61 ideas
| 21829 | Philosophy aims to understand how things (broadly understood) hang together (broadly understood) [Sellars] |
| 23917 | Contrary statements can both be reasonable, if they are meant in two different ways [Aristotle] |
| 8729 | Intuitionists deny excluded middle, because it is committed to transcendent truth or objects [Shapiro] |
| 8763 | The number 3 is presumably identical as a natural, an integer, a rational, a real, and complex [Shapiro] |
| 18249 | Cauchy gave a formal definition of a converging sequence. [Shapiro] |
| 8764 | Categories are the best foundation for mathematics [Shapiro] |
| 8762 | Two definitions of 3 in terms of sets disagree over whether 1 is a member of 3 [Shapiro] |
| 8760 | Numbers do not exist independently; the essence of a number is its relations to other numbers [Shapiro] |
| 8761 | A 'system' is related objects; a 'pattern' or 'structure' abstracts the pure relations from them [Shapiro] |
| 8744 | Logicism seems to be a non-starter if (as is widely held) logic has no ontology of its own [Shapiro] |
| 8749 | Term Formalism says mathematics is just about symbols - but real numbers have no names [Shapiro] |
| 8750 | Game Formalism is just a matter of rules, like chess - but then why is it useful in science? [Shapiro] |
| 8752 | Deductivism says mathematics is logical consequences of uninterpreted axioms [Shapiro] |
| 8753 | Critics resent the way intuitionism cripples mathematics, but it allows new important distinctions [Shapiro] |
| 8731 | Conceptualist are just realists or idealist or nominalists, depending on their view of concepts [Shapiro] |
| 8730 | 'Impredicative' definitions refer to the thing being described [Shapiro] |
| 6550 | Reduction requires that an object's properties consist of its constituents' properties and relations [Sellars] |
| 5869 | The thesis of the Form of the Good (or of anything else) is verbal and vacuous [Aristotle] |
| 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] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 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] |
| 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] |