Combining Philosophers

All the ideas for William Paley, Paul M. Pietroski and Geoffrey Hellman

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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]
19. Language / B. Reference / 5. Speaker's Reference
No language is semantically referential; it all occurs at the level of thought or utterance [Pietroski, by Hofweber]
28. God / B. Proving God / 3. Proofs of Evidence / b. Teleological Proof
Even an imperfect machine can exhibit obvious design [Paley]
Unlike a stone, the parts of a watch are obviously assembled in order to show the time [Paley]
From the obvious purpose and structure of a watch we must infer that it was designed [Paley]
No organ shows purpose more obviously than the eyelid [Paley]
All the signs of design found in a watch are also found in nature [Paley]