67 ideas
| 2510 | Traditionally philosophy is an a priori enquiry into general truths about reality [Katz] |
| 2516 | Most of philosophy begins where science leaves off [Katz] |
| 23917 | Contrary statements can both be reasonable, if they are meant in two different ways [Aristotle] |
| 10702 | Set theory's three roles: taming the infinite, subject-matter of mathematics, and modes of reasoning [Potter] |
| 10713 | Usually the only reason given for accepting the empty set is convenience [Potter] |
| 13044 | Infinity: There is at least one limit level [Potter] |
| 10708 | Nowadays we derive our conception of collections from the dependence between them [Potter] |
| 13546 | The 'limitation of size' principles say whether properties collectivise depends on the number of objects [Potter] |
| 10707 | Mereology elides the distinction between the cards in a pack and the suits [Potter] |
| 10704 | We can formalize second-order formation rules, but not inference rules [Potter] |
| 10703 | Supposing axioms (rather than accepting them) give truths, but they are conditional [Potter] |
| 10712 | If set theory didn't found mathematics, it is still needed to count infinite sets [Potter] |
| 17882 | It is remarkable that all natural number arithmetic derives from just the Peano Axioms [Potter] |
| 2521 | 'Real' maths objects have no causal role, no determinate reference, and no abstract/concrete distinction [Katz] |
| 13043 | A relation is a set consisting entirely of ordered pairs [Potter] |
| 5869 | The thesis of the Form of the Good (or of anything else) is verbal and vacuous [Aristotle] |
| 13042 | If dependence is well-founded, with no infinite backward chains, this implies substances [Potter] |
| 13041 | Collections have fixed members, but fusions can be carved in innumerable ways [Potter] |
| 10709 | Priority is a modality, arising from collections and members [Potter] |
| 22505 | The two right angles of a triangle necessitate that a quadrilateral has four [Aristotle] |
| 22513 | Knowing is having knowledge; understanding is using knowledge [Aristotle] |
| 2513 | We don't have a clear enough sense of meaning to pronounce some sentences meaningless or just analytic [Katz] |
| 2522 | Experience cannot teach us why maths and logic are necessary [Katz] |
| 23906 | Courage from spirit is natural and unconquerable, as seen in the young [Aristotle] |
| 20204 | Whether the mind has parts is irrelevant, since it obviously has distinct capacities [Aristotle] |
| 22506 | A man is the cause of what is within his power, and what he causes is in his power [Aristotle] |
| 22504 | Only a human being can be a starting point for an action [Aristotle] |
| 22510 | Some emotional states are too strong for human nature [Aristotle] |
| 23913 | Nearly all the good and bad states of character are concerned with feelings [Aristotle] |
| 2517 | Structuralists see meaning behaviouristically, and Chomsky says nothing about it [Katz] |
| 2519 | It is generally accepted that sense is defined as the determiner of reference [Katz] |
| 2520 | Sense determines meaning and synonymy, not referential properties like denotation and truth [Katz] |
| 2518 | Sentences are abstract types (like musical scores), not individual tokens [Katz] |
| 23918 | Akrasia is the clash of two feelings - goodness and pleasure [Aristotle] |
| 22515 | Choice results when deliberation brings together an opinion with an inclination [Aristotle] |
| 22508 | Unlike in inanimate things, in animate things actions have more than one starting point [Aristotle] |
| 22514 | The deliberative part of the soul discerns explanatory causes [Aristotle] |
| 22507 | An action is voluntary when it is accompanied by thought of some kind [Aristotle] |
| 23319 | We are responsible if our actions reflect our motivation [Aristotle, by Frede,M] |
| 22512 | Acts are voluntary if done knowingly, by the agent, and in his power to avoid it [Aristotle] |
| 22509 | What is natural for us is either there at birth, or appears by normal processes [Aristotle] |
| 18230 | No one would choose life just for activities not done for their own sake [Aristotle] |
| 23909 | Wearing a shoe is its intrinsic use, and selling it (as a shoe) is its coincidental use [Aristotle] |
| 5870 | Everything seeks, not a single good, but its own separate good [Aristotle] |
| 5877 | We judge people from their deeds because we cannot see their choices (which matter more) [Aristotle] |
| 5868 | Horses, birds and fish are not happy, lacking a divine aspect to their natures [Aristotle] |
| 5865 | Happiness involves three things, of which the greatest is either wisdom, virtue, or pleasure [Aristotle] |
| 5876 | Virtue is different from continence [Aristotle] |
| 5872 | Excellence is the best state of anything (like a cloak) which has an employment or function [Aristotle] |
| 5874 | Character virtues (such as courage) are of the non-rational part, which follows the rational part [Aristotle] |
| 22516 | Character is shown by what is or is not enjoyed, and virtue chooses the mean among them [Aristotle] |
| 22517 | We judge character not by their actions, but by their reasons for actions [Aristotle] |
| 5875 | Character (éthos) is developed from habit (ethos) [Aristotle] |
| 23914 | People sometimes exhibit both extremes together, but the mean is contrary to both of them [Aristotle] |
| 23911 | Possessors of a virtue tend to despise what reason shows to be its opposite [Aristotle] |
| 23910 | Greatness of soul produces all the virtues - and vice versa [Aristotle] |
| 23908 | If someone just looks at or listens to beautiful things, they would not be thought intemperate [Aristotle] |
| 23905 | Courage follows reason, which tells us to choose what is noble [Aristotle] |
| 23912 | Honour depends on what it is for, and whether it is bestowed by worthy people [Aristotle] |
| 5871 | Goods in the soul are more worthy than those outside it, as everybody wants them [Aristotle] |
| 23920 | Decent people can be friends with base people [Aristotle] |
| 23919 | Friendship cannot be immediate; it takes time, and needs testing [Aristotle] |
| 23915 | The main function of politics is to produce friendship [Aristotle] |
| 23916 | The best cure for mutual injustice is friendship [Aristotle] |
| 5866 | It is folly not to order one's life around some end [Aristotle] |
| 5878 | Eyes could be used for a natural purpose, or for unnatural seeing, or for a non-seeing activity [Aristotle] |
| 5873 | Each thing's function is its end [Aristotle] |