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