135 ideas
19693 | There is practical wisdom (for action), and theoretical wisdom (for deep understanding) [Aristotle, by Whitcomb] |
14456 | 'Socrates is human' expresses predication, and 'Socrates is a man' expresses identity [Russell] |
1575 | For Aristotle logos is essentially the ability to talk rationally about questions of value [Roochnik on Aristotle] |
16841 | Good inference has mechanism, precision, scope, simplicity, fertility and background fit [Lipton] |
1589 | Aristotle is the supreme optimist about the ability of logos to explain nature [Roochnik on Aristotle] |
16854 | Contrary pairs entail contradictions; one member entails negation of the other [Lipton] |
14426 | A definition by 'extension' enumerates items, and one by 'intension' gives a defining property [Russell] |
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] |
8468 | The sentence 'procrastination drinks quadruplicity' is meaningless, rather than false [Russell, by Orenstein] |
14454 | An argument 'satisfies' a function φx if φa is true [Russell] |
14453 | The Darapti syllogism is fallacious: All M is S, all M is P, so some S is P' - but if there is no M? [Russell] |
14427 | We can enumerate finite classes, but an intensional definition is needed for infinite classes [Russell] |
14428 | Members define a unique class, whereas defining characteristics are numerous [Russell] |
14447 | Infinity says 'for any inductive cardinal, there is a class having that many terms' [Russell] |
14440 | We may assume that there are infinite collections, as there is no logical reason against them [Russell] |
14443 | The British parliament has one representative selected from each constituency [Russell] |
14445 | Choice shows that if any two cardinals are not equal, one must be the greater [Russell] |
14444 | Choice is equivalent to the proposition that every class is well-ordered [Russell] |
14446 | We can pick all the right or left boots, but socks need Choice to insure the representative class [Russell] |
14459 | Reducibility: a family of functions is equivalent to a single type of function [Russell] |
14461 | Propositions about classes can be reduced to propositions about their defining functions [Russell] |
8469 | Russell's proposal was that only meaningful predicates have sets as their extensions [Russell, by Orenstein] |
8745 | Classes are logical fictions, and are not part of the ultimate furniture of the world [Russell] |
13282 | Aristotle relativises the notion of wholeness to different measures [Aristotle, by Koslicki] |
14452 | All the propositions of logic are completely general [Russell] |
14462 | In modern times, logic has become mathematical, and mathematics has become logical [Russell] |
10057 | Logic can only assert hypothetical existence [Russell] |
12444 | Logic is concerned with the real world just as truly as zoology [Russell] |
14464 | Logic can be known a priori, without study of the actual world [Russell] |
4730 | For Aristotle, the subject-predicate structure of Greek reflected a substance-accident structure of reality [Aristotle, by O'Grady] |
14458 | Asking 'Did Homer exist?' is employing an abbreviated description [Russell] |
10450 | Russell admitted that even names could also be used as descriptions [Russell, by Bach] |
14457 | Names are really descriptions, except for a few words like 'this' and 'that' [Russell] |
7311 | The only genuine proper names are 'this' and 'that' [Russell] |
14455 | 'I met a unicorn' is meaningful, and so is 'unicorn', but 'a unicorn' is not [Russell] |
14442 | If straight lines were like ratios they might intersect at a 'gap', and have no point in common [Russell] |
14438 | New numbers solve problems: negatives for subtraction, fractions for division, complex for equations [Russell] |
13510 | Could a number just be something which occurs in a progression? [Russell, by Hart,WD] |
14436 | A series can be 'Cut' in two, where the lower class has no maximum, the upper no minimum [Russell] |
14439 | A complex number is simply an ordered couple of real numbers [Russell] |
14421 | Discovering that 1 is a number was difficult [Russell] |
14424 | Numbers are needed for counting, so they need a meaning, and not just formal properties [Russell] |
14441 | The formal laws of arithmetic are the Commutative, the Associative and the Distributive [Russell] |
14420 | Infinity and continuity used to be philosophy, but are now mathematics [Russell] |
14431 | The definition of order needs a transitive relation, to leap over infinite intermediate terms [Russell] |
14422 | Any founded, non-repeating series all reachable in steps will satisfy Peano's axioms [Russell] |
14423 | '0', 'number' and 'successor' cannot be defined by Peano's axioms [Russell] |
14425 | A number is something which characterises collections of the same size [Russell] |
14434 | What matters is the logical interrelation of mathematical terms, not their intrinsic nature [Russell] |
14465 | Maybe numbers are adjectives, since 'ten men' grammatically resembles 'white men' [Russell] |
13414 | For Russell, numbers are sets of equivalent sets [Russell, by Benacerraf] |
14449 | There is always something psychological about inference [Russell] |
14463 | Existence can only be asserted of something described, not of something named [Russell] |
14429 | Classes are logical fictions, made from defining characteristics [Russell] |
14430 | If a relation is symmetrical and transitive, it has to be reflexive [Russell] |
14432 | 'Asymmetry' is incompatible with its converse; a is husband of b, so b can't be husband of a [Russell] |
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] |
14435 | The essence of individuality is beyond description, and hence irrelevant to science [Russell] |
12197 | Inferring q from p only needs p to be true, and 'not-p or q' to be true [Russell] |
14450 | All forms of implication are expressible as truth-functions [Russell] |
14460 | If something is true in all possible worlds then it is logically necessary [Russell] |
5991 | For Aristotle, knowledge is of causes, and is theoretical, practical or productive [Aristotle, by Code] |
16814 | Understanding is not mysterious - it is just more knowledge, of causes [Lipton] |
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] |
16111 | Aristotle wants to fit common intuitions, and therefore uses language as a guide [Aristotle, by Gill,ML] |
16825 | How do we distinguish negative from irrelevant evidence, if both match the hypothesis? [Lipton] |
16851 | The inference to observables and unobservables is almost the same, so why distinguish them? [Lipton] |
16799 | Inductive inference is not proof, but weighing evidence and probability [Lipton] |
16798 | We infer from evidence by working out what would explain that evidence [Lipton] |
16856 | It is more impressive that relativity predicted Mercury's orbit than if it had accommodated it [Lipton] |
16857 | Predictions are best for finding explanations, because mere accommodations can be fudged [Lipton] |
14433 | Mathematically expressed propositions are true of the world, but how to interpret them? [Russell] |
16971 | Plato says sciences are unified around Forms; Aristotle says they're unified around substance [Aristotle, by Moravcsik] |
16827 | If we make a hypothesis about data, then a deduction, where does the hypothesis come from? [Lipton] |
16804 | Induction is repetition, instances, deduction, probability or causation [Lipton] |
16823 | Standard induction does not allow for vertical inferences, to some unobservable lower level [Lipton] |
16800 | An inductive inference is underdetermined, by definition [Lipton] |
16858 | We can argue to support our beliefs, so induction will support induction, for believers in induction [Lipton] |
16832 | If something in ravens makes them black, it may be essential (definitive of ravens) [Lipton] |
16836 | My shoes are not white because they lack some black essence of ravens [Lipton] |
16831 | A theory may explain the blackness of a raven, but say nothing about the whiteness of shoes [Lipton] |
16833 | We can't turn non-black non-ravens into ravens, to test the theory [Lipton] |
16834 | To pick a suitable contrast to ravens, we need a hypothesis about their genes [Lipton] |
16802 | Bayes seems to rule out prior evidence, since that has a probability of one [Lipton] |
16803 | Bayes is too liberal, since any logical consequence of a hypothesis confirms it [Lipton] |
16801 | A hypothesis is confirmed if an unlikely prediction comes true [Lipton] |
16837 | Bayes involves 'prior' probabilities, 'likelihood', 'posterior' probability, and 'conditionalising' [Lipton] |
16839 | Explanation may be an important part of implementing Bayes's Theorem [Lipton] |
11243 | Aristotelian explanations are facts, while modern explanations depend on human conceptions [Aristotle, by Politis] |
16850 | Explanation may describe induction, but may not show how it justifies, or leads to truth [Lipton] |
16807 | An explanation gives the reason the phenomenon occurred [Lipton] |
16808 | An explanation is what makes the unfamiliar familiar to us [Lipton] |
16806 | An explanation is what is added to knowledge to yield understanding [Lipton] |
16822 | Seaching for explanations is a good way to discover the structure of the world [Lipton] |
3320 | Aristotle's standard analysis of species and genus involves specifying things in terms of something more general [Aristotle, by Benardete,JA] |
16816 | In 'contrastive' explanation there is a fact and a foil - why that fact, rather than this foil? [Lipton] |
16826 | With too many causes, find a suitable 'foil' for contrast, and the field narrows right down [Lipton] |
16811 | An explanation unifies a phenomenon with our account of other phenomena [Lipton] |
16810 | Deduction explanation is too easy; any law at all will imply the facts - together with the facts! [Lipton] |
16829 | We reject deductive explanations if they don't explain, not if the deduction is bad [Lipton] |
16809 | Good explanations may involve no laws and no deductions [Lipton] |
16812 | An explanation shows why it was necessary that the effect occurred [Lipton] |
16846 | A cause may not be an explanation [Lipton] |
16813 | To explain is to give either the causal history, or the causal mechanism [Lipton] |
16815 | Mathematical and philosophical explanations are not causal [Lipton] |
16849 | Explanations may be easier to find than causes [Lipton] |
16848 | Causal inferences are clearest when we can manipulate things [Lipton] |
16842 | We want to know not just the cause, but how the cause operated [Lipton] |
12000 | Aristotle regularly says that essential properties explain other significant properties [Aristotle, by Kung] |
16840 | To maximise probability, don't go beyond your data [Lipton] |
16824 | Is Inference to the Best Explanation nothing more than inferring the likeliest cause? [Lipton] |
16817 | Best Explanation as a guide to inference is preferable to best standard explanations [Lipton] |
16818 | The 'likeliest' explanation is the best supported; the 'loveliest' gives the most understanding [Lipton] |
16819 | IBE is inferring that the best potential explanation is the actual explanation [Lipton] |
16820 | Finding the 'loveliest' potential explanation links truth to understanding [Lipton] |
16828 | IBE is not passive treatment of data, but involves feedback between theory and data search [Lipton] |
16844 | A contrasting difference is the cause if it offers the best explanation [Lipton] |
16853 | We select possible explanations for explanatory reasons, as well as choosing among them [Lipton] |
16821 | Must we only have one explanation, and must all the data be made relevant? [Lipton] |
16838 | Bayesians say best explanations build up an incoherent overall position [Lipton] |
16855 | The best theory is boring: compare 'all planets move elliptically' with 'most of them do' [Lipton] |
16852 | Best explanation can't be a guide to truth, because the truth must precede explanation [Lipton] |
23300 | Aristotle and the Stoics denied rationality to animals, while Platonists affirmed it [Aristotle, by Sorabji] |
14451 | Propositions are mainly verbal expressions of true or false, and perhaps also symbolic thoughts [Russell] |
11240 | The notion of analytic truth is absent in Aristotle [Aristotle, by Politis] |
6559 | Aristotle never actually says that man is a rational animal [Aristotle, by Fogelin] |
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] |
16847 | Counterfactual causation makes causes necessary but not sufficient [Lipton] |
22729 | The concepts of gods arose from observing the soul, and the cosmos [Aristotle, by Sext.Empiricus] |