61 ideas
| 8014 | Resolve a complex into simple elements, then reconstruct the complex by using them [Hobbes, by MacIntyre] |
| 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] |
| 7559 | Every part of the universe is body, and non-body is not part of it [Hobbes] |
| 2356 | Appearance and reality can be separated by mirrors and echoes [Hobbes] |
| 8725 | Rationalism tries to apply mathematical methodology to all of knowledge [Shapiro] |
| 2357 | Dreams must be false because they seem absurd, but dreams don't see waking as absurd [Hobbes] |
| 2358 | Freedom is absence of opposition to action; the idea of 'free will' is absurd [Hobbes] |
| 6214 | Liberty and necessity are consistent, as when water freely flows, by necessity [Hobbes] |
| 23987 | The 'simple passions' are appetite, desire, love, aversion, hate, joy, and grief [Hobbes, by Goldie] |
| 2362 | The will is just the last appetite before action [Hobbes] |
| 2363 | Reason is usually general, but deliberation is of particulars [Hobbes] |
| 2360 | 'Good' is just what we desire, and 'Evil' what we hate [Hobbes] |
| 2368 | Men's natural desires are no sin, and neither are their actions, until law makes it so [Hobbes] |
| 2359 | Desire and love are the same, but in the desire the object is absent, and in love it is present [Hobbes] |
| 2370 | All voluntary acts aim at some good for the doer [Hobbes] |
| 2371 | A contract is a mutual transfer of rights [Hobbes] |
| 2372 | The person who performs first in a contract is said to 'merit' the return, and is owed it [Hobbes] |
| 8015 | Hobbes wants a contract to found morality, but shared values are needed to make a contract [MacIntyre on Hobbes] |
| 5337 | For Hobbes the Golden Rule concerns not doing things, whereas Jesus encourages active love [Hobbes, by Flanagan] |
| 2374 | In the violent state of nature, the merest suspicion is enough to justify breaking a contract [Hobbes] |
| 7127 | If men are good you should keep promises, but they aren't, so you needn't [Machiavelli] |
| 8016 | Fear of sanctions is the only motive for acceptance of authority that Hobbes can think of [MacIntyre on Hobbes] |
| 2375 | Suspicion will not destroy a contract, if there is a common power to enforce it [Hobbes] |
| 2379 | If there is a good reason for breaking a contract, the same reason should have stopped the making of it [Hobbes] |
| 2377 | No one who admitted to not keeping contracts could ever be accepted as a citizen [Hobbes] |
| 2373 | The first performer in a contract is handing himself over to an enemy [Hobbes] |
| 2382 | Someone who keeps all his contracts when others are breaking them is making himself a prey to others [Hobbes] |
| 2383 | Virtues are a means to peaceful, sociable and comfortable living [Hobbes] |
| 2376 | Injustice is the failure to keep a contract, and justice is the constant will to give what is owed [Hobbes] |
| 19764 | Hobbes attributed to savages the passions which arise in a law-bound society [Hobbes, by Rousseau] |
| 2367 | In time of war the life of man is solitary, poor, nasty, brutish and short [Hobbes] |
| 20566 | Hobbes says the people voluntarily give up their sovereignty, in a contract with a ruler [Hobbes, by Oksala] |
| 6309 | The principle foundations of all states are good laws and good armies [Machiavelli] |
| 6305 | To retain a conquered state, wipe out the ruling family, and preserve everything else [Machiavelli] |
| 6308 | A sensible conqueror does all his harmful deeds immediately, because people soon forget [Machiavelli] |
| 6306 | People are vengeful, so be generous to them, or destroy them [Machiavelli] |
| 2366 | There is not enough difference between people for one to claim more benefit than another [Hobbes] |
| 20485 | Hobbes says people are roughly equal; Locke says there is no right to impose inequality [Hobbes, by Wolff,J] |
| 2369 | If we seek peace and defend ourselves, we must compromise on our rights [Hobbes] |
| 20484 | We should obey the laws of nature, provided other people are also obeying them [Hobbes, by Wolff,J] |
| 7573 | The legal positivism of Hobbes said law is just formal or procedural [Hobbes, by Jolley] |
| 2380 | Punishment should only be for reform or deterrence [Hobbes] |
| 6307 | A desire to conquer, and men who do it, are always praised, or not blamed [Machiavelli] |
| 2361 | If fear of unknown powers is legal it is religion, if it is illegal it is superstition [Hobbes] |
| 7486 | Machiavelli emancipated politics from religion [Machiavelli, by Watson] |
| 2364 | Causation is only observation of similar events following each other, with nothing visible in between [Hobbes] |
| 2365 | Religion is built on ignorance and misinterpretation of what is unknown or frightening [Hobbes] |
| 2378 | Belief in an afterlife is based on poorly founded gossip [Hobbes] |