Combining Philosophers

All the ideas for Theodosius, Geoffrey Hellman and Roy Ellen

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11 ideas

6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / a. Structuralism
Structuralism is now common, studying relations, with no regard for what the objects might be [Hellman]
6. Mathematics / B. Foundations for Mathematics / 7. Mathematical Structuralism / c. Nominalist structuralism
Modal structuralism says mathematics studies possible structures, which may or may not be actualised [Hellman, by Friend]
Statements of pure mathematics are elliptical for a sort of modal conditional [Hellman, by Chihara]
Modal structuralism can only judge possibility by 'possible' models [Shapiro on Hellman]
Maybe mathematical objects only have structural roles, and no intrinsic nature [Hellman]
7. Existence / E. Categories / 1. Categories
Monothetic categories have fixed defining features, and polythetic categories do not [Ellen]
In symbolic classification, the categories are linked to rules [Ellen]
7. Existence / E. Categories / 2. Categorisation
Several words may label a category; one word can name several categories; some categories lack words [Ellen]
7. Existence / E. Categories / 5. Category Anti-Realism
Continuous experience sometimes needs imposition of boundaries to create categories [Ellen]
13. Knowledge Criteria / E. Relativism / 4. Cultural relativism
Classification is no longer held to be rooted in social institutions [Ellen]
15. Nature of Minds / A. Nature of Mind / 4. Other Minds / b. Scepticism of other minds
If we can't know minds, we can't know if Pyrrho was a sceptic [Theodosius, by Diog. Laertius]