51 ideas
4697 | There has been a distinct 'Social Turn' in recent philosophy, like the earlier 'Linguistic Turn' [O'Grady] |
4731 | Good reasoning will avoid contradiction, enhance coherence, not ignore evidence, and maximise evidence [O'Grady] |
4735 | Just as maps must simplify their subject matter, so thought has to be reductionist about reality [O'Grady] |
4703 | The epistemic theory of truth presents it as 'that which is licensed by our best theory of reality' [O'Grady] |
4701 | To say a relative truth is inexpressible in other frameworks is 'weak', while saying it is false is 'strong' [O'Grady] |
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] |
4705 | Logical relativism appears if we allow more than one legitimate logical system [O'Grady] |
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] |
4700 | A third value for truth might be "indeterminate", or a point on a scale between 'true' and 'false' [O'Grady] |
4704 | Wittgenstein reduced Russell's five primitive logical symbols to a mere one [O'Grady] |
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] |
4711 | Anti-realists say our theories (such as wave-particle duality) give reality incompatible properties [O'Grady] |
4698 | What counts as a fact partly depends on the availability of human concepts to describe them [O'Grady] |
4715 | We may say that objects have intrinsic identity conditions, but still allow multiple accounts of them [O'Grady] |
12033 | An object is identical with itself, and no different indiscernible object can share that [Russell/Whitehead, by Adams,RM] |
4719 | Maybe developments in logic and geometry have shown that the a priori may be relative [O'Grady] |
4720 | Sense-data are only safe from scepticism if they are primitive and unconceptualised [O'Grady] |
10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
4722 | Modern epistemology centres on debates about foundations, and about external justification [O'Grady] |
4724 | Internalists say the reasons for belief must be available to the subject, and externalists deny this [O'Grady] |
4723 | Coherence involves support from explanation and evidence, and also probability and confirmation [O'Grady] |
4709 | Ontological relativists are anti-realists, who deny that our theories carve nature at the joints [O'Grady] |
4725 | Contextualism says that knowledge is relative to its context; 'empty' depends on your interests [O'Grady] |
4732 | One may understand a realm of ideas, but be unable to judge their rationality or truth [O'Grady] |
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] |
4710 | Verificationism was attacked by the deniers of the analytic-synthetic distinction, needed for 'facts' [O'Grady] |
23453 | Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead] |
4717 | If we abandon the analytic-synthetic distinction, scepticism about meaning may be inevitable [O'Grady] |
4706 | Early Quine says all beliefs could be otherwise, but later he said we would assume mistranslation [O'Grady] |
4734 | Cryptographers can recognise that something is a language, without translating it [O'Grady] |
651 | Eurytus showed that numbers underlie things by making pictures of creatures out of pebbles [Eurytus, by Aristotle] |
4727 | The chief problem for fideists is other fideists who hold contrary ideas [O'Grady] |