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Single Idea 10168

[filed under theme 6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism ]

Full Idea

Formalist Structuralism endorses structural methodology in mathematics, but rejects semantic and metaphysical problems as either meaningless, or purely formal, or as inference relations.

Gist of Idea

Formalist Structuralism says the ontology is vacuous, or formal, or inference relations

Source

E Reck / M Price (Structures and Structuralism in Phil of Maths [2000], §3)

A Reaction

[very compressed] I find the third option fairly congenial, certainly in preference to rather platonist accounts of structuralism. One still needs to distinguish the mathematical from the non-mathematical in the inference relations.

The 13 ideas with the same theme [structuralism denying real objects or real structures]:

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]