81 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] |
| 9641 | Definitions should be replaceable by primitives, and should not be creative [Brown,JR] |
| 9634 | Set theory says that natural numbers are an actual infinity (to accommodate their powerset) [Brown,JR] |
| 9613 | Naïve set theory assumed that there is a set for every condition [Brown,JR] |
| 9615 | Nowadays conditions are only defined on existing sets [Brown,JR] |
| 9617 | The 'iterative' view says sets start with the empty set and build up [Brown,JR] |
| 9642 | A flock of birds is not a set, because a set cannot go anywhere [Brown,JR] |
| 9605 | If a proposition is false, then its negation is true [Brown,JR] |
| 9649 | Axioms are either self-evident, or stipulations, or fallible attempts [Brown,JR] |
| 9638 | Berry's Paradox finds a contradiction in the naming of huge numbers [Brown,JR] |
| 9604 | Mathematics is the only place where we are sure we are right [Brown,JR] |
| 9622 | 'There are two apples' can be expressed logically, with no mention of numbers [Brown,JR] |
| 9648 | π is a 'transcendental' number, because it is not the solution of an equation [Brown,JR] |
| 9621 | Mathematics represents the world through structurally similar models. [Brown,JR] |
| 9646 | There is no limit to how many ways something can be proved in mathematics [Brown,JR] |
| 9647 | Computers played an essential role in proving the four-colour theorem of maps [Brown,JR] |
| 9643 | Set theory may represent all of mathematics, without actually being mathematics [Brown,JR] |
| 9644 | When graphs are defined set-theoretically, that won't cover unlabelled graphs [Brown,JR] |
| 9625 | To see a structure in something, we must already have the idea of the structure [Brown,JR] |
| 9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
| 9606 | The irrationality of root-2 was achieved by intellect, not experience [Brown,JR] |
| 9612 | There is an infinity of mathematical objects, so they can't be physical [Brown,JR] |
| 9610 | Numbers are not abstracted from particulars, because each number is a particular [Brown,JR] |
| 9620 | Empiricists base numbers on objects, Platonists base them on properties [Brown,JR] |
| 9639 | Does some mathematics depend entirely on notation? [Brown,JR] |
| 9629 | For nomalists there are no numbers, only numerals [Brown,JR] |
| 9630 | The most brilliant formalist was Hilbert [Brown,JR] |
| 9608 | There are no constructions for many highly desirable results in mathematics [Brown,JR] |
| 9645 | Constructivists say p has no value, if the value depends on Goldbach's Conjecture [Brown,JR] |
| 16588 | I prefer a lack of form to mean non-existence, than to think of some quasi-existence [Augustine] |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| 22979 | Three main questions seem to be whether a thing is, what it is, and what sort it is [Augustine] |
| 23957 | We often trust our intuitions as rational, despite their lack of reflection [Solomon] |
| 22981 | Mind and memory are the same, as shown in 'bear it in mind' or 'it slipped from mind' [Augustine] |
| 22980 | Memory contains innumerable principles of maths, as well as past sense experiences [Augustine] |
| 22983 | We would avoid remembering sorrow or fear if that triggered the emotions afresh [Augustine] |
| 22977 | I can distinguish different smells even when I am not experiencing them [Augustine] |
| 22982 | Why does joy in my mind make me happy, but joy in my memory doesn't? [Augustine] |
| 22978 | Memory is so vast that I cannot recognise it as part of my mind [Augustine] |
| 23943 | Distinguishing reason from passion is based on an archaic 'faculty' theory [Solomon] |
| 22984 | Without memory I could not even speak of myself [Augustine] |
| 5982 | If the future does not exist, how can prophets see it? [Augustine] |
| 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] |
| 22976 | Memories are preserved separately, according to category [Augustine] |
| 9611 | 'Abstract' nowadays means outside space and time, not concrete, not physical [Brown,JR] |
| 9609 | The older sense of 'abstract' is where 'redness' or 'group' is abstracted from particulars [Brown,JR] |
| 9640 | A term can have not only a sense and a reference, but also a 'computational role' [Brown,JR] |
| 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] |
| 22985 | Everyone wants happiness [Augustine] |
| 23941 | 'Absurdity' is just the result of our wrong choices in life [Solomon] |
| 23955 | Ideologies are mythologies which guide our actions [Solomon] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
| 5984 | Maybe time is an extension of the mind [Augustine] |
| 22888 | To be aware of time it can only exist in the mind, as memory or anticipation [Augustine, by Bardon] |
| 5980 | How can ten days ahead be a short time, if it doesn't exist? [Augustine] |
| 5979 | If the past is no longer, and the future is not yet, how can they exist? [Augustine] |
| 5981 | The whole of the current year is not present, so how can it exist? [Augustine] |
| 5978 | I know what time is, until someone asks me to explain it [Augustine] |
| 5983 | I disagree with the idea that time is nothing but cosmic movement [Augustine] |
| 5977 | Heaven and earth must be created, because they are subject to change [Augustine] |
| 22887 | If God existed before creation, why would a perfect being desire to change things? [Augustine, by Bardon] |
| 5976 | If God is outside time in eternity, can He hear prayers? [Augustine] |