By Paul Newall (2005)
A familiar sight in the philosophy of science is reference to the underdetermination of theories by the available evidence. In this short paper we will explore some examples of this phenomenon and the reasons why it is posited as a problem.
In 1543, Nicholas Copernicus published his De revolutionibus orbium celestium and, in the years that followed, some philosophers and astronomers took up the idea of a Sun-centred universe with a moving Earth. However, when Cardinal Bellarmine had occasion to write to Foscarini about whether or not Galileo and others had been able to demonstrate the truth of heliocentrism, he suggested that
... it seems to me that Your Reverence and Galileo did prudently to content yourself with speaking, and not absolutely, as I have always believed that Copernicus spoke. For to say that, assuming the earth moves and the sun stands still, all the appearances are saved better than with eccentrics and epicycles, is to speak well; there is no danger in this, and it is sufficient for mathematicians.
He was discussing the notion that the Copernican system was able to save the appearances; that is, that it was possible to explain what was observed in the heavens on the basis of Copernicus’ theory. Although Bellarmine allowed that this theory could be considered better than the "eccentrics and epicycles" of the Ptolemaic/Aristotelian system, in fact it employed approximately the same number of these devices. Although Galileo was able to point to his telescopic work, this was unable to provide the demonstration he sought. The judgement of the day, then, was that it was impossible to choose between the Copernican and the Ptolemaic/Aristotelian systems on an empirical basis; and this is an assessment that philosophers and historians of science agree on today.
We call this situation underdetermination: the available data do not permit us to make a decision between two (or more) rival theories. Although some thinkers have suggested that this is only a minor problem, since it occurs only rarely, this is not the case. In particular, if we consider gravitational theories or the situation in contemporary physics since the advent of quantum theory, this position is untenable. Nevertheless, it is important to clarify the difficulty: underdetermination is found when we compare two large-scale theories, not isolated ones. This is because when we talk about a "theory", we do not mean (and cannot mean) a singleton, considered on its own. Following an argument from Quine, our theories are always interconnected, mutually supporting one another. In particular, any theory needs a host of auxiliary hypotheses in order for us to use it, which forms a criticism of methodological falsificationism.
Given that sometimes theories are undetermined, then, how can we decide between them? An obvious answer, of course, is not to decide at all. If we cannot find a way to make a demarcation then we could simply take an agnostic position and admit we do not know which is "better". In that case, we could divide our efforts between the two (or more) and see if there is subsequently a difference that comes to light as they are developed further. The is sometimes called methodological pluralism or the proliferation of theories.
A second response is to realise that empiricism does not hold the status once ascribed to it: we do not accept or reject theories based solely on the evidence for them but also on account of many non-empirical criteria, such as parsimony; internal consistency; beauty (for example, Copernicus’ certainty that a Sun-centred system was more aesthetically appealing); explanation; the ability to make novel predictions; and so on. This does not answer underdetermination so much as accept it as a limitation on empiricism, which can thus only take us so far in the matter of theory evaluation and choice.
The recognition that evidence is not the only heuristic we employ in deciding between theories allows us to distinguish between two forms of underdetermination: strong and weak. The first of these tells us that there is no way to distinguish between theories with the same observable consequences – called empirical equivalence – and points to the existence of an infinity of possible theories consistent with any finite data set. For example, the theories "general relativity" and "general relativity plus 'New Zealand will win the next Rugby World Cup'" are equally supported, but their comparison seems absurd.
Indeed, strong underdetermination is typically rejected because it fails to note that we do not claim to be able to choose between empirically equivalent theories on the basis of empirical criteria, which is impossible by definition. Moreover, it relies on an implicit separation of theory and observation: when we say that the evidence underdetermines the theory choice, we run up against theory-ladenness. Since we cannot distinguish between theory and observation in a straightforward fashion, we cannot appeal to or rely on theory-neutral observations and say that these disallow the possibility of making a choice. After all, the observations that give us this problem of underdetermination in the first place are themselves theory-laden. In brief, then, we cannot say that underdetermination makes theory choice impossible because we already use theory in obtaining the evidence that leads to underdetermined theories to begin with.
The combination of this limitation and untenable theory/observation distinction makes strong underdetermination too bold a claim.
The second form of underdetermination acknowledges these difficulties but makes a weaker claim; that is, that it is always possible to construct alternative theories which are empirically equivalent and also share many of the characteristics we desire in scientific theories. For example, suppose that a theory T1 represents the entirety of science at a given time and that P stands for the set of all observable phenomena – observable whether "naturally" or by extension using instruments. Assume then that T2 is a rival theory that has the same consequences in P. It follows that T1 and T2 are underdetermined and – more importantly – that no amount of advance in instrumentation will change the situation, since we can always construct a similar argument.
Another instance of underdetermination to concern ourselves with is that provided by Goodman’s New Riddle of Induction, discussed when looking at confirmation. By applying predicates like grue we can find theories that agree empirically to date but make differing predictions at some point in the future. In general, weak underdetermination is the recognition of the limits of evidentialism, the notion that we hold to our ideas insofar as they are supported by evidence.
To summarise, underdetermination is almost an acceptance that we are creative in our explanations and can typically find more than one for a given puzzle. It speaks against a naive form of empiricism and is only a problem for those who suppose that there is nothing more to science and scientific theories than an appeal to data.