129 ideas
| 19693 | There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb] |
| 1575 | For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle] |
| 1589 | Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle] |
| 3807 | Reason is and ought to be the slave of the passions [Hume] |
| 8200 | Aristotelian definitions aim to give the essential properties of the thing defined [Aristotle, by Quine] |
| 4385 | Aristotelian definition involves first stating the genus, then the differentia of the thing [Aristotle, by Urmson] |
| 9738 | Each line of a truth table is a model [Fitting/Mendelsohn] |
| 9727 | Modal logic adds □ (necessarily) and ◊ (possibly) to classical logic [Fitting/Mendelsohn] |
| 9726 | We let 'R' be the accessibility relation: xRy is read 'y is accessible from x' [Fitting/Mendelsohn] |
| 9737 | The symbol ||- is the 'forcing' relation; 'Γ ||- P' means that P is true in world Γ [Fitting/Mendelsohn] |
| 13136 | The prefix σ names a possible world, and σ.n names a world accessible from that one [Fitting/Mendelsohn] |
| 13727 | A 'constant' domain is the same for all worlds; 'varying' domains can be entirely separate [Fitting/Mendelsohn] |
| 9734 | Modern modal logic introduces 'accessibility', saying xRy means 'y is accessible from x' [Fitting/Mendelsohn] |
| 9736 | A 'model' is a frame plus specification of propositions true at worlds, written < G,R,||- > [Fitting/Mendelsohn] |
| 9735 | A 'frame' is a set G of possible worlds, with an accessibility relation R, written < G,R > [Fitting/Mendelsohn] |
| 9741 | Accessibility relations can be 'reflexive' (self-referring), 'transitive' (carries over), or 'symmetric' (mutual) [Fitting/Mendelsohn] |
| 13149 | S5: a) if n ◊X then kX b) if n ¬□X then k ¬X c) if n □X then k X d) if n ¬◊X then k ¬X [Fitting/Mendelsohn] |
| 13141 | Negation: if σ ¬¬X then σ X [Fitting/Mendelsohn] |
| 13138 | Disj: a) if σ ¬(X∨Y) then σ ¬X and σ ¬Y b) if σ X∨Y then σ X or σ Y [Fitting/Mendelsohn] |
| 13142 | Existential: a) if σ ◊X then σ.n X b) if σ ¬□X then σ.n ¬X [n is new] [Fitting/Mendelsohn] |
| 13144 | T reflexive: a) if σ □X then σ X b) if σ ¬◊X then σ ¬X [Fitting/Mendelsohn] |
| 13145 | D serial: a) if σ □X then σ ◊X b) if σ ¬◊X then σ ¬□X [Fitting/Mendelsohn] |
| 13146 | B symmetric: a) if σ.n □X then σ X b) if σ.n ¬◊X then σ ¬X [n occurs] [Fitting/Mendelsohn] |
| 13147 | 4 transitive: a) if σ □X then σ.n □X b) if σ ¬◊X then σ.n ¬◊X [n occurs] [Fitting/Mendelsohn] |
| 13148 | 4r rev-trans: a) if σ.n □X then σ □X b) if σ.n ¬◊X then σ ¬◊X [n occurs] [Fitting/Mendelsohn] |
| 9740 | If a proposition is possibly true in a world, it is true in some world accessible from that world [Fitting/Mendelsohn] |
| 9739 | If a proposition is necessarily true in a world, it is true in all worlds accessible from that world [Fitting/Mendelsohn] |
| 13137 | Conj: a) if σ X∧Y then σ X and σ Y b) if σ ¬(X∧Y) then σ ¬X or σ ¬Y [Fitting/Mendelsohn] |
| 13140 | Bicon: a)if σ(X↔Y) then σ(X→Y) and σ(Y→X) b) [not biconditional, one or other fails] [Fitting/Mendelsohn] |
| 13139 | Implic: a) if σ ¬(X→Y) then σ X and σ ¬Y b) if σ X→Y then σ ¬X or σ Y [Fitting/Mendelsohn] |
| 13143 | Universal: a) if σ ¬◊X then σ.m ¬X b) if σ □X then σ.m X [m exists] [Fitting/Mendelsohn] |
| 9742 | The system K has no accessibility conditions [Fitting/Mendelsohn] |
| 13114 | □P → P is not valid in D (Deontic Logic), since an obligatory action may be not performed [Fitting/Mendelsohn] |
| 9743 | The system D has the 'serial' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
| 9744 | The system T has the 'reflexive' conditon imposed on its accessibility relation [Fitting/Mendelsohn] |
| 9746 | The system K4 has the 'transitive' condition on its accessibility relation [Fitting/Mendelsohn] |
| 9745 | The system B has the 'reflexive' and 'symmetric' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9747 | The system S4 has the 'reflexive' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9748 | System S5 has the 'reflexive', 'symmetric' and 'transitive' conditions on its accessibility relation [Fitting/Mendelsohn] |
| 9404 | Modality affects content, because P→◊P is valid, but ◊P→P isn't [Fitting/Mendelsohn] |
| 13112 | In epistemic logic knowers are logically omniscient, so they know that they know [Fitting/Mendelsohn] |
| 13111 | Read epistemic box as 'a knows/believes P' and diamond as 'for all a knows/believes, P' [Fitting/Mendelsohn] |
| 13113 | F: will sometime, P: was sometime, G: will always, H: was always [Fitting/Mendelsohn] |
| 13728 | The Barcan says nothing comes into existence; the Converse says nothing ceases; the pair imply stability [Fitting/Mendelsohn] |
| 13729 | The Barcan corresponds to anti-monotonicity, and the Converse to monotonicity [Fitting/Mendelsohn] |
| 13282 | Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki] |
| 4730 | For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady] |
| 9725 | 'Predicate abstraction' abstracts predicates from formulae, giving scope for constants and functions [Fitting/Mendelsohn] |
| 8649 | Two numbers are equal if all of their units correspond to one another [Hume] |
| 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] |
| 13276 | The unmoved mover and the soul show Aristotelian form as the ultimate mereological atom [Aristotle, by Koslicki] |
| 13277 | The 'form' is the recipe for building wholes of a particular kind [Aristotle, by Koslicki] |
| 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] |
| 13730 | The Indiscernibility of Identicals has been a big problem for modal logic [Fitting/Mendelsohn] |
| 9428 | Nothing we clearly imagine is absolutely impossible [Hume] |
| 4766 | Necessity only exists in the mind, and not in objects [Hume] |
| 13725 | □ must be sensitive as to whether it picks out an object by essential or by contingent properties [Fitting/Mendelsohn] |
| 13731 | Objects retain their possible properties across worlds, so a bundle theory of them seems best [Fitting/Mendelsohn] |
| 13726 | Counterpart relations are neither symmetric nor transitive, so there is no logic of equality for them [Fitting/Mendelsohn] |
| 5991 | For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code] |
| 6526 | Hume says objects are not a construction, but an imaginative leap [Hume, by Robinson,H] |
| 11239 | The notion of a priori truth is absent in Aristotle [Aristotle, by Politis] |
| 23312 | Aristotle is a rationalist, but reason is slowly acquired through perception and experience [Aristotle, by Frede,M] |
| 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] |
| 16111 | Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML] |
| 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] |
| 16971 | Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik] |
| 7446 | The idea of inductive evidence, around 1660, made Hume's problem possible [Hume, by Hacking] |
| 11243 | Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis] |
| 3320 | Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA] |
| 12000 | Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung] |
| 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] |
| 23300 | Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji] |
| 11240 | The notion of analytic truth is absent in Aristotle [Aristotle, by Politis] |
| 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] |
| 6559 | Aristotle never actually says that man is a rational animal [Aristotle, by Fogelin] |
| 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] |
| 11150 | It is the mark of an educated mind to be able to entertain an idea without accepting it [Aristotle] |
| 3037 | Aristotle said the educated were superior to the uneducated as the living are to the dead [Aristotle, by Diog. Laertius] |
| 8660 | There are potential infinities (never running out), but actual infinity is incoherent [Aristotle, by Friend] |
| 12058 | Aristotle's matter can become any other kind of matter [Aristotle, by Wiggins] |
| 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] |
| 22729 | The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus] |
| 21296 | If all of my perceptions were removed by death, nothing more is needed for total annihilation [Hume] |