101 ideas
| 3807 | Reason is and ought to be the slave of the passions [Hume] |
| 15945 | Second-order set theory just adds a version of Replacement that quantifies over functions [Lavine] |
| 15914 | An 'upper bound' is the greatest member of a subset; there may be several of these, so there is a 'least' one [Lavine] |
| 15921 | Collections of things can't be too big, but collections by a rule seem unlimited in size [Lavine] |
| 15937 | Those who reject infinite collections also want to reject the Axiom of Choice [Lavine] |
| 15936 | The Power Set is just the collection of functions from one collection to another [Lavine] |
| 15899 | Replacement was immediately accepted, despite having very few implications [Lavine] |
| 15930 | Foundation says descending chains are of finite length, blocking circularity, or ungrounded sets [Lavine] |
| 15920 | Pure collections of things obey Choice, but collections defined by a rule may not [Lavine] |
| 15898 | The controversy was not about the Axiom of Choice, but about functions as arbitrary, or given by rules [Lavine] |
| 15919 | The 'logical' notion of class has some kind of definition or rule to characterise the class [Lavine] |
| 15900 | The iterative conception of set wasn't suggested until 1947 [Lavine] |
| 15931 | The iterative conception needs the Axiom of Infinity, to show how far we can iterate [Lavine] |
| 15932 | The iterative conception doesn't unify the axioms, and has had little impact on mathematical proofs [Lavine] |
| 15933 | Limitation of Size: if it's the same size as a set, it's a set; it uses Replacement [Lavine] |
| 15913 | A collection is 'well-ordered' if there is a least element, and all of its successors can be identified [Lavine] |
| 15926 | Second-order logic presupposes a set of relations already fixed by the first-order domain [Lavine] |
| 15934 | Mathematical proof by contradiction needs the law of excluded middle [Lavine] |
| 15907 | Mathematics is nowadays (thanks to set theory) regarded as the study of structure, not of quantity [Lavine] |
| 15942 | Every rational number, unlike every natural number, is divisible by some other number [Lavine] |
| 15922 | For the real numbers to form a set, we need the Continuum Hypothesis to be true [Lavine] |
| 18250 | Cauchy gave a necessary condition for the convergence of a sequence [Lavine] |
| 15904 | The two sides of the Cut are, roughly, the bounding commensurable ratios [Lavine] |
| 15912 | Counting results in well-ordering, and well-ordering makes counting possible [Lavine] |
| 15949 | The theory of infinity must rest on our inability to distinguish between very large sizes [Lavine] |
| 15947 | The infinite is extrapolation from the experience of indefinitely large size [Lavine] |
| 15940 | The intuitionist endorses only the potential infinite [Lavine] |
| 15909 | 'Aleph-0' is cardinality of the naturals, 'aleph-1' the next cardinal, 'aleph-ω' the ω-th cardinal [Lavine] |
| 15915 | Ordinals are basic to Cantor's transfinite, to count the sets [Lavine] |
| 15917 | Paradox: the class of all ordinals is well-ordered, so must have an ordinal as type - giving a bigger ordinal [Lavine] |
| 15918 | Paradox: there is no largest cardinal, but the class of everything seems to be the largest [Lavine] |
| 8649 | Two numbers are equal if all of their units correspond to one another [Hume] |
| 15929 | Set theory will found all of mathematics - except for the notion of proof [Lavine] |
| 15935 | Modern mathematics works up to isomorphism, and doesn't care what things 'really are' [Lavine] |
| 15928 | Intuitionism rejects set-theory to found mathematics [Lavine] |
| 21291 | There is no medium state between existence and non-existence [Hume] |
| 11942 | Power is the possibility of action, as discovered by experience [Hume] |
| 11949 | There may well be powers in things, with which we are quite unacquainted [Hume] |
| 11950 | We have no idea of powers, because we have no impressions of them [Hume] |
| 11941 | The distinction between a power and its exercise is entirely frivolous [Hume] |
| 11098 | Momentary impressions are wrongly identified with one another on the basis of resemblance [Hume, by Quine] |
| 7954 | If we see a resemblance among objects, we apply the same name to them, despite their differences [Hume] |
| 21293 | Individuation is only seeing that a thing is stable and continuous over time [Hume] |
| 12048 | The only meaning we have for substance is a collection of qualities [Hume] |
| 13424 | Aristotelians propose accidents supported by substance, but they don't understand either of them [Hume] |
| 21300 | A change more obviously destroys an identity if it is quick and observed [Hume] |
| 21299 | Changing a part can change the whole, not absolutely, but by its proportion of the whole [Hume] |
| 1330 | If a republic can retain identity through many changes, so can an individual [Hume] |
| 1321 | If identity survives change or interruption, then resemblance, contiguity or causation must unite the parts of it [Hume] |
| 21302 | If a ruined church is rebuilt, its relation to its parish makes it the same church [Hume] |
| 21303 | We accept the identity of a river through change, because it is the river's nature [Hume] |
| 21301 | The purpose of the ship makes it the same one through all variations [Hume] |
| 21290 | Multiple objects cannot convey identity, because we see them as different [Hume] |
| 1207 | Both number and unity are incompatible with the relation of identity [Hume] |
| 21289 | 'An object is the same with itself' is meaningless; it expresses unity, not identity [Hume] |
| 21292 | Saying an object is the same with itself is only meaningful over a period of time [Hume] |
| 9428 | Nothing we clearly imagine is absolutely impossible [Hume] |
| 4766 | Necessity only exists in the mind, and not in objects [Hume] |
| 6526 | Hume says objects are not a construction, but an imaginative leap [Hume, by Robinson,H] |
| 6489 | Associationism results from having to explain intentionality just with sense-data [Robinson,H on Hume] |
| 6182 | Even Hume didn't include mathematics in his empiricism [Hume, by Kant] |
| 12417 | Mathematicians only accept their own proofs when everyone confims them [Hume] |
| 5548 | Hume became a total sceptic, because he believed that reason was a deception [Hume, by Kant] |
| 7446 | The idea of inductive evidence, around 1660, made Hume's problem possible [Hume, by Hacking] |
| 21806 | Memory, senses and understanding are all founded on the imagination [Hume] |
| 3819 | Hume's 'bundle' won't distinguish one mind with ten experiences from ten minds [Searle on Hume] |
| 1317 | A person is just a fast-moving bundle of perceptions [Hume] |
| 1331 | The parts of a person are always linked together by causation [Hume] |
| 1388 | Hume gives us an interesting sketchy causal theory of personal identity [Perry on Hume] |
| 21297 | A person is simply a bundle of continually fluctuating perceptions [Hume] |
| 1316 | Introspection always discovers perceptions, and never a Self without perceptions [Hume] |
| 1333 | Memory only reveals personal identity, by showing cause and effect [Hume] |
| 1332 | We use memory to infer personal actions we have since forgotten [Hume] |
| 21305 | Memory not only reveals identity, but creates it, by producing resemblances [Hume] |
| 21307 | Who thinks that because you have forgotten an incident you are no longer that person? [Hume] |
| 21306 | Causation unites our perceptions, by producing, destroying and modifying each other [Hume] |
| 21294 | A continuous lifelong self must be justified by a single sustained impression, which we don't have [Hume] |
| 21295 | When I introspect I can only observe my perceptions, and never a self which has them [Hume] |
| 21298 | We pretend our perceptions are continuous, and imagine a self to fill the gaps [Hume] |
| 21304 | Identity in the mind is a fiction, like that fiction that plants and animals stay the same [Hume] |
| 7357 | People who control others with fluent language often end up being hated [Kongzi (Confucius)] |
| 20030 | If one event causes another, the two events must be wholly distinct [Hume, by Wilson/Schpall] |
| 6692 | For Hume, practical reason has little force, because we can always modify our desires [Hume, by Graham] |
| 8257 | Reason alone can never be a motive to any action of the will [Hume] |
| 22374 | You can only hold people responsible for actions which arise out of their character [Hume] |
| 7358 | All men prefer outward appearance to true excellence [Kongzi (Confucius)] |
| 7362 | Humans are similar, but social conventions drive us apart (sages and idiots being the exceptions) [Kongzi (Confucius)] |
| 22382 | We cannot discover vice by studying a wilful murder; that only arises from our own feelings [Hume] |
| 4008 | Modern science has destroyed the Platonic synthesis of scientific explanation and morality [Hume, by Taylor,C] |
| 8067 | The problem of getting to 'ought' from 'is' would also apply in getting to 'owes' or 'needs' [Anscombe on Hume] |
| 4578 | You can't move from 'is' to 'ought' without giving some explanation or reason for the deduction [Hume] |
| 3650 | Total selfishness is not irrational [Hume] |
| 7360 | Do not do to others what you would not desire yourself [Kongzi (Confucius)] |
| 7359 | Excess and deficiency are equally at fault [Kongzi (Confucius)] |
| 7363 | The virtues of the best people are humility, maganimity, sincerity, diligence, and graciousness [Kongzi (Confucius)] |
| 7361 | Men of the highest calibre avoid political life completely [Kongzi (Confucius)] |
| 23393 | Confucianism assumes that all good developments have happened, and there is only one Way [Norden on Kongzi (Confucius)] |
| 14301 | We have no good concept of solidity or matter, because accounts of them are all circular [Hume] |
| 8382 | For Hume a constant conjunction is both necessary and sufficient for causation [Hume, by Crane] |
| 19274 | Hume seems to presuppose necessary connections between mental events [Kripke on Hume] |
| 21296 | If all of my perceptions were removed by death, nothing more is needed for total annihilation [Hume] |