54 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] |
| 16554 | Activities have place, rate, duration, entities, properties, modes, direction, polarity, energy and range [Machamer/Darden/Craver] |
| 3523 | Shadows are supervenient on their objects, but not reducible [Maslin] |
| 3517 | 'Ontology' means 'study of things which exist' [Maslin] |
| 10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
| 16556 | Penicillin causes nothing; the cause is what penicillin does [Machamer/Darden/Craver] |
| 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] |
| 16562 | We understand something by presenting its low-level entities and activities [Machamer/Darden/Craver] |
| 16563 | The explanation is not the regularity, but the activity sustaining it [Machamer/Darden/Craver] |
| 16555 | Functions are not properties of objects, they are activities contributing to mechanisms [Machamer/Darden/Craver] |
| 16528 | Mechanisms are not just push-pull systems [Machamer/Darden/Craver] |
| 16529 | Mechanisms are systems organised to produce regular change [Machamer/Darden/Craver] |
| 16530 | A mechanism explains a phenomenon by showing how it was produced [Machamer/Darden/Craver] |
| 16553 | Our account of mechanism combines both entities and activities [Machamer/Darden/Craver] |
| 16559 | Descriptions of explanatory mechanisms have a bottom level, where going further is irrelevant [Machamer/Darden/Craver] |
| 16564 | There are four types of bottom-level activities which will explain phenomena [Machamer/Darden/Craver] |
| 3538 | Analogy to other minds is uncheckable, over-confident and chauvinistic [Maslin] |
| 16561 | We can abstract by taking an exemplary case and ignoring the detail [Machamer/Darden/Craver] |
| 3540 | If we are brains then we never meet each other [Maslin] |
| 3518 | I'm not the final authority on my understanding of maths [Maslin] |
| 3530 | Denial of purely mental causation will lead to epiphenomenalism [Maslin] |
| 3520 | Token-identity removes the explanatory role of the physical [Maslin] |
| 8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
| 3528 | Causality may require that a law is being followed [Maslin] |
| 3525 | Strict laws make causation logically necessary [Maslin] |
| 3527 | Strict laws allow no exceptions and are part of a closed system [Maslin] |
| 16558 | Laws of nature have very little application in biology [Machamer/Darden/Craver] |