48 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] |
| 3061 | Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius] |
| 8693 | An 'abstraction principle' says two things are identical if they are 'equivalent' in some respect [Boolos] |
| 7337 | In Mosaic legal theory, crimes are sins and sins are crimes [Johnson,P] |
| 7339 | Because human life is what is sacred, Mosaic law has no death penalty for property violations [Johnson,P] |
| 7353 | The Pharisees undermined slavery, by giving slaves responsibility and status in law courts [Johnson,P] |
| 7340 | Mosaic law was the first to embody the rule of law, and equality before the law [Johnson,P] |
| 7338 | Man's life is sacred, because it is made in God's image [Johnson,P] |
| 7348 | The Jews sharply distinguish human and divine, but the Greeks pull them closer together [Johnson,P] |
| 7336 | A key moment is the idea of a single moral God, who imposes his morality on humanity [Johnson,P] |
| 7341 | Sampson illustrates the idea that religious heroes often begin as outlaws and semi-criminals [Johnson,P] |
| 7342 | Isaiah moved Israelite religion away from the local, onto a more universal plane [Johnson,P] |
| 7355 | The Torah pre-existed creation, and was its blueprint [Johnson,P] |
| 7344 | Judaism involves circumcision, Sabbath, Passover, Pentecost, Tabernacles, New Year, and Atonement [Johnson,P] |
| 7345 | In exile the Jews became a nomocracy [Johnson,P] |
| 7347 | Zoroastrians believed in one eternal beneficent being, Creator through the holy spirit [Johnson,P] |
| 7349 | Immortality based on judgement of merit was developed by the Egyptians (not the Jews) [Johnson,P] |
| 7354 | The main doctrine of the Pharisees was belief in resurrection and the afterlife [Johnson,P] |
| 7356 | Pious Jews saw heaven as a vast library [Johnson,P] |