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Full Idea
If objects depend on the other objects, this would mean an 'upward' dependence, in that they depend on the structure to which they belong, where the physical realm has a 'downward' dependence, with structures depending on their constituents.
Gist of Idea
In mathematical structuralism the small depends on the large, which is the opposite of physical structures
Source
Øystein Linnebo (Structuralism and the Notion of Dependence [2008], III)
Book Ref
-: 'The Philosophical Quarterly' [-], p.68
A Reaction
This nicely captures an intuition I have that there is something wrong with a commitment primarily to 'structures'. Our only conception of such things is as built up out of components. Not that I am committing to mathematical 'components'!
| 14083 | Structuralism is right about algebra, but wrong about sets [Linnebo] |
| 14085 | 'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo] |
| 14084 | Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo] |
| 14086 | 'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo] |
| 14087 | 'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo] |
| 14088 | An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo] |
| 14090 | In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo] |
| 14089 | Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo] |
| 14091 | There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo] |