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 [Friend on Hellman] |
9557 | Statements of pure mathematics are elliptical for a sort of modal conditional [Chihara on Hellman] |
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 [MacBride on Chihara] |
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] |