The Duhem problem can be expressed as follows:
A physicist disputes a certain law; he calls into doubt a certain theoretical point. How will be justify these doubts? From the proposition under indictment he will derive the prediction of an experimental fact; he will bring into existence the conditions under which this fact should be produced; if the predicted fact is not produced, the proposition which served as the basis of the prediction will be irremediably condemned. (Duhem, The Aim and Structure of Physical Theory, Princeton University Press. Translated from the French by Philip P. Wiener.1954, p. 184)
By means of this mode of inference we falsify the whole system (the theory as well as the initial conditions) which was required for the deduction of the statement p, i.e. of the falsified statement. Thus it cannot be asserted of any one statement of the system that it is, or is not, specifically upset by the falsification. Only if p is independent of some part of the system can we say that this part is not involved in the falsification. (Popper, The Logic of Scientific Discovery, 76)
A naive theory of science might say that when testing a theory T, if an observation-statement O is found to agree or disagree with the logical consequences of T, O either supports or refutes T. This can be expressed as follows:
- If T is true, then O is true.
- T is false.
However, theories do not exist in a vacuum. Scientists adopt unproblematical auxiliary hypotheses or theories, along with metaphysical assumptions, which I will refer to as ‘background knowledge’ (K). Since the scientist accepts a great deal of background knowledge, including conjectures about the validity of the observation report, the status of the modus tollens argument looks something like this:
- If T and K1 and K1 … and Kn is true, then O is true.
- Either T or K1 or K2 … or Kn is false.
A ‘critical experiment’, by which I mean a supposed decisive, justified falsification of a theory by appealing to an observation-report, is never as decisive as one would wish. Either the theory under examination is false, or a piece of the background knowledge, including how the test was prepared, is false. Thus, there are three possible choices the scientist can make: either they (1) protect the fundamental theory by suggesting an error in the experimental setup, (2) challenge one piece of the background knowledge, or (3) challenge the theory.
No matter the choice made by the scientist, there is no guarantee of success. The Duhem problem is the way things are, and is insurmountable to every and all philosophy of science that takes the link between testing and theory into account. Thus, criticizing any particular philosophy of science by resorting to the Duhem problem does not discredit the theory, since there are, and can be, no other approaches that eliminate the theory-dependence, even if these theories are implicit, of observation-reports. Duhem, though, provided an early methodological or heuristic to follow: he hoped that the theory, along with the background knowledge, would develop in such a way as to account for a wider range of phenomena, to ‘adhere more closely to reality’. This methodological rule — increase the range of predicted phenomena — is one of several proposed rules that, while not justifying the truth of any theory (for no justification can be found), keeps scientific practice from becoming insular or hermeneutic.
There is no logic or automatic method for determining if the theory, background knowledge, or observation-report is mistaken. There is only more work to be done. Scientists when confronted with a falsifying observation-report can adopt several very different strategies, ranging from revision or rejection of the theory, modification of background knowledge, or denial of the observation-report. Both Popper and Duhem proposed similar principles for the scientist, namely that criticism should first be directed towards the competing theories rather than background knowledge, and a check of the observation-report to determine if it is the result of experimental error.
(As an aside, I should note that while I think Popper’s demarcation criteria of falsifiability of statements — that there must exist, at least in principle, a possible conflict between a universal statement and an existential statement — has been superseded by Bartley’s demarcation criteria of the criticizability of statements — a proposal is rationally adopted if there are some significant criticisms that it has overcome, the Duhem problem does not invalidate Popper’s solution to the demarcation problem. Popper stressed in his Logic that the assumed background knowledge, along with initial conditions, are necessary in order to test a theory. The Duhem problem is only directed at any singular attempt at falsifying a theory: it’s much harder than you’d think.)
… if we take each of the two theories (between which the crucial experiment is to decide) together with all this background knowledge, as indeed we must, then we decide between two systems which differ only over the two theories which are at stake. It further overlooks the fact that we do not assert the refutation of the theory as such, but of the theory together with that background knowledge; parts of which, if other crucial experiments can be designed, may indeed one day be rejected as responsible for the failure. (Popper, Conjectures and Refutations, 1963, 112, italics mine)
Popper is on to something of importance here: there may be many cases in the history of science where two different systems differ only in the two competing theories in question. In this case, after putting aside any experimental error (this is why theories must be in principle interpersonally and repeatedly testable), it may be possible to prefer the surviving theory over the refuted theory after a crucial experiment. However, there do exist other cases where the two rival systems are divided by many assumptions. This is the kind of revolutionary science described by Kuhn’s paradigm theory.
These situations are somewhat rare and not as revolutionary as one would think, since a great amount of knowledge, even in close proximity to the revolution, remain intact. However, these are the kind of situations where a great amount of time may be needed to parse out the implications of the rival systems until one system appears to be superior to the other. This may take decades. It may be better to keep two competing theories that are presently equally corroborated by the present data than jumping the gun and choosing one over the other. Between these two extreme situations, there exist a spectrum of time and energy necessary, along with a spectrum of crucial to not-so-crucial tests that can be conducted, to resolve the problem of which rival theory is to be preferred.
An ad hoc adjustment or ‘saving throw’ is an addition or change to background knowledge that weaken the chances to put it to the test. Any sort of ad hoc adjustment immunizes the theory from criticism and reduces it content. There can be no change if the ‘hard core’ of a theory is allowed to be protected from criticism. Since it is always possible to modify theories so as to ‘save’ them from refutation, Popper appealed to the methodological decision not to avoid refutations.
Auxiliary hypotheses may be introduced, as Popper and Duhem point out, if they can be tested independently of the theory they are intended to ‘save’. For instance, the auxiliary hypothesis of the existence of the planet Neptune was introduced to account for the irregularities in the orbit of Uranus. This addition to the background knowledge is not ad hoc in nature, since the location of the hypothetical planet was predicted with great precision. Thus, Neptune was located rapidly by two independent observers, making a significant problem for Newtonian theory into a vindication for the theory when an exactly predicted unobserved planet was put to the test. In short, the introduction of an auxiliary hypothesis strengthens the theoretical system only if it increases the chances to put it to the test.
Popper adopts this preference for auxiliary hypotheses over ad hoc adjustments not due to any sort of justification, but as a tentative proposal. It very well may be the case that in some instances, ad hoc adjustments may save a true theory; however, there would be no way to determine whether or not the theory is true or false in this case, since it has made it verboten to test it in some way. If scientists want each progressive theory to explain more about the world than the theories they supersede, any sort of adjustment to a theory must explain more about the world, that is, be as testable as possible.