28 ideas
23326 | In the third century Stoicism died out, replaced by Platonism, with Aristotelian ethics [Frede,M] |
23335 | In late antiquity nearly all philosophers were monotheists [Frede,M] |
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] |
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] |
10699 | Does a bowl of Cheerios contain all its sets and subsets? [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] |
10697 | Identity is clearly a logical concept, and greatly enhances predicate calculus [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] |
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] |
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] |
23333 | The idea of free will achieved universal acceptance because of Christianity [Frede,M] |
23337 | The Stoics needed free will, to allow human choices in a divinely providential cosmos [Frede,M] |
23334 | For Christians man has free will by creation in God's image (as in Genesis) [Frede,M] |
23336 | There is no will for Plato or Aristotle, because actions come directly from perception of what is good [Frede,M] |
23313 | The Gnostic demiurge (creator) is deluded, and doesn't care about us [Frede,M] |