Combining Texts

All the ideas for 'Identity and Spatio-Temporal Continuity', 'Iteration Again' and 'Structuralism and the Notion of Dependence'

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11 ideas

4. Formal Logic / F. Set Theory ST / 5. Conceptions of Set / f. Limitation of Size
Limitation of Size is weak (Fs only collect is something the same size does) or strong (fewer Fs than objects) [Boolos, by Potter]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / b. Varieties of structuralism
'Deductivist' structuralism is just theories, with no commitment to objects, or modality [Linnebo]
Non-eliminative structuralism treats mathematical objects as positions in real abstract structures [Linnebo]
'Modal' structuralism studies all possible concrete models for various mathematical theories [Linnebo]
'Set-theoretic' structuralism treats mathematics as various structures realised among the sets [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / d. Platonist structuralism
Structuralism differs from traditional Platonism, because the objects depend ontologically on their structure [Linnebo]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / e. Structuralism critique
Structuralism is right about algebra, but wrong about sets [Linnebo]
In mathematical structuralism the small depends on the large, which is the opposite of physical structures [Linnebo]
7. Existence / C. Structure of Existence / 4. Ontological Dependence
There may be a one-way direction of dependence among sets, and among natural numbers [Linnebo]
8. Modes of Existence / B. Properties / 4. Intrinsic Properties
An 'intrinsic' property is either found in every duplicate, or exists independent of all externals [Linnebo]
9. Objects / A. Existence of Objects / 5. Individuation / e. Individuation by kind
'Ultimate sortals' cannot explain ontological categories [Westerhoff on Wiggins]