20 ideas
12452 | Our dislike of contradiction in logic is a matter of psychology, not mathematics [Brouwer] |
7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [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] |
12451 | Scientific laws largely rest on the results of counting and measuring [Brouwer] |
12454 | Intuitionists only accept denumerable sets [Brouwer] |
12453 | Neo-intuitionism abstracts from the reuniting of moments, to intuit bare two-oneness [Brouwer] |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
15642 | If kinds depend only on what can be observed, many underlying essences might produce the same kind [Eagle] |
15643 | Nominal essence mistakenly gives equal weight to all underlying properties that produce appearances [Eagle] |
15645 | Nominal essence are the observable properties of things [Eagle] |
10117 | Intuitonists in mathematics worried about unjustified assertion, as well as contradiction [Brouwer, by George/Velleman] |
15641 | Kinds are fixed by the essential properties of things - the properties that make it that kind of thing [Eagle] |