Questions: Underdetermination and the Duhem-Quine Thesis

Question 1

A physicist derives prediction P from main hypothesis H combined with auxiliary assumptions A. The experiment yields not-P. What does this logically establish?

• A. H is false and should be abandoned
• B. A is false and should be revised
• C. At least one element of the conjunction H ∧ A is false, but logic alone cannot determine which
• D. Both H and A are false, since both were required to derive P

Answer: (C)

This is the formal structure of the Duhem-Quine thesis. Modus tollens tells you that if (H ∧ A) → P and ¬P, then ¬(H ∧ A). But ¬(H ∧ A) is equivalent to ¬H ∨ ¬A — at least one is false. Logic alone cannot distribute the blame. You can save H by blaming A (miscalibrated instruments, wrong background assumption) or blame H by accepting A. This is why failed predictions never straightforwardly falsify a single hypothesis.

Question 2

When Uranus's orbit deviated from Newtonian predictions, astronomers posited Neptune rather than abandoning Newton's laws. What does the Duhem-Quine thesis say about this strategy?

• A. The strategy was invalid because Newtonian mechanics was the hypothesis actually being tested in isolation
• B. The strategy was logically available — revising the auxiliary (the planet-count assumption) rather than the main law — and happened to be correct in this case
• C. The strategy only works if the auxiliary hypothesis is independently verifiable before the experiment
• D. The strategy proves that underdetermination does not apply to well-established theories like Newtonian mechanics

Answer: (B)

The Duhem-Quine thesis makes this a general logical point, not a special exception for Newton. Any time a prediction fails, revising an auxiliary is a logically available response. In the Uranus case, the auxiliary was 'we know all the planets perturbing Uranus's orbit' — a reasonable assumption to question. Le Verrier revised it by hypothesizing a new planet, and the telescope confirmed Neptune. The thesis says this was always an option; its success was an empirical discovery, not a logical necessity. The Mercury/Vulcan case shows the same strategy can fail.

Question 3

According to the Duhem-Quine thesis, a single experiment that contradicts a theory's prediction conclusively refutes that theory.

• T. True
• F. False

Answer: False

This is exactly what the Duhem-Quine thesis denies. A refuting observation shows that the conjunction H ∧ A is false, not that H alone is false. Scientists can always respond by revising one of the auxiliary hypotheses — about instruments, background conditions, or other known laws — rather than abandoning the main theory. Simple falsificationism (Popper's original view) overlooks this. Whether to revise H or A is a scientific judgment that appeals to criteria like simplicity, coherence, and prior probability — not a logical compulsion.

Question 4

The Duhem-Quine thesis implies that when a prediction fails, logic alone does not determine which element of the theoretical web should be abandoned.

• T. True
• F. False

Answer: True

This is the direct statement of the thesis. The failed prediction only entails that the total conjunction of hypotheses (H ∧ A₁ ∧ A₂ ∧ ... ∧ Aₙ) is false. Which element to reject is a choice underdetermined by logic. Scientists appeal to non-logical criteria — simplicity, conservatism (minimize revision), internal coherence, explanatory power — to make this choice. Quine argued this holism extends to the entire web of belief, with no sharp science/philosophy boundary.

Question 5

The Neptune case and the Vulcan case both involved the same logical strategy in response to anomalous observations. Why does one count as science working correctly and the other as a research program that ultimately failed?

Model answer: In both cases, astronomers protected Newton's laws by revising an auxiliary (the assumption that all gravitating bodies were known) and hypothesizing an undetected planet. The Neptune strategy succeeded: the hypothesized planet was found where predicted, confirming the auxiliary revision. The Vulcan strategy failed: no planet was found where predicted, and continued adjustments to the auxiliary grew increasingly implausible. Eventually, Einstein's general relativity explained Mercury's precession without any additional planet, making Newton's laws themselves the thing to revise. The Duhem-Quine thesis says both strategies were logically available; which was correct was an empirical question, not a logical one.

This is why the thesis does not make science arbitrary, even though it shows that no single experiment compels theory rejection. Scientists are always free to protect a theory by revising auxiliaries, but continued failures of that strategy — and the emergence of a better theory — eventually make theory revision the more rational choice. The thesis undermines naive falsificationism without collapsing into relativism: empirical evidence still constrains rational theory choice, just not by simple deduction.