8639 | If numbers are supposed to be patterns, each number can have many patterns [Frege] |
9977 | Ordinals can't be defined just by progression; they have intrinsic qualities [Russell] |
9627 | Different versions of set theory result in different underlying structures for numbers [Zermelo, by Brown,JR] |
9829 | The identity of a number may be fixed by something outside structure - by counting [Dummett] |
9828 | Numbers aren't fixed by position in a structure; it won't tell you whether to start with 0 or 1 [Dummett] |
9192 | The number 4 has different positions in the naturals and the wholes, with the same structure [Dummett] |
18116 | Numbers can't be positions, if nothing decides what position a given number has [Bostock] |
18117 | Structuralism falsely assumes relations to other numbers are numbers' only properties [Bostock] |
10815 | We don't need 'abstract structures' to have structural truths about successor functions [Lewis] |
10629 | If structures are relative, this undermines truth-value and objectivity [Hale/Wright] |
10628 | The structural view of numbers doesn't fit their usage outside arithmetical contexts [Hale/Wright] |
18500 | How could structures be mathematical truthmakers? Maths is just true, without truthmakers [Heil] |
10274 | Does someone using small numbers really need to know the infinite structure of arithmetic? [Shapiro] |
10186 | If set theory is used to define 'structure', we can't define set theory structurally [Burgess] |
10187 | Abstract algebra concerns relations between models, not common features of all the models [Burgess] |
10188 | How can mathematical relations be either internal, or external, or intrinsic? [Burgess] |
9628 | Sets seem basic to mathematics, but they don't suit structuralism [Brown,JR] |
10171 | The existence of an infinite set is assumed by Relativist Structuralism [Reck/Price] |
8926 | For mathematical objects to be positions, positions themselves must exist first [MacBride] |
14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
14505 | Some questions concern mathematical entities, rather than whole structures [Koslicki] |
17932 | If 'in re' structures relies on the world, does the world contain rich enough structures? [Colyvan] |