58 ideas
18005 | Philosophy aims to become more disciplined about categories [Ryle] |
18004 | We can't do philosophy without knowledge of types and categories [Ryle] |
13985 | A true proposition seems true of one fact, but a false proposition seems true of nothing at all. [Ryle] |
13984 | Two maps might correspond to one another, but they are only 'true' of the country they show [Ryle] |
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] |
13979 | Logic studies consequence, compatibility, contradiction, corroboration, necessitation, grounding.... [Ryle] |
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] |
10832 | '∀x x=x' only means 'everything is identical to itself' if the range of 'everything' is fixed [Boolos] |
10800 | The values of variables can't determine existence, because they are just expressions [Ryle, by Quine] |
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] |
13988 | Many sentences do not state facts, but there are no facts which could not be stated [Ryle] |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
14297 | A dispositional property is not a state, but a liability to be in some state, given a condition [Ryle] |
14300 | No physical scientist now believes in an occult force-exerting agency [Ryle] |
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] |
10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
13983 | Representation assumes you know the ideas, and the reality, and the relation between the two [Ryle] |
2622 | Can one movement have a mental and physical cause? [Ryle] |
1353 | Reporting on myself has the same problems as reporting on you [Ryle] |
1354 | We cannot introspect states of anger or panic [Ryle] |
2624 | I cannot prepare myself for the next thought I am going to think [Ryle] |
2620 | Dualism is a category mistake [Ryle] |
2388 | Behaviour depends on desires as well as beliefs [Chalmers on Ryle] |
3354 | You can't explain mind as dispositions, if they aren't real [Benardete,JA on Ryle] |
2387 | How can behaviour be the cause of behaviour? [Chalmers on Ryle] |
13980 | If you like judgments and reject propositions, what are the relata of incoherence in a judgment? [Ryle] |
8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
13978 | Husserl and Meinong wanted objective Meanings and Propositions, as subject-matter for Logic [Ryle] |
13977 | When I utter a sentence, listeners grasp both my meaning and my state of mind [Ryle] |
13976 | 'Propositions' name what is thought, because 'thoughts' and 'judgments' are too ambiguous [Ryle] |
13981 | Several people can believe one thing, or make the same mistake, or share one delusion [Ryle] |
13987 | We may think in French, but we don't know or believe in French [Ryle] |
13989 | There are no propositions; they are just sentences, used for thinking, which link to facts in a certain way [Ryle] |
13982 | If we accept true propositions, it is hard to reject false ones, and even nonsensical ones [Ryle] |
20239 | Unlike us, the early Greeks thought envy was a good thing, and hope a bad thing [Hesiod, by Nietzsche] |