58 ideas
23948 | Wisdom needs both thought and passion, with each reflecting on the other [Solomon] |
23942 | Philosophy is creating an intellectual conceptual structure for life [Solomon] |
23945 | Reason is actually passions, guided by perspicacious reflection [Solomon] |
17774 | Definitions make our intuitions mathematically useful [Mayberry] |
17773 | Proof shows that it is true, but also why it must be true [Mayberry] |
17795 | Set theory can't be axiomatic, because it is needed to express the very notion of axiomatisation [Mayberry] |
17796 | There is a semi-categorical axiomatisation of set-theory [Mayberry] |
17800 | The misnamed Axiom of Infinity says the natural numbers are finite in size [Mayberry] |
17801 | The set hierarchy doesn't rely on the dubious notion of 'generating' them [Mayberry] |
17803 | Limitation of size is part of the very conception of a set [Mayberry] |
17786 | The mainstream of modern logic sees it as a branch of mathematics [Mayberry] |
17788 | First-order logic only has its main theorems because it is so weak [Mayberry] |
17791 | Only second-order logic can capture mathematical structure up to isomorphism [Mayberry] |
17787 | Big logic has one fixed domain, but standard logic has a domain for each interpretation [Mayberry] |
17790 | No Löwenheim-Skolem logic can axiomatise real analysis [Mayberry] |
17779 | 'Classificatory' axioms aim at revealing similarity in morphology of structures [Mayberry] |
17778 | Axiomatiation relies on isomorphic structures being essentially the same [Mayberry] |
17780 | 'Eliminatory' axioms get rid of traditional ideal and abstract objects [Mayberry] |
17789 | No logic which can axiomatise arithmetic can be compact or complete [Mayberry] |
17784 | Real numbers can be eliminated, by axiom systems for complete ordered fields [Mayberry] |
17782 | Greek quantities were concrete, and ratio and proportion were their science [Mayberry] |
17781 | Real numbers were invented, as objects, to simplify and generalise 'quantity' [Mayberry] |
17799 | Cantor's infinite is an absolute, of all the sets or all the ordinal numbers [Mayberry] |
17797 | Cantor extended the finite (rather than 'taming the infinite') [Mayberry] |
17775 | If proof and definition are central, then mathematics needs and possesses foundations [Mayberry] |
17776 | The ultimate principles and concepts of mathematics are presumed, or grasped directly [Mayberry] |
17777 | Foundations need concepts, definition rules, premises, and proof rules [Mayberry] |
17804 | Axiom theories can't give foundations for mathematics - that's using axioms to explain axioms [Mayberry] |
17792 | 1st-order PA is only interesting because of results which use 2nd-order PA [Mayberry] |
17793 | It is only 2nd-order isomorphism which suggested first-order PA completeness [Mayberry] |
17794 | Set theory is not just first-order ZF, because that is inadequate for mathematics [Mayberry] |
17802 | We don't translate mathematics into set theory, because it comes embodied in that way [Mayberry] |
17805 | Set theory is not just another axiomatised part of mathematics [Mayberry] |
17785 | Real numbers as abstracted objects are now treated as complete ordered fields [Mayberry] |
23957 | We often trust our intuitions as rational, despite their lack of reflection [Solomon] |
1556 | By nature people are close to one another, but culture drives them apart [Hippias] |
23943 | Distinguishing reason from passion is based on an archaic 'faculty' theory [Solomon] |
23952 | I say bodily chemistry and its sensations have nothing to do with emotions [Solomon] |
23954 | Emotions are judgements about ourselves, and our place in the world [Solomon] |
23960 | Emotions are defined by their objects [Solomon] |
23961 | The heart of an emotion is its judgement of values and morality [Solomon] |
23965 | Emotions can be analysed under fifteen headings [Solomon] |
23959 | Some emotions are externally directed, others internally [Solomon] |
23936 | It is only our passions which give our lives meaning [Solomon] |
23963 | Which emotions we feel depends on our sense of our own powers [Solomon] |
23946 | The passions are subjective, concerning what is important to me, rather than facts [Solomon] |
23940 | Emotions are strategies for maximising our sense of dignity and self-esteem [Solomon] |
23949 | Passions exist as emotions, moods and desires, which all generate meaning [Solomon] |
23956 | The Myth of the Passions says they are irrational, uncontrolled and damaging [Solomon] |
23953 | Feeling is a superficial aspect of emotion, and may be indeterminate, or even absent [Solomon] |
23964 | There are no 'basic' emotions, only socially prevalent ones [Solomon] |
23937 | It is reason which needs the anchorage of passions, rather than vice versa [Solomon] |
23947 | Dividing ourselves into confrontational reason and passion destroys our harmonious whole [Solomon] |
23958 | The supposed irrationality of our emotions is often tactless or faulty expression of them [Solomon] |
23944 | Emotions are our life force, and the source of most of our values [Solomon] |
23962 | Lovers adopt the interests of their beloved, rather than just valuing them [Solomon] |
23941 | 'Absurdity' is just the result of our wrong choices in life [Solomon] |
23955 | Ideologies are mythologies which guide our actions [Solomon] |