# The College of All Minds — The Truly Hardest Exam in the World
## Paper VI — Philosophy and Logic

*Confined to theoretical philosophy: formal logic, epistemology, metaphysics of science, philosophy of mathematics, and the philosophy of physics and biology. No moral, political or value-philosophy content.*

1. Is logical entailment a transitive relation? Defend your answer.
2. Do Gödel's incompleteness theorems bear on the thesis that the mind is a machine?
3. Can there be vague objects, or only vague descriptions?
4. Is it possible to define truth non-circularly for a language containing its own truth predicate?
5. What does the Löwenheim–Skolem theorem show about the determinacy of mathematical reference?
6. Are there absolutely undecidable mathematical propositions?
7. Do the paradoxes of quantum mechanics pose a threat to classical logic?
8. Is set-theoretic Platonism compatible with our capacity to know mathematical facts?
9. What, if anything, does reverse mathematics teach us about foundations?
10. Can mathematical facts explain physical phenomena?
11. Is chemistry reducible to physics? State the criterion of reduction you use.
12. Does teleological explanation have an ineliminable role in biology?
13. What is a law of nature, and could the laws have been otherwise?
14. Is there a coherent notion of metaphysical modality distinct from logical and physical modality?
15. Compare the Russellian and Strawsonian treatments of definite descriptions.
16. Can there be time without change, or change without time?
17. Is the principle of bivalence defensible in the face of the future?
18. What does quantum entanglement imply for our concept of causation?
19. Is there a livable interpretation of probability that is neither frequentist nor subjectivist?
20. Can modal logic tell us anything about reality, or only about our language?
21. Is the a priori / a posteriori distinction coherent and explanatory? Draw it or reject it.
22. What is the best response to the underdetermination of theory by evidence?
23. Are laws of nature relations among universals, or regularities, or neither?
24. Does the success of science give us reason to believe its unobservable posits?
25. Is identity across time a further fact, or fixed by qualitative continuity?
26. What is a natural kind, and does the periodic table exhibit them?
27. Can there be a consistent version of verificationism, and would it be plausible?
28. What does it mean to say a physical theory is background-independent, and is that a virtue?
29. Is arithmetic analytic, synthetic a priori, or empirical?
30. What is the strongest challenge to a law of classical logic, and can it be resisted?

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