49 ideas
9542 | The best known axiomatization of PL is Whitehead/Russell, with four axioms and two rules [Russell/Whitehead, by Hughes/Cresswell] |
17884 | Mathematical set theory has many plausible stopping points, such as finitism, and predicativism [Koellner] |
17893 | 'Reflection principles' say the whole truth about sets can't be captured [Koellner] |
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] |
21122 | Liberal Nationalism says welfare states and democracy needed a shared sense of nationality [Shorten] |
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] |
17894 | We have no argument to show a statement is absolutely undecidable [Koellner] |
18248 | A real number is the class of rationals less than the number [Russell/Whitehead, by Shapiro] |
17890 | There are at least eleven types of large cardinal, of increasing logical strength [Koellner] |
17887 | PA is consistent as far as we can accept, and we expand axioms to overcome limitations [Koellner] |
17891 | Arithmetical undecidability is always settled at the next stage up [Koellner] |
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] |
10040 | Russell showed, through the paradoxes, that our basic logical intuitions are self-contradictory [Russell/Whitehead, by Gödel] |
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] |
23453 | Propositions as objects of judgement don't exist, because we judge several objects, not one [Russell/Whitehead] |
21136 | Utilitarians conflate acts and omissions; causing to drown and failing to save are the same [Shorten] |
21135 | There are eight different ways in which groups of people can be oppressed [Shorten, by PG] |
21118 | Constitutional Patriotism unites around political values (rather than national identity) [Shorten] |
21129 | Democracy is a method of selection, or it involves participation, or it concerns public discussion [Shorten] |
21130 | Some say democracy is intrinsically valuable, others that it delivers good outcomes [Shorten] |
21126 | Representative should be either obedient, or sensible, or typical [Shorten] |
21128 | There is 'mirror representation' when the institution statistically reflects the population [Shorten] |
21127 | In a changed situation a Mandated Representative can't keep promises and fight for constituents [Shorten] |
21117 | Liberal citizens have a moral requirement to respect freedom and equality [Shorten] |
21134 | Maybe the rational autonomous liberal individual is merely the result of domination [Shorten] |
21113 | Liberal equality concerns rights, and liberal freedom concerns choice of ends [Shorten] |
21121 | Liberal Nationalism encourages the promotion of nationalistic values [Shorten] |
21115 | Liberalism should not make assumptions such as the value of choosing your own life plan [Shorten] |
21114 | Liberals treat individuals as mutual strangers, rather than as social beings [Shorten] |
21123 | Liberal Nationalism is more communitarian, and Constitutional Patriotism more cosmopolitan [Shorten] |
21124 | Religious toleration has been institutionalised by the separation of church and state [Shorten] |