Underdetermination of theory

Why can two incompatible theories fit every observation ever recorded, and how does a science choose between them anyway?

There is a familiar worry about what happens when a prediction fails: the failure indicts a whole bundle of assumptions and never says which member is guilty. That is a real problem, and a different one from this.

Here nothing has failed. Every prediction came out right. And still there sits a second theory, incompatible with the first, saying something else entirely about what the world is made of — and agreeing with the first about every observation anyone has made or could make. If evidence settles scientific questions, and the evidence is silent, what is left? Yet science does choose, constantly, and does not seem to be flipping coins.

Start with the clearest real case, because the abstract version invites doubt about whether such rivals exist at all. Newtonian mechanics is compatible with the universe being at absolute rest, and equally compatible with its drifting at any constant velocity you like. Newton saw this himself. The two hypotheses differ about a real physical fact and produce identical consequences for every measurement, because only relative motion shows up in the equations. That is no philosopher's contrivance; it is a corollary of the theory.

Once you have one, you can manufacture more. Take any theory and add a clause leaving its observable consequences untouched — a demon arranging matters, a world created recently complete with fossils, or simply the claim that the observable consequences hold and the unobservable machinery does not. Bas van Fraassen made the last move systematic: for any theory there is always the weaker claim that it is empirically adequate, compatible with everything the full theory predicts and committing you to far less.

So rivals are available on demand. Does that settle it? Push back on the recipe rather than the conclusion. A manufactured rival is built out of the original by attaching a clause; it inherits all its content and adds nothing. Realists say that disqualifies it as a genuine alternative — there is no rival research programme there, nothing anyone could work in. The reply, fairly, is that "genuine rival" is now carrying the whole argument and nobody has given a criterion for it.

The more damaging objection is Laudan and Leplin's (recalled from the early 1990s), and it attacks the premise. Calling two theories empirically equivalent means they have the same observational consequences — but a theory has observational consequences only with auxiliary assumptions, and those change as neighbouring sciences develop. What counts as observable changes too, whenever an instrument extends the range. So a pair equivalent today may be separated tomorrow by a link nobody had yet made, and the sweeping claim that two theories agree on all possible evidence is one nobody is positioned to establish. Empirical equivalence, on this view, is a temporary relation mistaken for a permanent one.

Grant that, and the practical question survives: today, with the evidence tied, on what basis do you choose? On the criteria scientists actually cite — simplicity, breadth of scope, consistency with well-established neighbouring theory, fruitfulness in generating new work. Kuhn set out a list of this kind and made the crucial observation about it: these are values rather than rules. They conflict, one theory being simpler while another has wider scope, and they carry no fixed weights, which is why competent people applying the same values reach different verdicts for a period.

That leaves the question that divides the field. Are the virtues evidence, or preferences? A realist argues that a virtue-guided method which kept producing successful novel predictions would be a miracle if the virtues tracked nothing true. Van Fraassen's answer, in The Scientific Image (1980), is that we should accept theories as empirically adequate and treat the extra virtues as pragmatic — reasons to use a theory, not to believe its unobservable parts. Both positions are held by serious people now, and what turns on it is concrete: whether "the best theory we have" is a claim about the world or about our tools.

The most useful correction is to keep two claims apart, because they are routinely run together under one name.

One is the holist thesis: any hypothesis can be held true come what may, by revising something else in the web. That is a claim about how failure is absorbed, argued by Duhem and pressed further by Quine in "Two Dogmas of Empiricism" (1951), and it is taken up in the companion walk-through on scientific testability. The other, the subject here, is contrastive: for a given theory there exist incompatible rivals agreeing with it on all observations. Neither entails the other. The first says evidence cannot single out the culprit; the second says evidence cannot single out the theory.

Two honesty notes. The strong contrastive thesis — rivals for every theory, agreeing on all possible evidence — has never been demonstrated; it rests on a handful of genuine cases plus a recipe for making artificial ones, and its universality is asserted rather than shown. And the Newtonian case has an instructive ending: the question of absolute rest was not resolved by new evidence but dissolved, when relativity removed the structure that made the two hypotheses distinct. That is a third way an underdetermined pair can end, and it belongs beside "evidence decides" and "the virtues decide" — sometimes the rivals stop being rivals.

• Whether the history of discarded successful theories undercuts the argument that success indicates truth.

Every term the collection defines is gathered in the glossary.