52 ideas
7920 | Descriptive metaphysics aims at actual structure, revisionary metaphysics at a better structure [Strawson,P] |
7922 | Descriptive metaphysics concerns unchanging core concepts and categories [Strawson,P] |
7921 | Close examination of actual word usage is the only sure way in philosophy [Strawson,P] |
10842 | The fact which is stated by a true sentence is not something in the world [Strawson,P] |
10843 | Facts aren't exactly true statements, but they are what those statements say [Strawson,P] |
10844 | The statement that it is raining perfectly fits the fact that it is raining [Strawson,P] |
10841 | The word 'true' always refers to a possible statement [Strawson,P] |
10482 | The logic of ZF is classical first-order predicate logic with identity [Boolos] |
10492 | A few axioms of set theory 'force themselves on us', but most of them don't [Boolos] |
18192 | Do the Replacement Axioms exceed the iterative conception of sets? [Boolos, by Maddy] |
7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
10485 | Naïve sets are inconsistent: there is no set for things that do not belong to themselves [Boolos] |
10484 | The iterative conception says sets are formed at stages; some are 'earlier', and must be formed first [Boolos] |
13547 | Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter] |
10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
14249 | Boolos reinterprets second-order logic as plural logic [Boolos, by Oliver/Smiley] |
10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
10736 | Boolos showed how plural quantifiers can interpret monadic second-order logic [Boolos, by Linnebo] |
10780 | Any sentence of monadic second-order logic can be translated into plural first-order logic [Boolos, by Linnebo] |
10829 | A sentence can't be a truth of logic if it asserts the existence of certain sets [Boolos] |
10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [Boolos] |
8358 | There are no rules for the exact logic of ordinary language, because that doesn't exist [Strawson,P] |
6413 | 'The present King of France is bald' presupposes existence, rather than stating it [Strawson,P, by Grayling] |
8354 | Russell asks when 'The King of France is wise' would be a true assertion [Strawson,P] |
10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
13671 | Second-order quantifiers are just like plural quantifiers in ordinary language, with no extra ontology [Boolos, by Shapiro] |
10267 | We should understand second-order existential quantifiers as plural quantifiers [Boolos, by Shapiro] |
10698 | Plural forms have no more ontological commitment than to first-order objects [Boolos] |
7806 | Boolos invented plural quantification [Boolos, by Benardete,JA] |
10834 | Weak completeness: if it is valid, it is provable. Strong: it is provable from a set of sentences [Boolos] |
13841 | Why should compactness be definitive of logic? [Boolos, by Hacking] |
10491 | Infinite natural numbers is as obvious as infinite sentences in English [Boolos] |
10483 | Mathematics and science do not require very high orders of infinity [Boolos] |
10833 | Many concepts can only be expressed by second-order logic [Boolos] |
10490 | Mathematics isn't surprising, given that we experience many objects as abstract [Boolos] |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
10488 | It is lunacy to think we only see ink-marks, and not word-types [Boolos] |
10487 | I am a fan of abstract objects, and confident of their existence [Boolos] |
16980 | We need a logical use of 'object' as predicate-worthy, and an 'ontological' use [Strawson,P] |
10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
16979 | It makes no sense to ask of some individual thing what it is that makes it that individual [Strawson,P] |
3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
9282 | I can only apply consciousness predicates to myself if I can apply them to others [Strawson,P] |
9263 | A person is an entity to which we can ascribe predicates of consciousness and corporeality [Strawson,P] |
8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
8356 | The meaning of an expression or sentence is general directions for its use, to refer or to assert [Strawson,P] |
10430 | Reference is mainly a social phenomenon [Strawson,P, by Sainsbury] |
10448 | If an expression can refer to anything, it may still instrinsically refer, but relative to a context [Bach on Strawson,P] |
8355 | Expressions don't refer; people use expressions to refer [Strawson,P] |
8357 | If an utterance fails to refer then it is a pseudo-use, though a speaker may think they assert something [Strawson,P] |
9281 | The idea of a predicate matches a range of things to which it can be applied [Strawson,P] |