hidden [Goldie] |
| 23976 | If we have a 'feeling towards' an object, that gives the recognition a different content [Goldie] |
| 23977 | When actions are performed 'out of' emotion, they appear to be quite different [Goldie] |
| 23980 | It is best to see emotions holistically, as embedded in a person's life narrative [Goldie] |
| 23982 | If emotions are 'towards' things, they can't be bodily feelings, which lack aboutness [Goldie] |
| 23968 | If reasons are seen impersonally (as just causal), then feelings are an irrelevant extra [Goldie] |
| 23969 | We have feelings of which we are hardly aware towards things in the world [Goldie] |
| 23984 | An emotion needs episodes of feeling, but not continuously [Goldie] |
| 24001 | Moods can focus as emotions, and emotions can blur into moods [Goldie] |
| 23970 | Emotions are not avocado pears, with a rigid core and changeable surface [Goldie] |
| 23986 | Early Chinese basic emotions: joy, anger, sadness, fear, love, disliking, and liking [Goldie] |
| 23991 | Cross-cultural studies of facial expressions suggests seven basic emotions [Goldie] |
| 23985 | A basic emotion is the foundation of a hierarchy, such as anger for types of annoyance [Goldie] |
| 23967 | Some emotions are direct responses, and neither rational nor irrational [Goldie] |
| 23971 | Emotional thought is not rational, but it can be intelligible [Goldie] |
| 23975 | Learning an evaluative property like 'dangerous' is also learning an emotion [Goldie] |
| 23983 | We call emotions 'passions' because they are not as controlled as we would like [Goldie] |
| 23999 | Emotional control is hard, but we are responsible for our emotions over long time periods [Goldie] |
| 23994 | Emotions are not easily changed, as new knowledge makes little difference, and akrasia is possible [Goldie] |
| 23998 | Emotional control is less concerned with emotional incidents, and more with emotional tendencies [Goldie] |
| 13448 | The domain of an assertion is restricted by context, either semantically or pragmatically [Rayo/Uzquiano] |
| 23995 | Akrasia can be either overruling our deliberation, or failing to deliberate [Goldie] |
| 24000 | Justifying reasons say you were right; excusing reasons say your act was explicable [Goldie] |
| 24003 | Character traits are both possession of and lack of dispositions [Goldie] |
| 24002 | We over-estimate the role of character traits when explaining behaviour [Goldie] |
| 24004 | Psychologists suggest we are muddled about traits, and maybe they should be abandoned [Goldie] |
| 23993 | Our capabilities did not all evolve during the hunter gathering period [Goldie] |