60 ideas
23966 | The personal view can still be objective, so I call sciences 'impersonal', rather than objective [Goldie] |
17749 | Post proved the consistency of propositional logic in 1921 [Walicki] |
17765 | Propositional language can only relate statements as the same or as different [Walicki] |
17764 | Boolean connectives are interpreted as functions on the set {1,0} [Walicki] |
17752 | The empty set is useful for defining sets by properties, when the members are not yet known [Walicki] |
17753 | The empty set avoids having to take special precautions in case members vanish [Walicki] |
17610 | The Axiom of Choice paradoxically allows decomposing a sphere into two identical spheres [Maddy] |
17759 | Ordinals play the central role in set theory, providing the model of well-ordering [Walicki] |
17741 | To determine the patterns in logic, one must identify its 'building blocks' [Walicki] |
17620 | Critics of if-thenism say that not all starting points, even consistent ones, are worth studying [Maddy] |
17747 | A 'model' of a theory specifies interpreting a language in a domain to make all theorems true [Walicki] |
17748 | The L-S Theorem says no theory (even of reals) says more than a natural number theory [Walicki] |
17605 | Hilbert's geometry and Dedekind's real numbers were role models for axiomatization [Maddy] |
17625 | If two mathematical themes coincide, that suggest a single deep truth [Maddy] |
17763 | Axiomatic systems are purely syntactic, and do not presuppose any interpretation [Walicki] |
17761 | A compact axiomatisation makes it possible to understand a field as a whole [Walicki] |
17757 | Members of ordinals are ordinals, and also subsets of ordinals [Walicki] |
17758 | Ordinals are transitive sets of transitive sets; or transitive sets totally ordered by inclusion [Walicki] |
17755 | Ordinals are the empty set, union with the singleton, and any arbitrary union of ordinals [Walicki] |
17756 | The union of finite ordinals is the first 'limit ordinal'; 2ω is the second... [Walicki] |
17760 | Two infinite ordinals can represent a single infinite cardinal [Walicki] |
17615 | Every infinite set of reals is either countable or of the same size as the full set of reals [Maddy] |
17762 | In non-Euclidean geometry, all Euclidean theorems are valid that avoid the fifth postulate [Walicki] |
17754 | Inductive proof depends on the choice of the ordering [Walicki] |
17618 | Set-theory tracks the contours of mathematical depth and fruitfulness [Maddy] |
17614 | The connection of arithmetic to perception has been idealised away in modern infinitary mathematics [Maddy] |
17742 | Scotus based modality on semantic consistency, instead of on what the future could allow [Walicki] |
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] |
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] |