Philosophy of Science

I

Introduction

Philosophy of Science, investigation into the general nature of scientific practice. The questions considered in the philosophy of science include: how scientific theories are developed, assessed, and changed; and whether science is capable of revealing the truth about hidden entities and processes in nature. The subject is as old and as widespread as science itself. Some scientists have taken a keen interest in the philosophy of science and a few, such as Galileo, Isaac Newton, and Albert Einstein, have made important contributions. Most scientists, however, have been content to leave the philosophy of science to the philosophers, preferring to get on with doing science rather than spending too much time considering in general terms how science is done. Among philosophers, the philosophy of science has always been a central subject. In the Western tradition, the most important figures before the 20th century include Aristotle, René Descartes, John Locke, David Hume, Immanuel Kant, and John Stuart Mill. Much of the philosophy of science is indistinguishable from epistemology, the theory of knowledge, a subject considered by virtually every philosopher.

II

The Problem of Induction

The results of observation and experiment provide the evidence for a scientific theory, but they cannot prove that the theory is correct. Even the most modest empirical generalization, say, that all water boils at the same temperature, goes beyond what can be strictly deduced from the evidence. If scientific theories did not say more than the evidence used to support them, they would have little use. They could not be used to predict the course of nature, and they would have no explanatory power.

The non-demonstrative or inductive link between evidence and theory raises one of the central problems in the theory of knowledge, the problem of induction, given its classic formulation by the 18th-century Scottish philosopher David Hume. Hume considered simple predictions based on past observations, for example, the prediction that the Sun will rise tomorrow, given that it has been observed to rise in the past. Life would be impossible without anticipating the future, but Hume constructed a remarkable argument to show that these inferences are rationally indefensible. This conclusion may be incredible, but Hume's argument has yet to be conclusively answered. He admitted that inductive inferences have been at least moderately reliable so far, or we would not be alive to consider the problem, but he claimed that we can only have a reason to continue to trust induction if we have some reason to believe that induction will continue to be reliable in future. Hume then argued that no such reason is possible. The nub of the problem is that the claim that induction will be reliable in future is itself a prediction, and so could only be justified inductively, which would beg the question. In particular, to argue that induction will probably work in future because it has worked in the past is to argue in a circle, assuming induction in order to justify it. If this sceptical argument is sound, inductive knowledge appears impossible, and there is no rational argument we can give to dissuade someone who takes the view, say, that it is safer to leave the room by the window than by the door.

The problem of induction applies directly to science. Without some answer to Hume's argument, there is no reason to believe any part of a scientific theory that goes beyond what has actually been observed. The point is not that scientific theories are never absolutely certain: that is or ought to be a truism. The point is rather that we have no reason whatever for supposing, say, that water we have not tested will boil at the same temperature as water we have tested. Philosophers have made a sustained effort to resist this sceptical conclusion. Some have tried to show that scientists' standards for weighing evidence and making inference are somehow rational by definition; others that the past success of our inductive policies can be used to justify their future use without vicious circularity. A third approach is to argue that, while we cannot show that induction will work in future, we can show that it will work if any method of prediction does, so we are rational to use it. More recently, a number of philosophers have argued that the actual reliability of our inductive practices, something that Hume does not deny, is sufficient to yield inductive knowledge without a further requirement that the reliability be justified.

Karl Popper has offered a more radical solution to the problem of induction, a solution that forms the basis for his influential philosophy of science. According to Popper, Hume's argument that inductive inferences are rationally indefensible is simply correct. This does not, however, threaten the rationality of science, whose inferences are, appearances to the contrary, exclusively deductive. Popper's central idea is that while the evidence will never entail that a theory is true, it may refute the theory, entailing that it is false. Thus, no number of black ravens entails that all ravens are black, but a single white raven entails that the generalization is false. Scientists can thus know that a theory is false, without recourse to induction. Moreover, faced with a choice between two competing theories, they can exercise a rational preference, if one of the theories has been refuted but the other not, since it is rational to prefer a theory that might be true over one known to be false. Induction never enters the picture, so Hume's argument is defused.

This ingenious solution to the problem of induction faces a number of objections. If it were correct, scientists would never have any reason to believe that any of their theories or hypotheses are even approximately correct or that any of the predictions drawn from them are true, since these judgements could only be inductively justified. Moreover, it appears that Popper's position does not even allow scientists to know that a theory is false, since, according to him, the evidence that might contradict a theory can itself never be known to be correct. Unfortunately, the inductive inferences that scientists make seem neither avoidable nor justifiable.

III

The Problem of Description

Although Hume's discussion of the justification of induction is a milestone in the history of philosophy, he only offered a crude description of how, for better or worse, inductive practices actually work. He held that inductive inference is just habit formation. Having seen many black ravens, we tacitly apply the rule of “more of the same” and expect that the next raven we encounter will also be black. This clearly does not do justice to scientists' inferential practice, since they infer from the observation of entities of one sort to the existence and behaviour of entities of a quite different and often unobservable sort. “More of the same” will not take scientists from what is seen in the laboratory to the existence of electrons or electromagnetic fields. How then do scientists test their theories, weigh the evidence, and make inferences? This is the problem of description in contrast to Hume's problem of justification.

The descriptive problem may seem easy to solve: just ask scientists to describe what they do. This is an illusion. Scientists may be good at weighing evidence, but they are not good at giving a principled account of how they do it. This is no more surprising than the fact that native speakers of the English language are largely incapable of specifying the principles by which they distinguish grammatical from ungrammatical sentences. What is more surprising is how difficult the descriptive problem of induction has been to solve, even for philosophers of science who have devoted their careers to it.

Perhaps the most popular account of how scientific theories are tested is the hypothetico-deductive model, according to which theories are tested by checking the predictions they entail. Evidence that shows a prediction to be correct supports the theory, evidence incompatible with the prediction refutes the theory, and any other evidence is irrelevant. If scientists have enough supporting evidence and no refuting evidence, they may infer that the tested theory is correct. This model, rough though it is, seems at first to be a reasonable reflection of scientific practice, but it is beset with difficulties. Most of these show that the hypothetico-deductive model is over-permissive, treating irrelevant evidence as if it provided support. To mention just one problem, most scientific theories do not entail any observable consequences on their own, but only in conjunction with various background assumptions. Without some restriction on admissible assumptions, the model will permit any observation to count as evidence for almost any theory. This is an absurd result, but it is surprisingly difficult to specify the appropriate restrictions.

Given the difficulties facing the hypothetico-deductive model, some philosophers have lowered their sights and attempted to give a better model of inductive support for a more limited range of cases. The simplest case is an empirical generalization such as “all ravens are black”. Here it seems clear that black ravens support the hypothesis, non-black ravens refute it, and non-ravens are irrelevant. Yet even this modest account has its problems. Suppose we apply the same sort of account to the slightly odd-sounding hypothesis that all non-black things are not ravens. Non-black non-ravens (white flowers, for example) support it, non-black ravens would refute it, and black objects are irrelevant. The trouble comes when we notice that this hypothesis is equivalent to the original raven hypothesis: to say that all non-black things are non-ravens is just an unusual way of saying that all ravens are black. So surely whatever evidence supports the one hypothesis supports the other? This leaves us, however, with the extremely odd result that the observation of white flowers provides evidence that all ravens are black. This raven paradox seems a logical trick, but it has proved remarkably difficult to resolve.

IV

Explanation

Recent work on the problem of describing inferential practices in science has attempted to avoid the weaknesses of the hypothetico-deductive model by going beyond logical relations to account for the bearing of evidence on theory. Some accounts attempt to describe how the plausibility of theories and hypotheses may vary in advance of testing, and have linked this idea to a formal calculus of probabilities. Others appeal to the specific content of hypotheses under test, especially the causal claims many of them make. In the 19th century, John Stuart Mill gave an account of inferences from effects to causes that can be expanded to provide a model of scientific inference. One way the expansion has been attempted is by appeal to the notion of explanation. The basic idea of the model of “inference to the best explanation” is that scientists infer from the available evidence to the hypothesis that would, if correct, provide the best explanation of that evidence.

If “inference to the best explanation” is to be more than a slogan, however, some independent account of scientific explanation is required. The starting point for most contemporary philosophical work on the nature of scientific explanation is the deductive-nomological model, according to which a scientific explanation is a deduction of a description of the phenomenon to be explained from a set of premises that includes at least one law of nature. Thus, one might explain why the mercury in a thermometer rose by citing the rise in temperature and a law linking temperature and volume for the metal. One challenge for this account is to question what makes something a law of nature, another central topic in the philosophy of science. Not all true generalizations are laws of nature. For example, the statement that all gold spheres have a diameter of less than ten miles is presumably true but is not a law. Genuine laws of nature appear to have a kind of necessity that the statement about gold spheres lacks. They describe not just how things actually behave but how in some sense they must behave. It is, however, far from obvious how that notion of necessity should be articulated.

Another difficulty for the deductive-nomological model of explanation is that, like the hypothetico-deductive account of testing to which it bears a striking structural similarity, the model is too permissive. For example, the period (the duration of one swing) of a particular pendulum can be deduced from the law that relates to the period and length of pendulums in general, together with the length of that particular pendulum. The length of the pendulum is normally regarded as explaining the period. However, the deduction can be carried out in the reverse direction: it is possible to calculate the length of the pendulum if its period is known. But the period is not normally regarded as explaining the length of the pendulum. So while the deduction works in both directions, explanation is regarded as going in one direction only. Difficulties of this sort have led some philosophers to develop causal models of explanation, according to which we explain events by giving information about their causal histories. This approach is attractive, but it calls for an analysis of causation, a project that faces many of the same difficulties as that of analysing laws of nature. In addition, more needs to be said about which causes of an event explain it. The Big Bang is presumably part of the causal history of every event, but does not provide an adequate explanation for most of them. Once again, there is a problem of excessive permissiveness.