44 ideas
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] |
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] |
10489 | We deal with abstract objects all the time: software, poems, mistakes, triangles.. [Boolos] |
20653 | Six reduction levels: groups, lives, cells, molecules, atoms, particles [Putnam/Oppenheim, by Watson] |
8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
4761 | The 'error theory' of morals says there is no moral knowledge, because there are no moral facts [Mackie, by Engel] |
8337 | Some says mental causation is distinct because we can recognise single occurrences [Mackie] |
8342 | Mackie tries to analyse singular causal statements, but his entities are too vague for events [Kim on Mackie] |
8343 | Necessity and sufficiency are best suited to properties and generic events, not individual events [Kim on Mackie] |
8385 | A cause is part of a wider set of conditions which suffices for its effect [Mackie, by Crane] |
8335 | Necessary conditions are like counterfactuals, and sufficient conditions are like factual conditionals [Mackie] |
8336 | The INUS account interprets single events, and sequences, causally, without laws being known [Mackie] |
8333 | A cause is an Insufficient but Necessary part of an Unnecessary but Sufficient condition [Mackie] |
8395 | Mackie has a nomological account of general causes, and a subjunctive conditional account of single ones [Mackie, by Tooley] |
8334 | The virus causes yellow fever, and is 'the' cause; sweets cause tooth decay, but they are not 'the' cause [Mackie] |
1472 | The propositions that God is good and omnipotent, and that evil exists, are logically contradictory [Mackie, by PG] |
1473 | Is evil an illusion, or a necessary contrast, or uncontrollable, or necessary for human free will? [Mackie, by PG] |