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'Function and Concept', '12: Colossians' and 'Structuralism and the Notion of Dependence'
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8 ideas
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
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'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo]
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'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo]
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'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo]
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Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo]
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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 [Linnebo]
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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 [Linnebo]
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In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo]
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6. Mathematics / C. Sources of Mathematics / 6. Logicism / a. Early logicism
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Arithmetic is a development of logic, so arithmetical symbolism must expand into logical symbolism [Frege]
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