Ideas from 'Structuralism and the Notion of Dependence' by Øystein Linnebo [2008], by Theme Structure

[found in 'The Philosophical Quarterly' (ed/tr -) [- ,]].

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6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / b. Varieties of structuralism
'Deductivist' structuralism is just theories, with no commitment to objects, or modality
'Modal' structuralism studies all possible concrete models for various mathematical theories
Non-eliminative structuralism treats mathematical objects as positions in real abstract structures
'Set-theoretic' structuralism treats mathematics as various structures realised among the sets
6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / d. Platonist structuralism
Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure
6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / e. Structuralism critique
Structuralism is right about algebra, but wrong about sets
In mathematical structuralism the small depends on the large, which is the opposite of physical structures
7. Existence / C. Structure of Existence / 4. Ontological Dependence
There may be a one-way direction of dependence among sets, and among natural numbers
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
An 'intrinsic' property is either found in every duplicate, or exists independent of all externals