21 ideas
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] |
13733 | Frege considered definite descriptions to be genuine singular terms [Frege, by Fitting/Mendelsohn] |
9874 | Contradiction arises from Frege's substitutional account of second-order quantification [Dummett on Frege] |
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] |
18252 | Real numbers are ratios of quantities, such as lengths or masses [Frege] |
18271 | We can't prove everything, but we can spell out the unproved, so that foundations are clear [Frege] |
10623 | Frege defined number in terms of extensions of concepts, but needed Basic Law V to explain extensions [Frege, by Hale/Wright] |
9975 | Frege ignored Cantor's warning that a cardinal set is not just a concept-extension [Tait on Frege] |
18165 | My Basic Law V is a law of pure logic [Frege] |
10700 | First- and second-order quantifiers are two ways of referring to the same things [Boolos] |
9190 | A concept is a function mapping objects onto truth-values, if they fall under the concept [Frege, by Dummett] |
13665 | Frege took the study of concepts to be part of logic [Frege, by Shapiro] |
17993 | Laws are relations of kinds, quantities and qualities, supervening on the essences of a domain [Vetter] |