57 ideas
| 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] |
| 9240 | Love creates a necessity concerning what to care about [Frankfurt] |
| 14367 | An explanation is a causal graph [Woodward,J, by Strevens] |
| 9264 | Persons are distinguished by a capacity for second-order desires [Frankfurt] |
| 9266 | A person essentially has second-order volitions, and not just second-order desires [Frankfurt] |
| 9267 | Free will is the capacity to choose what sort of will you have [Frankfurt] |
| 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] |
| 9265 | The will is the effective desire which actually leads to an action [Frankfurt] |
| 20015 | Freedom of action needs the agent to identify with their reason for acting [Frankfurt, by Wilson/Schpall] |
| 9228 | Ranking order of desires reveals nothing, because none of them may be considered important [Frankfurt] |
| 9270 | A 'wanton' is not a person, because they lack second-order volitions [Frankfurt] |
| 9269 | A person may be morally responsible without free will [Frankfurt] |
| 9238 | Morality isn't based on reason; moral indignation is quite unlike disapproval of irrationality [Frankfurt] |
| 9232 | It is by caring about things that we infuse the world with importance [Frankfurt] |
| 9234 | If you don't care about at least one thing, you can't find reasons to care about anything [Frankfurt] |
| 9229 | What is worthwhile for its own sake alone may be worth very little [Frankfurt] |
| 9233 | Our criteria for evaluating how to live offer an answer to the problem [Frankfurt] |
| 9235 | Rather than loving things because we value them, I think we value things because we love them [Frankfurt] |
| 9236 | Love can be cool, and it may not involve liking its object [Frankfurt] |
| 9237 | The paradigm case of pure love is not romantic, but that between parents and infants [Frankfurt] |
| 9239 | I value my children for their sake, but I also value my love for them for its own sake [Frankfurt] |
| 9227 | We might not choose a very moral life, if the character or constitution was deficient [Frankfurt] |
| 9230 | People want to fulfill their desires, but also for their desires to be sustained [Frankfurt] |
| 9241 | Loving oneself is not a failing, but is essential to a successful life [Frankfurt] |
| 9300 | Boredom is serious, not just uncomfortable; it threatens our psychic survival [Frankfurt] |
| 9231 | Freedom needs autonomy (rather than causal independence) - embracing our own desires and choices [Frankfurt] |
| 9635 | Given atomism at one end, and a finite universe at the other, there are no physical infinities [Brown,JR] |