Paper VI — Philosophy

30 QUESTIONS

Paper VI is confined by its rubric to theoretical philosophy, and covers four regions of it. In logic and the theory of truth it examines entailment and its transitivity, vagueness in objects and in descriptions, non-circular definitions of truth, bivalence and the open future, and the strongest challenge to a law of classical logic. In the philosophy of mathematics it examines Platonism against our capacity to know, absolute undecidability, the Löwenheim–Skolem theorem and the determinacy of reference, reverse mathematics, and whether arithmetic is analytic, synthetic a priori or empirical. In the metaphysics of science it examines laws and modality, natural kinds and the periodic table, identity across time, background independence, and the reality of unobservable posits. In the philosophy of physics and biology it examines quantum logic and entanglement, causation, teleology, reduction, and whether Gödel’s theorems bear on the thesis that the mind is a machine.

The paper examines argument, and admits nothing else. No moral, political or value-philosophical question is set, and none may be answered; a candidate who converts a metaphysical question into an ethical one has failed to answer it. What is required is the ability to state a position in its strongest form, to identify the premise on which it actually rests, and to say what would count against it — with the technical results handled as results, so that a claim about Löwenheim–Skolem or about incompleteness is held to the theorem rather than to its reputation. This is the only paper unchanged by Examination Expansion v5.0: neither the ontology of the musical work nor the vagueness of a geographical boundary is admissible under its rubric, the second being in any case already treated abstractly by its third question.

Scope

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.

Conduct of the response

Answer in the idiom of the college: provocations invite a disciplined essay; technical problems require correct, quantitative reasoning; interdisciplinary questions require two fields to be brought together. A response is an argument, not a survey; where the question admits a position, one is to be taken at the outset and defended. It must be exactly as technical as the question requires, and no more, and its course must remain followable by the educated layman. It may not exceed three thousand words, exclusive of equations, figures, tables, and references; the limit is a ceiling, not a target, and of two answers of equal force the shorter is judged the better. The full statement of the response required is given on the Responses page.

1.
Is logical entailment a transitive relation? Defend your answer.

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2.
Do Gödel's incompleteness theorems bear on the thesis that the mind is a machine?

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3.
Can there be vague objects, or only vague descriptions?

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4.
Is it possible to define truth non-circularly for a language containing its own truth predicate?

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5.
What does the Löwenheim–Skolem theorem show about the determinacy of mathematical reference?

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6.
Are there absolutely undecidable mathematical propositions?

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7.
Do the paradoxes of quantum mechanics pose a threat to classical logic?

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8.
Is set-theoretic Platonism compatible with our capacity to know mathematical facts?

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9.
What, if anything, does reverse mathematics teach us about foundations?

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10.
Can mathematical facts explain physical phenomena?

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11.
Is chemistry reducible to physics? State the criterion of reduction you use.

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12.
Does teleological explanation have an ineliminable role in biology?

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13.
What is a law of nature, and could the laws have been otherwise?

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14.
Is there a coherent notion of metaphysical modality distinct from logical and physical modality?

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15.
Compare the Russellian and Strawsonian treatments of definite descriptions.

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16.
Can there be time without change, or change without time?

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17.
Is the principle of bivalence defensible in the face of the future?

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18.
What does quantum entanglement imply for our concept of causation?

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19.
Is there a livable interpretation of probability that is neither frequentist nor subjectivist?

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20.
Can modal logic tell us anything about reality, or only about our language?

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21.
Is the a priori / a posteriori distinction coherent and explanatory? Draw it or reject it.

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22.
What is the best response to the underdetermination of theory by evidence?

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23.
Are laws of nature relations among universals, or regularities, or neither?

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24.
Does the success of science give us reason to believe its unobservable posits?

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25.
Is identity across time a further fact, or fixed by qualitative continuity?

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26.
What is a natural kind, and does the periodic table exhibit them?

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27.
Can there be a consistent version of verificationism, and would it be plausible?

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28.
What does it mean to say a physical theory is background-independent, and is that a virtue?

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29.
Is arithmetic analytic, synthetic a priori, or empirical?

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30.
What is the strongest challenge to a law of classical logic, and can it be resisted?

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Paper VI was retitled Philosophy by Examination Renaming v3.3. Its questions and rubric stand verbatim and unrenumbered.

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