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Full Idea
Usually structuralism and nominalism are considered rivals. But structuralism can also be the first step in a strategy of nominalist reconstrual or paraphrase.
Gist of Idea
Structuralism and nominalism are normally rivals, but might work together
Source
JP Burgess / G Rosen (A Subject with No Object [1997], II.C.0)
Book Ref
Burgess,J/Rosen,G: 'A Subject with No Object' [OUP 1997], p.147
A Reaction
Hellman and later Chihara seem to be the main proponents of nominalist structuralism. My sympathies lie with this strategy. Are there objects at the nodes of the structure, or is the structure itself platonic? Mill offers a route.
| 12329 | If mathematics is a logic of the possible, then questions of existence are not intrinsic to it [Badiou] |
| 8698 | Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend] |
| 9557 | Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara] |
| 10263 | Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman] |
| 8922 | Maybe mathematical objects only have structural roles, and no intrinsic nature [Hellman] |
| 10221 | Is there is no more to structures than the systems that exemplify them? [Shapiro] |
| 10248 | Number statements are generalizations about number sequences, and are bound variables [Shapiro] |
| 9925 | Structuralism and nominalism are normally rivals, but might work together [Burgess/Rosen] |
| 10192 | We can replace existence of sets with possibility of constructing token sentences [Chihara, by MacBride] |
| 10168 | Formalist Structuralism says the ontology is vacuous, or formal, or inference relations [Reck/Price] |
| 10178 | Maybe we should talk of an infinity of 'possible' objects, to avoid arithmetic being vacuous [Reck/Price] |
| 8696 | Structuralist says maths concerns concepts about base objects, not base objects themselves [Friend] |
| 8695 | Structuralism focuses on relations, predicates and functions, with objects being inessential [Friend] |