Combining Philosophers

All the ideas for Anaxarchus, Andr Gallois and Geoffrey Hellman

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13 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]
9. Objects / B. Unity of Objects / 3. Unity Problems / b. Cat and its tail
A CAR and its major PART can become identical, yet seem to have different properties [Gallois]
9. Objects / E. Objects over Time / 1. Objects over Time
Gallois hoped to clarify identity through time, but seems to make talk of it impossible [Hawley on Gallois]
If things change they become different - but then no one thing undergoes the change! [Gallois]
9. Objects / E. Objects over Time / 4. Four-Dimensionalism
4D: time is space-like; a thing is its history; past and future are real; or things extend in time [Gallois]
9. Objects / F. Identity among Objects / 3. Relative Identity
Gallois is committed to identity with respect to times, and denial of simple identity [Gallois, by Sider]
9. Objects / F. Identity among Objects / 6. Identity between Objects
Occasional Identity: two objects can be identical at one time, and different at others [Gallois, by Hawley]
If two things are equal, each side involves a necessity, so the equality is necessary [Gallois]
13. Knowledge Criteria / D. Scepticism / 1. Scepticism
Anaxarchus said that he was not even sure that he knew nothing [Anaxarchus, by Diog. Laertius]