56 ideas
| 22338 | An unexamined life can be virtuous [Murdoch] |
| 22337 | Philosophy must keep returning to the beginning [Murdoch] |
| 23563 | Philosophy moves continually between elaborate theories and the obvious facts [Murdoch] |
| 5438 | Hermeneutics of tradition is sympathetic, hermeneutics of suspicion is hostile [Ricoeur, by Mautner] |
| 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] |
| 9619 | David's 'Napoleon' is about something concrete and something abstract [Brown,JR] |
| 22591 | We know perfection when we see what is imperfect [Murdoch] |
| 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] |
| 22709 | We should first decide what are the great works of art, with aesthetic theory following from that [Murdoch] |
| 22341 | Literature is the most important aspect of culture, because it teaches understanding of living [Murdoch] |
| 22715 | Great art proves the absurdity of art for art's sake [Murdoch] |
| 22714 | Because art is love, it improves us morally [Murdoch] |
| 22347 | Appreciating beauty in art or nature opens up the good life, by restricting selfishness [Murdoch] |
| 22712 | Art and morals are essentially the same, and are both identical with love [Murdoch] |
| 22339 | Love is a central concept in morals [Murdoch] |
| 22348 | Ordinary human love is good evidence of transcendent goodness [Murdoch] |
| 22713 | Love is realising something other than oneself is real [Murdoch] |
| 22343 | If I attend properly I will have no choices [Murdoch] |
| 22349 | Art trains us in the love of virtue [Murdoch] |
| 22340 | It is hard to learn goodness from others, because their virtues are part of their personal history [Murdoch] |
| 22350 | Only trivial virtues can be possessed on their own [Murdoch] |
| 22346 | Moral reflection and experience gradually reveals unity in the moral world [Murdoch] |
| 20765 | Man is a brave naked will, separate from a background of values and realities [Murdoch] |
| 22342 | Kantian existentialists care greatly for reasons for action, whereas Surrealists care nothing [Murdoch] |
| 22351 | Only a philosopher might think choices create values [Murdoch] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |
| 22345 | Moral philosophy needs a central concept with all the traditional attributes of God [Murdoch] |