28 ideas
10571 | Concern for rigour can get in the way of understanding phenomena [Fine,K] |
7785 | The use of plurals doesn't commit us to sets; there do not exist individuals and collections [Boolos] |
10565 | There is no stage at which we can take all the sets to have been generated [Fine,K] |
10699 | Does a bowl of Cheerios contain all its sets and subsets? [Boolos] |
10564 | We might combine the axioms of set theory with the axioms of mereology [Fine,K] |
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] |
10569 | If you ask what F the second-order quantifier quantifies over, you treat it as first-order [Fine,K] |
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] |
10570 | Assigning an entity to each predicate in semantics is largely a technical convenience [Fine,K] |
10573 | Dedekind cuts lead to the bizarre idea that there are many different number 1's [Fine,K] |
10575 | Why should a Dedekind cut correspond to a number? [Fine,K] |
10574 | Unless we know whether 0 is identical with the null set, we create confusions [Fine,K] |
10560 | Set-theoretic imperialists think sets can represent every mathematical object [Fine,K] |
10568 | Logicists say mathematics can be derived from definitions, and can be known that way [Fine,K] |
10563 | A generative conception of abstracts proposes stages, based on concepts of previous objects [Fine,K] |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
16639 | Only individual bodies exist [Bacon] |
16033 | There are only individual bodies containing law-based powers, and the Forms are these laws [Bacon] |
21950 | Science must clear away the idols of the mind if they are ever going to find the truth [Bacon] |
10561 | Abstraction-theoretic imperialists think Fregean abstracts can represent every mathematical object [Fine,K] |
10562 | We can combine ZF sets with abstracts as urelements [Fine,K] |
10567 | We can create objects from conditions, rather than from concepts [Fine,K] |