93 ideas
| 16841 | Good inference has mechanism, precision, scope, simplicity, fertility and background fit [Lipton] |
| 16854 | Contrary pairs entail contradictions; one member entails negation of the other [Lipton] |
| 9542 | The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell] |
| 21720 | Russell saw Reducibility as legitimate for reducing classes to logic [Linsky,B on Russell/Whitehead] |
| 10044 | Russell denies extensional sets, because the null can't be a collection, and the singleton is just its element [Russell/Whitehead, by Shapiro] |
| 18208 | We regard classes as mere symbolic or linguistic conveniences [Russell/Whitehead] |
| 8204 | Lewis's 'strict implication' preserved Russell's confusion of 'if...then' with implication [Quine on Russell/Whitehead] |
| 9359 | Russell's implication means that random sentences imply one another [Lewis,CI on Russell/Whitehead] |
| 21707 | Russell unusually saw logic as 'interpreted' (though very general, and neutral) [Russell/Whitehead, by Linsky,B] |
| 10036 | In 'Principia' a new abstract theory of relations appeared, and was applied [Russell/Whitehead, by Gödel] |
| 18248 | A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro] |
| 18152 | Russell takes numbers to be classes, but then reduces the classes to numerical quantifiers [Russell/Whitehead, by Bostock] |
| 10025 | Russell and Whitehead took arithmetic to be higher-order logic [Russell/Whitehead, by Hodes] |
| 8683 | Russell and Whitehead were not realists, but embraced nearly all of maths in logic [Russell/Whitehead, by Friend] |
| 10037 | 'Principia' lacks a precise statement of the syntax [Gödel on Russell/Whitehead] |
| 10093 | The ramified theory of types used propositional functions, and covered bound variables [Russell/Whitehead, by George/Velleman] |
| 8691 | The Russell/Whitehead type theory was limited, and was not really logic [Friend on Russell/Whitehead] |
| 10305 | In 'Principia Mathematica', logic is exceeded in the axioms of infinity and reducibility, and in the domains [Bernays on Russell/Whitehead] |
| 8684 | Russell and Whitehead consider the paradoxes to indicate that we create mathematical reality [Russell/Whitehead, by Friend] |
| 8746 | To avoid vicious circularity Russell produced ramified type theory, but Ramsey simplified it [Russell/Whitehead, by Shapiro] |
| 12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
| 16814 | Understanding is not mysterious - it is just more knowledge, of causes [Lipton] |
| 19527 | We don't acquire evidence and then derive some knowledge, because evidence IS knowledge [Williamson] |
| 19528 | Knowledge is prior to believing, just as doing is prior to trying to do [Williamson] |
| 19529 | Belief explains justification, and knowledge explains belief, so knowledge explains justification [Williamson] |
| 19530 | A neutral state of experience, between error and knowledge, is not basic; the successful state is basic [Williamson] |
| 19531 | Internalism about mind is an obsolete view, and knowledge-first epistemology develops externalism [Williamson] |
| 19536 | Knowledge-first says your total evidence IS your knowledge [Williamson] |
| 19526 | Surely I am acquainted with physical objects, not with appearances? [Williamson] |
| 10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
| 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] |
| 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] |
| 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] |
| 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] |
| 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] |
| 21725 | The multiple relations theory says assertions about propositions are about their ingredients [Russell/Whitehead, by Linsky,B] |
| 23474 | A judgement is a complex entity, of mind and various objects [Russell/Whitehead] |
| 23455 | The meaning of 'Socrates is human' is completed by a judgement [Russell/Whitehead] |
| 23480 | The multiple relation theory of judgement couldn't explain the unity of sentences [Morris,M on Russell/Whitehead] |
| 18275 | Only the act of judging completes the meaning of a statement [Russell/Whitehead] |
| 19534 | How does inferentialism distinguish the patterns of inference that are essential to meaning? [Williamson] |
| 19535 | Internalist inferentialism has trouble explaining how meaning and reference relate [Williamson] |
| 19533 | Inferentialist semantics relies on internal inference relations, not on external references [Williamson] |
| 19532 | Truth-conditional referential semantics is externalist, referring to worldly items [Williamson] |
| 23453 | Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead] |
| 16847 | Counterfactual causation makes causes necessary but not sufficient [Lipton] |