Underdetermination is a relation between evidence and theory. More accurately, it is a relation between the propositions that express the (relevant) evidence and the propositions that constitute the theory.
The claim that evidence underdetermines theory may mean two things: first, that the evidence cannot prove the truth of the theory, and second, that the evidence cannot render the theory probable.
Let us call the first deductive underdetermination and the second inductive (or ampliative) underdetermination. Both kinds of claims are supposed to have a certain epistemic implication, namely that belief in theory is never warranted by the evidence. This is the underdetermination thesis.
Deductive underdetermination is pervasive in all interesting cases of scientific theory. If the theory is not just a summary of the evidence, the evidence cannot determine, in the sense of proving, the theory. For instance, no finite amount of evidence of the form Aai & Bai can entail an unrestricted universal generalization of the form All A’s are B.
Deductive underdetermination rests on the claim that the link between evidence and (interesting) theory is not deductive. What is the epistemic problem it is supposed to create? Given that the link is not deductive, it is claimed that we can never justifiably believe in the truth of a theory, no matter what the evidence is.
However, it would be folly to think that deductive underdetermination creates a genuine epistemic problem. There are enough reasons available for the claim that belief in theory can be justified even if the theory is not proven by the evidence: Warrant-conferring methods need not be deductive.
Deductive underdetermination speaks against simplistic accounts of the hypothetico-deductive method, which presuppose that the epistemic warrant for a theory is solely a matter of entailing correct observational consequences. Two or more rival theories (together with suitable initial conditions) may entail exactly the same observational consequences.
Given the above presupposition, it follows that the observational consequences cannot warrant belief in one theory over its rivals. Though simplistic accounts of the hypothetico-deductive method need to be jettisoned, there are ways to meet the challenge of deductive underdetermination, even if we stay close to hypothetico-deductivism.
Since theories entail observational consequences only with the aid of auxiliary assumptions, and since the available auxiliary assumptions may change over time, the set of observational consequences of a theory is not circumscribed once and for all.
Hence, even if, for the time being, two (or more) theories entail the same observational consequences, there may be future auxiliary assumptions such that, when conjoined with one of them, they yield fresh observational consequences that can shift the evidential balance in favor of it over its rivals.
Besides, a more radical (though plausible) thought is that theories may get (indirect) support from pieces of evidence that do not belong to their observational consequences.
Inductive underdetermination takes for granted that any attempt to prove a theory on the basis of evidence is futile. Still, it is argued, no evidence can confirm a theory or make it probable, or no evidence can confirm a theory more than its rivals. This claim is rather odd. In all its generality, it is a recapitulation of inductive skepticism.
If induction lacks justification, then no inductively established theory is warranted by the evidence. Yet induction does not lack justification. In any case, according to recent externalist-reliabilist theories of justification, belief in theory is justified if induction is reliable; and there is no argument that it is not.
If inductive scepticism is set aside, inductive underdetermination must relate to problems with the theory of confirmation. For on any theory of confirmation, the evidence (even if it is restricted to observational consequences) can render a theory probable or more probable than its rivals.
That is, the evidence can raise the probability of a theory. So inductive underdetermination must rest on some arguments that question the confirmatory role of the evidence vis-à-vis the theory. There is a battery of such arguments, but they may be classified under two types.
The first capitalizes on the fact that no evidence can affect the probability of the theory unless the theory is assigned some nonzero initial probability. In fact, given the fact that two or more rival theories are assigned different prior probabilities, the evidence can confirm one more than the others, or even make one highly probable.
The challenge, then, is this: Where do these prior probabilities come from? A total denial of the legitimacy of any prior probabilities would amount to inductive skepticism. Inductive underdetermination would be inductive skepticism. The more interesting version of inductive underdetermination does not challenge the need to employ prior probabilities, but rather their epistemic credentials.
If, it is argued, prior probabilities have epistemic force, then the evidence can warrant a high degree of belief in a theory (or greater degree of belief in a theory than its rivals). But, it is added, how can prior probabilities have any epistemic force?
The subjective Bayesians’ appeal to subjective prior probabilities (degrees of belief) accentuates rather than meets this challenge. Bayesians typically argue that, in the long run, the prior probabilities wash out: even widely different prior probabilities will converge, in the limit, to the same posterior probability, if agents conditionalize on the same evidence.
But this is scant consolation because, apart from the fact that in the long-run we are all dead, the convergence-of-opinion theorem holds only under limited and very well-defined circumstances that can hardly be met in ordinary scientific cases. The alternative is to claim that prior probabilities have epistemic force because they express rational degrees of belief, based, for instance, on plausibility or explanatory judgements.
This claim faces many challenges, but its defense might well be necessary for blocking the epistemic implications of inductive underdetermination. In its favor, it can be said that rational belief in theory is not solely a matter of looking for strict observational evidence.
The second type of argument rests on the claim that theories that purport to refer to unobservable entities are, somehow, unconfirmable. The problem is supposed to be that since there cannot be direct observational access to unobservable entities, no observational evidence can support the truth of a theory that posits them, and no evidence can support a theory more than others that posit different unobservable entities.
The distinctive element of the second type of argument is that the resulting inductive underdetermination is selective. It does not deny that observational generalisations can be confirmed. Hence, it does not deny that the evidence can confirm or render probable observational theories. It denies that the same can be the case for theories that refer to unobservable entities.
Even if a sharp distinction between observable and unobservable entities were granted (though it is by no means obvious that it should), this selective inductive underdetermination has a bite only if the methods that lead to, and warrant, belief in observable entities and observational generalizations are different from the methods that lead to, and warrant, belief in theories that posit unobservable entities.
Yet the methods are the same. In particular, explanatory considerations play an indispensable role in both cases. In the end, this kind of selective inductive underdetermination undermines itself: it either collapses into inductive skepticism or has no force at all.
It is commonly argued that there can be totally empirically equivalent theories— that is, theories that entail exactly the same observational consequences under any circumstances.
In its strong form, this claim (let’s call it the Empirical Equivalence Thesis, EET) asserts that any theory has empirically equivalent rivals (some of which might be hitherto unconceived). EET is an entry point for the epistemic thesis of total underdetermination: that there can be no evidential reason to believe in the truth of any theory.
But there is no formal proof of EET, though a number of cases have been suggested ranging from Descartes’ “evil demon” hypothesis to the hypothesis that for every theory T there is an empirically equivalent rival asserting that T is empirically adequate yet false, or that the world is as if T were true.
One can, of course, argue that these rival hypotheses have only philosophical value and drive only an abstract philosophical doubt. In science, it is often hard to come by just one totally empirically adequate theory, much less a bunch of them.
Yet it seems that there is a genuine case of empirical equivalence of theories of quantum mechanics. Alternative interpretations of the quantum-mechanical formalism constitute empirically equivalent but different theories that explain the world according to different principles and mechanisms.
The most typical rivalry is between the orthodox understanding of quantum theory—the “Copenhagen interpretation,” according to which a particle cannot have a precise position and momentum at the same time—and the Bohmian understanding of quantum theory—the hidden-variables interpretation, according to which particles always have a definite position and velocity, and hence momentum.
On Bohm’s theory, particles have two kinds of energy: the usual (classical) energy and a “quantum potential” energy. More recently, there have been three particularly well-developed theories (the Bohmian quantum mechanics, the many-worlds interpretation, and the spontaneous-collapse approach) such that there is no observational way to tell them apart.
And it seems that there cannot be an observational way to tell them apart. This situation is particularly unfortunate, but one may respond that the ensued underdetermination is local rather than global; hence the possible skepticism that follows is local.
The Duhem-Quine thesis has been suggested as an algorithm for generating empirically equivalent theories. Briefly put, this thesis starts with the undeniable premise that all theories entail observational consequences only with the help of auxiliary assumptions and concludes that it is always possible that a theory, together with suitable auxiliaries, can accommodate any recalcitrant evidence.
A corollary, then, is that for any evidence and any two rival theories T and T’, there are suitable auxiliaries A such that T’ and A will be empirically equivalent to T (together with its own auxiliaries). Hence, it is argued, no evidence can tell two theories apart. It is questionable that the Duhem-Quine thesis is true. There is no proof that nontrivial auxiliary assumptions can always be found.
But let us assume, for the sake of the argument, that it is true. What does it show? Since the Duhem-Quine thesis implies that any theory can be saved from refutation, it does create some genuine problems to a falsificationist (Popperian) account of theory testing— that is, the view that theories are tested by attempting to refute them.
If attempted refutations are the sole test for theories, two incompatible theories that are not refuted by the evidence are equally well tested by it. But the Duhem-Quine thesis does not create a similar problem to an inductivist. From the fact that any theory can be suitably adjusted so that it resists refutation it does not follow that all theories are equally well confirmed by the evidence.
An inductivist can argue that the empirical evidence does not lend equal inductive support to two empirically congruent theories. It is not necessarily the case that the auxiliary assumptions that are needed to save a theory from refutation will themselves be well supported by the evidence.
Since it is reasonable to think that the degree of support of the auxiliary assumptions associated with a theory is reflected in the degree of support of the theory, it follows that not all theories that entail the same evidence are equally well supported by it.
EET has generated much philosophical discussion. An argument favored by the logical positivists is that such cases of total underdetermination are illusions: the rival theories are simply notational variants. This move presupposes that theories are not taken at face value.
For anyone who does not subscribe to a verificationist criterion of meaning, this move is moot. It does make sense to say that there can be distinct but totally empirically equivalent theories. The hard issue is not to exclude their possibility on a priori grounds but to find ways to distinguish their epistemic worth, should we find ourselves in such a predicament.
Another move, favored by Quine, is to go for pragmatism: The balance is shifted to the theory we (our community) favor, simply because it is our theory. This raises the spectre of epistemic relativism. Yet another move is to go for skepticism: among rival totally empirically equivalent theories one is true, but we cannot possibly come to know or justifiably believe which this is.
This skeptical answer might be supplemented with some differential stance towards the rival theories, but this differential treatment will not be based on epistemic reasons but rather on pragmatic considerations.
Indeed, social constructivists have seized upon this in order to claim that social, political, and ideological factors break observational ties among theories: hence, they argue, belief in theory is socially determined.
The general problem with the skeptical move is that it rests on a restricted account of what counts as evidence (or reason) for justified belief; it counts only observations as possible epistemic reason for belief. But rational belief may well be a function of other epistemic reasons—for instance, the theoretical virtues that a theory possesses.
This last thought ushers in yet another possibility: that empirically equivalent theories may well differ in their explanatory power. Insofar as explanatory power can offer epistemic credentials to a theory, it can break supposed epistemic ties among totally empirically equivalent rivals.
This move makes rational belief a more complex affair and tallies with the intuitions of scientific and common sense. Yet it faces the problem of justifying the claim that theoretical virtues are epistemic reasons— that is, that a virtuous theory (a theory with great explanatory power) is more likely to be true than a less virtuous one.
This is not an unsolvable problem. There are, broadly, two ways to tackle it. One is to argue (rather implausibly) that some theoretical virtues are constitutive marks of truth. The other is to argue for a broad conception of evidence that takes the theoretical virtues to be empirical and contingent marks of truth.
A central element in this latter argument is that theories can get extra credence by entailing novel predictions—that is, predictions such that information about the predicted phenomenon was not previously known and not used in the construction of the theory. In the end, the epistemic relations between evidence and theory cannot be exhausted by their logico-semantic relations.