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
14085

'Deductivist' structuralism is just theories, with no commitment to objects, or modality

14086

'Modal' structuralism studies all possible concrete models for various mathematical theories

14084

Noneliminative structuralism treats mathematical objects as positions in real abstract structures

14087

'Settheoretic' structuralism treats mathematics as various structures realised among the sets

6. Mathematics / B. Foundations for Mathematics / 6. Mathematical Structuralism / d. Platonist structuralism
14089

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
14083

Structuralism is right about algebra, but wrong about sets

14090

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
14091

There may be a oneway direction of dependence among sets, and among natural numbers

8. Modes of Existence / B. Properties / 4. Intrinsic Properties
14088

An 'intrinsic' property is either found in every duplicate, or exists independent of all externals
