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Full Idea
One result of the structuralist perspective is a healthy blurring of the distinction between mathematical and ordinary objects. ..'According to the structuralist, physical configurations often instantiate mathematical patterns'.
Gist of Idea
Structuralism blurs the distinction between mathematical and ordinary objects
Source
Stewart Shapiro (Philosophy of Mathematics [1997], 8.4)
Book Ref
Shapiro,Stewart: 'Philosophy of Mathematics:structure and ontology' [OUP 1997], p.256
A Reaction
[The quotation is from Penelope Maddy 1988 p.28] This is probably the main reason why I found structuralism interesting, and began to investigate it.
| 14429 | Classes are logical fictions, made from defining characteristics [Russell] |
| 9497 | Without modality, Armstrong falls back on fictionalism to support counterfactual laws [Bird on Armstrong] |
| 8909 | Abstractions may well be verbal fictions, in which we ignore some features of an object [Lewis] |
| 10023 | Talk of mirror images is 'encoded fictions' about real facts [Hodes] |
| 8864 | We quantify over events, worlds, etc. in order to make logical possibilities clearer [Yablo] |
| 19494 | Fictionalism allows that simulated beliefs may be tracking real facts [Yablo] |
| 19489 | For me, fictions are internally true, without a significant internal or external truth-value [Yablo] |
| 19490 | Make-believe can help us to reason about facts and scientific procedures [Yablo] |
| 19491 | 'The clouds are angry' can only mean '...if one were attributing emotions to clouds' [Yablo] |
| 10262 | Fictionalism eschews the abstract, but it still needs the possible (without model theory) [Shapiro] |
| 10277 | Structuralism blurs the distinction between mathematical and ordinary objects [Shapiro] |
| 12445 | If fictional objects really don't exist, then they aren't abstract objects [Azzouni] |