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L03 Under-determination

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Mock exam Q6: "The under-determination thesis was first formulated by Duhem and later strengthened by Quine. State this thesis in Duhem's own version, and explain it with an example." (half a page)

Must hit:

1. The formal version. If premises $\{P_1,\dots ,P_n\}$ deductively entail an observation statement $O$, and experiment establishes $O^{\prime }$ where $O^{\prime }$ entails not-$O$, then the conjunction of the premises is false. It does not follow that any particular premise is false.
2. The consequence. There is no crucial experiment that irrefutably decides between two hypotheses, because a hypothesis is only ever tested together with auxiliary assumptions (including the theory of the apparatus).
3. An example. An astronomical theory conflicts with telescope observations: the conflict does not say whether the astronomy or the optics of the telescope is at fault. (Poincare’s sphere is the impressive alternative.)

Losing marks: stating the slogan (“theory is under-determined by data”) instead of the premises-and-conjunction version, or giving no example.

Mock exam Q3: Einstein (1953) said that if the eclipse measurement had not shown the shift, "Then I am very sorry for the dear Lord, for the theory is correct." Would, and-or could, this be acceptable for Popper? (10 points)

Follow the official key:

1. No, assuming the measurement was correct: the theory is falsified and has to be rejected. Einstein shows a dogmatic attitude.
2. However, perhaps the measurement was not correct. Given the Duhem-Quine thesis, scientists can always put the blame elsewhere (an auxiliary assumption, the measurement) and retain the theory.
3. But for Popper this is acceptable only if there are independent reasons for rejecting the measurement result. Otherwise it is an ad hoc hypothesis, which lowers the theory’s scientific status.

Losing marks: stopping at “no”, or saying Duhem-Quine lets Einstein off without the independent-reasons condition.

Does under-determination show that theory choice is arbitrary? Answer using Duhem, Quine and Laudan.

• Duhem: no. Logic alone does not settle which premise to give up, but good sense does: some opinions are “perfectly unreasonable” even though no contradiction forces you to drop them. Choice is not formal, which is different from arbitrary.
• Quine: pushes hardest. Any statement can be held true “come what may” if you make drastic enough adjustments elsewhere (pleading hallucination, even revising logic).
• Laudan: logically possible is not rational. Quine argues in an “evaluative vacuum” and never examines the ampliative rules of theory choice to show they are too weak to decide. Only the egalitarian thesis (every theory is as well supported as every rival) would make choice arbitrary, and nothing in Quine establishes it.
• Verdict: holism shows a theory can be saved, not that it is reasonable to save it.

Explain under-determination using Poincare's sphere, and say what conclusion Poincare draws.

• A world inside a sphere of radius $R$. Description 1: a Euclidean disk with temperature $T=R^2-r^2$ (hottest at the centre, zero at the edge), and every body expands in proportion to $T$, so everything shrinks towards the edge. Description 2: inhabitants, whose rulers shrink with them, never reach the edge and find space infinite and non-Euclidean.
• No experiment separates the two, because every experimental set-up can itself be described in either picture.
• Conclusion: geometry is conventional, neither a priori (against Kant) nor a posteriori. We pick the description that is simplest for us, like choosing metres over yards. There is no fact of the matter.
• Link to Duhem: the geometry is one of the auxiliary assumptions that rides along in every test.

What was Popper's own concession about the empirical basis, and why does it matter for this lecture?

No objective facts force the acceptance of an observation report. Science accepts its empirical basis by intersubjective agreement, so accepting a report that falsifies a theory is ultimately a human decision. That admission is the crack Duhem widens into under-determination.

In logical terms, what exactly does a failed prediction refute according to Duhem?

Only the conjunction $P_1\wedge \cdots \wedge P_n$. Modus tollens gives $\neg (P_1\wedge \cdots \wedge P_n)$, which means “at least one premise is false”, never “this particular premise is false”. Falsification is ambiguous.

What is a crucial experiment, who is the idea associated with, and what are Duhem's two reasons there is no such thing?

An experimentum crucis (Bacon, Hooke, Newton): “an irrefutable procedure for transforming one of the two hypotheses before us into a demonstrated truth”.

1. Hypotheses are only tested together with auxiliary assumptions, the apparatus included, so a result never isolates one hypothesis.
2. There may be unconceived alternatives: hypotheses nobody has thought of, which the experiment cannot rule out (developed later by Stanford).

What is Duhem's "good sense", what two questions does De Haro raise about it, and what does it show about Duhem's conclusion?

Bon sens: “certain opinions which do not fall under the hammer of the principle of contradiction are in any case perfectly unreasonable.” It is what decides when logic does not. De Haro’s questions: what is good sense, and how can a scientist be “an impartial and faithful judge”? It shows Duhem concludes theory choice is not formal. He does not conclude it is arbitrary.

Name Quine's two dogmas of empiricism (1951) and state what each one claims.

1. Reductionism: every scientific statement is logically equivalent to a statement in a special empiricist language (of immediate experience, or of physical things). This is the verification theory of meaning.
2. The analytic-synthetic distinction: a sharp line between statements true by meaning alone and statements true because of how the world is.

What is Quine's objection to each dogma?

• Reductionism: you cannot test statements in isolation. No statement has its own private stock of empirical consequences.
• Analytic-synthetic: the difference between conceptual scheme and fact is “of degree only”. Analytic statements are just the limiting case: true statements with no empirical content, confirmed however the world turns out.

Why does Quine say that "at bottom the two dogmas are identical"?

Both assume statements can be assessed one at a time. Reductionism says each statement has its own confirming experiences; the analytic-synthetic distinction says some statements have none. Deny that statements face experience individually and both dogmas fall together.

Describe Quine's web of belief: where does experience touch it, what sits at the centre, and is the centre immune to revision?

Our total knowledge is “a man-made fabric which impinges on experience only along the edges” (or a field of force whose boundary conditions are experience). A conflict at the periphery forces readjustments in the interior, and there is “much latitude of choice” about which statements to revise. Geography and history sit near the edge, physics further in, mathematics and logic at the centre. The centre is not immune, only expensive: revising it forces the largest rearrangement. It is not a different kind of truth.

How does the Duhem-Quine thesis go beyond Duhem's own thesis?

Duhem: a hypothesis is tested together with a bundle of auxiliary assumptions (in physics). Quine: the bundle is the whole web of belief, logic and mathematics included, so almost any statement can be kept true if you pay elsewhere. A disconfirming observation only touches the edge, and auxiliary hypotheses absorb the blow. Laudan catalogues the available moves as Quine’s “four stratagems”.

What is Stein's criticism of Quine?

Quine’s scepticism about meanings is unearned. He writes analyticity off as “picturesque” (attributing it to Leibniz) and treats intensions as leftovers of Aristotelian essences, instead of engaging the Frege-Carnap theory of meaning. He simply assumes an empiricist must be sceptical about meanings.

Sense versus reference: define both, give the alternative names and the classic example, and state the possible-worlds account of intension.

• Sense (intension): the linguistic meaning of the words.
• Reference (extension): the object the words pick out.
• “Morning star” and “evening star” differ in sense but both refer to Venus.
• Possible-worlds account: the intension of a sentence $S$ is the maximal set of possible worlds where $S$ is true, equivalently a function from possible worlds to truth values.

What is Laudan's core objection to Quine's "any statement can be held true come what may"? Give his phrase.

Quine discusses under-determination in an “evaluative vacuum”: he treats a course of action as fine because it is logically possible, without asking whether it is rational. To support his claim he would have to examine the ampliative rules of theory choice and show they are always too ambiguous to decide between any two theories. He never does. Rationality includes epistemic warrant, above all the evidence: you can plead hallucination, but that does not make it reasonable.

State Laudan's two under-determination theses, and say which one he thinks threatens epistemology and why.

1. Non-uniqueness: for any theory $T$ and any evidence supporting it, there is at least one rival as well supported as $T$.
2. Egalitarian (stronger): every theory is as well supported as any of its rivals.

Only the egalitarian thesis is a threat. Non-uniqueness says a rival exists, not that it is equally good in every respect or that no further evidence or methodological consideration could separate them; methodology’s job is precisely to choose among survivors. The egalitarian thesis says there is never anything to choose on, which would make methodology idle.

Under which of Laudan's two theses does Quine's empirical under-determination fall?

The slides leave this open; the defensible answer: at most non-uniqueness. It claims a theory has at least one empirically equivalent but theoretically inequivalent rival, and Quine (1975) calls it an open question whether any such case exists. It is even weaker than non-uniqueness, since empirical equivalence is not yet equal evidential support (Laudan and Leplin). The claim sometimes read as egalitarian is Quine’s holism from Two Dogmas (“held true come what may”), which is what Laudan’s objection targets.

Define empirical under-determination (Quine 1975), and say why it is a problem for scientific realism.

Two theory formulations that are empirically equivalent (they entail the same observation sentences) but theoretically inequivalent (they differ in their theoretical sentences). The data cannot decide between them. Realism problem: if no evidence can tell which is right, which one are you a realist about?

Distinguish semantic from epistemic under-determination.

• Semantic: about meaning and interpretation, and independent of the evidence.
• Epistemic: about the empirical evidence and what it can settle.

Dualities are potential cases of semantic under-determination.

Distinguish transient under-determination from the strong thesis, and say which one is common.

Transient: the evidence available now does not decide, but more evidence later does. This is very common in scientific practice. The strong thesis (empirical under-determination) says rival formulations stay undecided by all possible observations, so more evidence would not help.

Do real cases of empirical equivalence exist? Give the positions of Laudan and Leplin, Quine, and Stanford.

• Laudan and Leplin: contrived examples always involve the relativity of motion (the impossibility of distinguishing apparent from absolute motion). Historical cases: Ptolemy vs Copernicus (which created the idea of empirical equivalence) and Einstein vs Lorentz.
• Quine (1975): whether any cases exist is an “open question”.
• Stanford (2006): critics may demand that “serious, nonsceptical, and genuinely distinct empirical equivalents” actually be produced, rather than presumed.

Upshot: the strong thesis is widely asserted and thinly evidenced.

What is Quine's "common core" point, and what three conditions must hold for under-determination to arise?

If a theory’s observation conditionals are finite, their conjunction is itself a theory formulation: it is implied by every empirically equivalent rival and conflicts with none, so it is a shared core, and nothing is under-determined. Under-determination “lurks” only where there are two formulations that:

1. are irreconcilable,
2. each imply exactly the observation conditionals plus extraneous theoretical matter,
3. and no formulation fits more tightly.

All three at once is a heavy burden, which explains why real examples are scarce.

What was Kant's view of the status of geometry and Newton's laws, and what changed in the 19th century that put pressure on it?

Geometry and Newton’s three laws are synthetic a priori: independent of experience, yet adding content beyond logic. Specific forces (the inverse-square law) and their parameters are empirical, synthetic a posteriori. Pressure: non-Euclidean geometries were shown to be consistent (Gauss, Riemann), so Euclidean geometry is no longer the only possible one.

What is Poincare's view of geometry (book and year), and what is his first argument for it?

Science and Hypothesis (1902): geometry is neither a priori nor a posteriori but conventional. We choose the geometry that describes experience most simply, but alternatives are possible. First argument: we do not perceive space as three-dimensional directly. The visual field is prima facie two-dimensional and only derivatively 3D, and tactile space could be multi-dimensional. We discover the structure of space by experiment, but that structure is not unique.

Why, for Poincare, do we call the sphere world Euclidean even though nothing forces us to?

Our senses are habituated to Euclidean space, so for us it is simpler to describe a Euclidean disk plus a physical law (bodies expand with temperature). Beings like us who grew up inside the sphere would call it non-Euclidean. There is no fact of the matter: it is a convention, like metres versus yards.

Where does the lecture land: one line each for Duhem, Quine, empirical under-determination, and dualities?

• Duhem: under-determination is real and is resolved in practice by good sense rather than logic.
• Quine: scepticism about meanings undercuts non-empirical knowledge; the web of belief defeats both dogmas and rejects the verification principle.
• Empirical under-determination: very common as the transient kind.
• Dualities: potential cases of semantic under-determination, and on De Haro’s own view not a threat to a cautious scientific realism (the lecturer’s own research, and he sets the exam).

Keep three theses apart: Duhem's thesis, the Duhem-Quine thesis, and empirical under-determination. One sentence each.

• Duhem’s thesis: a failed prediction refutes only the conjunction of hypothesis and auxiliaries, so no crucial experiment.
• Duhem-Quine thesis (holism): the bundle is the whole web of belief, so any statement can be kept true by adjusting elsewhere.
• Empirical under-determination (Quine 1975): there can be empirically equivalent but theoretically inequivalent theory formulations, so even all possible data do not decide.

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