POPPER’S THEORY OF SCIENCE
Popper’s arguments for his claim that empirical character is empirical refutability are very compelling. Logically, observation reports can contradict theories but not entail them in any way.
Philosophically, Popper’s view is the doctrine of learning from experience as a special case of learning from mistakes, of the critical method. Socially, it presents students of nature as human rather than as unerring supermen. Historically, it opens wide vistas of new studies of the history of science uncharted by the modern science textbook. Popper’s greatest contribution to the philosophy of science seems to me to be rooted in the simple idea that since empirical character is empirical refutability, scientific research is a special case of Socratic dialogue. But I deny that the empirical character of science is all that makes science what it is.It is not difficult to find empirical developments, i.e., empirical refutations, outside the field of science. Thales’s metaphysical doctrine (“all is water”) was refuted empirically when water was first decomposed; Moebius (as I. Lakatos would say) may have refuted empirically the mathematical theory “all surfaces have two sides”; Faraday refuted empirically some spiritualistic superstitions; Marx’s prophecy about the geographical location of the socialist revolution has been refuted by his Russian followers; and this amounts to the refutation of his materialism since it entails the valuelessness of imaginative ideas; the very important philosophical doctrine about the universality of common sense (which even Duhem still advocated) is empirically refutable by comparative studies. Necessarily, either such cases should be viewed as scientific or Popper’s proposal should be considered inadequate. My choice is the latter: I propose to use Popper’s convention as a convention concerning the empirical character of science, not concerning empirical science as such.
There is no difficulty in admitting that daily experience, as well as some developments of mathematics (or metaphysics, or any other field of intellectual or practical development), manifest a certain empirical character, even though they do not belong to empirical science. Empirical science manifests its empirical character more systematically than mathematics, and it manifests other characteristics as well, which are lacking in mathematics.But what about the claim that theories manifesting empirical character, i.e., refutable theories, also necessarily manifest the other characteristics of science, i.e., they have informative content, explanatory power, simplicity, abstractness, generality, and precision? I simply reject this claim. As I have said earlier, I interpret a great deal of Popper’s discussion in his classical work to be an attempt to support this claim. I consider the value of that part of his discussion as a valid criticism of his opponents and as stimulating heuristic material, but as very far from being a finished product.
To maintain my thesis I must contradict Popper here. He would say that research is conducted toward the finding and the testing of highly testable hypotheses, whereas I say that it is very often conducted toward the finding and the testing of metaphysically relevant hypotheses. And as a rule, I shall later show, research tends to begin with hypotheses which have a low degree of testability or are not testable at all. Consequently investigators often have to use great ingenuity to test a barely testable hypothesis, and even first improve a hypothesis to the point of rendering it testable to some degree. If the aim of science were merely producing testable hypotheses and then testing them such procedures would be irrational. But the aim of science, or rather the aims of science, are different.
The aim of science is to attempt to comprehend the world rationally, as we all agree (including the positivists who should disagree).
But this is too vague. What is the rational method and what is comprehension? Rationality, said Popper, is manifest in empirical tests. He later generalized this: the rational method is the critical method. Is metaphysics rationally debatable? Yes. I shall argue that the study of a hypothesis of a low degree of testability is often conducted with a view to criticizing some metaphysical theory upon which it may have some bearing. So much for rationality. As to comprehension, Popper views it as deductive explanation, and he has suggested that explanatory power goes with refutability. I deny that explanation is the only method of comprehension. As I shall show later, the attempt to coordinate our various explanations within one metaphysical framework is not explanation, yet it is, in some weaker sense, an attempt at comprehension. Moreover, I deny that explanatory power is always dependent on refutability. Already in the last section of his great book Popper has noted that some theoretical systems may have some explanatory power and yet be untestable. I have already mentioned examples of refuted theories of little or no explanatory power.Degrees of testability are, I think, of little practical importance. All that matters is that we may test in at least one way an interesting theory. According to Popper, there are two factors contributing to the degree of testability of a theory, the number of possible events which may refute that theory, and the probability of each potential refutation. To my mind the possibility of observing the next refuting event is all that matters, not the number of possible refutations. As it is the number of all excluded possibilities which is the content of the hypothesis, content is not the same as practical testability. Ad hoc explanations have some empirical content yet are untestable. Explanatory power is not content, and not even truthcontent (i.e., that part of a theory’s content which is true), but I should say (in agreement with Leibniz’s idea as I understand it), known-truthcontent (i.e., the overlap of a theory’s content with the class of true observation-reports).
And high explanatory power is not the sole characteristic of a satisfactory explanation. As I have learned from Popper himself, a satisfactory explanation must be independently testable. Thus, Weyl’s theory which unifies Maxwell’s and Einstein’s has a high explanatory power and a high degree of testability, but no known independent testability, and thus it is not considered scientific. Simplicity depends not only on explanatory power and the paucity of parameters, as Popper mentions in his early work, but also on depth, as he now says. Nor does abstractness go together with universality: Boyle’s law is more general but less abstract than the theory of consumers’ demand, and the Heitler-London theory is more abstract but less general than Schroedinger’s theory.The result is pluralism: we may admire one theory for its boldness, another for its explanatory power, another for its elegance; and yet another, I suggest, for the light it throws on some topical metaphysical issues.
There seem to be very good reasons for Popper’s correlation of a higher degree of testability with a higher degree of explanatory power, etc., and these reasons are of heuristic value. One reason of Popper’s is this: If one theory explains another theory, it is obviously not less refutable than the other. If one theory explains another theory as a first approximation, then it is more precise, and a higher degree of precision goes together with a higher degree of testability. This is so because a more precise theory excludes more (logically) possible states of affairs, thereby possessing both a higher informative content and a better (a priori) chance of being refuted, or a lesser a priori probability. These arguments are valuable but insufficient and partly incorrect.
In his classical paper ‘The Nature of Philosophical Problems and Their Roots in Science’ Popper has given an admirable account of Pythagoras’s metaphysics and the history of its refutation. When I read this excellent essay I decided to study under Popper; so the title of the present chapter adverts to his, partly for sentimental reasons. Yet, perhaps because my prejudice in favor of metaphysics came first, I was unhappy about his taking Pythagorean metaphysics to be scientific. Since his reason was that this metaphysics was refuted, I was bound to examine his refutability criterion for the demarcation of science. I now propose his empirical refutability criterion to be the criterion of empirical character, not of empirical science as such. Empirical science is the set of highly informative and simple explanations which exhibit independent empirical character - satisfactory explanations, for short. I owe this idea to Popper himself: in his lecture courses Popper presents science rather in this way than in the way he does in his classical Logic of Scientific Discovery.
VI.