9992 | The 'extension of a concept' in general may be quantitatively completely indeterminate [Cantor] |
9949 | There is the concept, the object falling under it, and the extension (a set, which is also an object) [Frege, by George/Velleman] |
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] |
10020 | Frege's biggest error is in not accounting for the senses of number terms [Hodes on Frege] |
10553 | A number is a class of classes of the same cardinality [Frege, by Dummett] |
10029 | Numbers need to be objects, to define the extension of the concept of each successor to n [Frege, by George/Velleman] |
10625 | Frege had a motive to treat numbers as objects, but not a justification [Hale/Wright on Frege] |
13871 | Frege claims that numbers are objects, as opposed to them being Fregean concepts [Frege, by Wright,C] |
9954 | "Number of x's such that ..x.." is a functional expression, yielding a name when completed [Frege, by George/Velleman] |
10139 | Frege gives an incoherent account of extensions resulting from abstraction [Fine,K on Frege] |
10028 | For Frege the number of F's is a collection of first-level concepts [Frege, by George/Velleman] |
9902 | Frege's incorrect view is that a number is an equivalence class [Benacerraf on Frege] |
17814 | The natural number n is the set of n-membered sets [Frege, by Yourgrau] |
13872 | Numbers are second-level, ascribing properties to concepts rather than to objects [Frege, by Wright,C] |
9816 | For Frege, successor was a relation, not a function [Frege, by Dummett] |
9953 | Numbers are more than just 'second-level concepts', since existence is also one [Frege, by George/Velleman] |
13887 | Frege started with contextual definition, but then switched to explicit extensional definition [Frege, by Wright,C] |
13897 | Each number, except 0, is the number of the concept of all of its predecessors [Frege, by Wright,C] |
17636 | A cardinal number may be defined as a class of similar classes [Frege, by Russell] |
9973 | The number of F's is the extension of the second level concept 'is equipollent with F' [Frege, by Tait] |
16500 | Frege showed that numbers attach to concepts, not to objects [Frege, by Wiggins] |
9990 | Frege replaced Cantor's sets as the objects of equinumerosity attributions with concepts [Frege, by Tait] |
7738 | Zero is defined using 'is not self-identical', and one by using the concept of zero [Frege, by Weiner] |
9856 | Frege's account of cardinals fails in modern set theory, so they are now defined differently [Dummett on Frege] |
17819 | A set doesn't have a fixed number, because the elements can be seen in different ways [Yourgrau on Frege] |
17820 | If you can subdivide objects many ways for counting, you can do that to set-elements too [Yourgrau on Frege] |
16890 | Frege's problem is explaining the particularity of numbers by general laws [Frege, by Burge] |
8630 | Individual numbers are best derived from the number one, and increase by one [Frege] |
11029 | 'Exactly ten gallons' may not mean ten things instantiate 'gallon' [Rumfitt on Frege] |
17460 | A statement of number contains a predication about a concept [Frege] |
10013 | Numerical statements have first-order logical form, so must refer to objects [Frege, by Hodes] |
18181 | The Number for F is the extension of 'equal to F' (or maybe just F itself) [Frege] |
18103 | Numbers are objects because they partake in identity statements [Frege, by Bostock] |
9586 | In a number-statement, something is predicated of a concept [Frege] |
3331 | If '5' is the set of all sets with five members, that may be circular, and you can know a priori if the set has content [Benardete,JA on Frege] |
14117 | Numbers are properties of classes [Russell] |
17817 | Defining 'three' as the principle of collection or property of threes explains set theory definitions [Yourgrau] |
13894 | Sameness of number is fundamental, not counting, despite children learning that first [Wright,C] |
12215 | The existence of numbers is not a matter of identities, but of constituents of the world [Fine,K] |
18182 | The extension of concepts is not important to me [Maddy] |
18177 | In the ZFC hierarchy it is impossible to form Frege's set of all three-element sets [Maddy] |
8297 | Numbers are universals, being sets whose instances are sets of appropriate cardinality [Lowe] |
17902 | A successor is the union of a set with its singleton [George/Velleman] |
17461 | Some 'how many?' answers are not predications of a concept, like 'how many gallons?' [Rumfitt] |