display all the ideas for this combination of texts
2 ideas
| 10262 | Fictionalism eschews the abstract, but it still needs the possible (without model theory) [Shapiro] |
| Full Idea: Fictionalism takes an epistemology of the concrete to be more promising than concrete-and-abstract, but fictionalism requires an epistemology of the actual and possible, secured without the benefits of model theory. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 7.2) | |
| A reaction: The idea that possibilities (logical, natural and metaphysical) should be understood as features of the concrete world has always struck me as appealing, so I have (unlike Shapiro) no intuitive problems with this proposal. |
| 10277 | Structuralism blurs the distinction between mathematical and ordinary objects [Shapiro] |
| 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'. | |
| From: Stewart Shapiro (Philosophy of Mathematics [1997], 8.4) | |
| 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. |