50 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] |
| 10830 | Second-order logic metatheory is set-theoretic, and second-order validity has set-theoretic problems [Boolos] |
| 10225 | Monadic second-order logic might be understood in terms of plural quantifiers [Boolos, by Shapiro] |
| 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] |
| 23551 | It is necessary for a belief that it be held for a length of time [Fricker,M] |
| 23558 | Offering knowledge needs accuracy and sincerity; receiving it needs testimonial justice [Fricker,M] |
| 23553 | Testimonial judgement is not logical, but produces reasons and motivations [Fricker,M] |
| 23550 | Burge says we are normally a priori entitled to believe testimony [Fricker,M] |
| 23552 | We assess testimonial probabilities by the speaker, the listener, the facts, and the circumstances [Fricker,M] |
| 23555 | Assessing credibility involves the impact of both the speaker's and the listener's social identity [Fricker,M] |
| 23554 | Judgements can be unreflective and non-inferential, yet rational, by being sensitive to experience [Fricker,M] |
| 8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
| 23557 | To judge agents in remote times and cultures we need a moral resentment weaker than blame [Fricker,M] |
| 8388 | Causation is either direct realism, Humean reduction, non-Humean reduction or theoretical realism [Tooley] |
| 8389 | Causation distinctions: reductionism/realism; Humean/non-Humean states; observable/non-observable [Tooley] |
| 8416 | Reductionists can't explain accidents, uninstantiated laws, probabilities, or the existence of any laws [Tooley] |
| 8393 | We can only reduce the direction of causation to the direction of time if we are realist about the latter [Tooley] |
| 8390 | Causation is directly observable in pressure on one's body, and in willed action [Tooley] |
| 8418 | Quantum physics suggests that the basic laws of nature are probabilistic [Tooley] |
| 8392 | Probabilist laws are compatible with effects always or never happening [Tooley] |
| 8399 | The actual cause may not be the most efficacious one [Tooley] |
| 8391 | In counterfactual worlds there are laws with no instances, so laws aren't supervenient on actuality [Tooley] |
| 8394 | Explaining causation in terms of laws can't explain the direction of causation [Tooley] |
| 8398 | Causation is a concept of a relation the same in all worlds, so it can't be a physical process [Tooley] |