Category: The Logic of Scientific Discovery

Routledge: 2002.

Science: deductive testing

Whatever may be our eventual answer to the question of the empirical basis, one thing must be clear: if we adhere to our demand that scientific statements must be objective, then those statements which belong to the empirical basis of science must also be objective, i.e. inter-subjectively testable. Yet inter-subjective testability always implies that, from the statements which are to be tested, other testable statements can be deduced. Thus if the basic statements in their turn are to be inter-subjectively testable, there can be no ultimate statements in science: there can be no statements in science which cannot be tested, and therefore none which cannot in principle be refuted, by falsifying some of the conclusions which can be deduced from them.

We thus arrive at the following view. Systems of theories are tested by deducing from them statements of a lesser level of universality. These statements in their turn, since they are to be inter-subjectively testable, must be testable in like manner — and so ad infinitum.

It might be thought that this view leads to an infinite regress, and that it is therefore untenable. In section 1, when criticizing induction, I raised the objection that it may lead to an infinite regress; and it might well appear to the reader now that the very same objection can be urged against that procedure of deductive testing which I myself advocate. However, this is not so. The deductive method of testing cannot establish or justify the statements which are being tested; nor is it intended to do so. Thus there is no danger of an infinite regress. But it must be admitted that the situation to which I have drawn attention — testability ad infinitum and the absence of ultimate statements which are not in need of tests — does create a problem. For, clearly, tests cannot in fact be carried on ad infinitum: sooner or later we have to stop. Without discussing this problem here in detail, I only wish to point out that the fact that the tests cannot go on for ever does not clash with my demand that every scientific statement must be testable. For I do not demand that every scientific statement must have in fact been tested before it is accepted. I only demand that every such statement must be capable of being tested; or in other words, I refuse to accept the view that there are statements in science which we have, resignedly, to accept as true merely because it does not seem possible, for logical reasons, to test them. [25-6]

Consistency is paramount

A consistent system … divides the set of all possible statements into two: those which it contradicts and those with which it is compatible. (Among the latter are the conclusions which can be derived from it.) This is why consistency is the most general requirement for a system, whether empirical or non-empirical, if it is to be of any use at all.

Besides being consistent, an empirical system should satisfy a further condition: it must be falsifiable. The two condi­tions are to a large extent analogous. Statements which do not satisfy the condition of consistency fail to differentiate between any two statements within the totality of all possible statements. Statements which do not satisfy the condition of falsifiability fail to differentiate between any two statements within the totality of all possible empirical basic state­ments. [72-3]

Natural laws as prohibitions

The theories of natural science, and especially what we call natural laws, have the form of strictly universal statements; thus they can be expressed in the form of negations of strictly existential statements, or, as we may say, in the form of non-existence statements (or ‘there-is-not’ statements). For example, the law of conservation of energy can be ex­pressed in the form: ‘There is no perpetual motion machine’, or the hypothesis of the electrical elementary charge in the form: ‘There is no electrical charge other than a multiple of the electrical elementary charge’.

In this formulation we see that natural laws might be compared to ‘proscriptions’ or ‘prohibitions’. They do not assert that something exists or is the case; they deny it. They insist on the non-existence of certain things or states of affairs, proscribing or prohibiting, as it were, these things or states of affairs: they rule them out. And it is precisely because they do this that they are falsifiable. If we accept as true one singular statement which, as it were, infringes the prohibition by asserting the existence of a thing (or the occurrence of an event) ruled out by the law, then the law is refuted. (An instance would be, ‘In such-and-such a place, there is an apparatus which is a perpetual motion machine’.) [48]

The asymmetry between verifiability and falsifiability

Again, the attempt might be made to turn against me my own criticism of the inductivist criterion of demarcation; for it might seem that objections can be raised against falsifiability as a criterion of demarcation similar to those which I my­self raised against verifiability.

This attack would not disturb me. My proposal is based upon an asymmetry between verifiability and falsifiability; an asymmetry which results from the logical form of universal statements. For these are never derivable from singular statements, but can be contradicted by singular statements. Consequently it is possible by means of purely deductive inferences (with the help of the modus tollens of classical logic) to argue from the truth of singular statements to the falsity of universal statements. Such an argument to the falsity of universal statements is the only strictly deductive kind of inference that proceeds, as it were, in the ‘inductive direction’; that is, from singular to univeral statements. [19]

Knowledge without dogma

I have tried to show that the most important of the traditional problems of epistemology — those connected with the growth of knowledge — transcend the two standard methods of linguistic analysis and require the analysis of scientific knowledge. But the last thing I wish to do, however, is to advocate another dogma. Even the analysis of science — the ‘philosophy of science’ — is threatening to become a fashion, a specialism. Yet philosophers should not be specialists. For myself, I am interested in science and in philosophy only because I want to learn something about the riddle of the world in which we live, and the riddle of man’s knowledge of that world. And I believe that only a revival of interest in these riddles can save the sciences and philosophy from narrow specialization and from an obscurantist faith in the expert’s special skill, and in his personal knowledge and authority; a faith that so well fits our ‘post-rationalist’ and ‘post-critical’ age, proudly dedicated to the destruction of the tradition of rational philosophy, and of rational thought itself. [xxvi]

Science, Philosophy, and Method

And yet, I am quite ready to admit that there is a method which might be described as ‘the one method of philosophy’. But it is not characteristic of philosophy alone; it is, rather, the one method of all rational discussion, and therefore of the natural sciences as well as of philosophy. The method I have in mind is that of stating one’s problem clearly and of examining its various proposed solutions critically.

I have italicized the words ‘rational discussion’ and ‘critically’ in order to stress that I equate the rational attitude and the critical attitude. The point is that, whenever we propose a solution to a problem, we ought to try as hard as we can to overthrow our solution, rather than defend it. Few of us, unfortunately, practise this precept; but other people, fortunately, will supply the criticism for us if we fail to supply it ourselves. Yet criticism will be fruitful only if we state our problem as clearly as we can and put our solution in a sufficiently definite form—a form in which it can be critically discussed.

I do not deny that something which may be called ‘logical analysis’ can play a role in this process of clarifying and scrutinizing our problems and our proposed solutions; and I do not assert that the methods of ‘logical analysis’ or ‘language analysis’ are necessarily useless. My thesis is, rather, that these methods are far from being the only ones which a philosopher can use with advantage, and that they are in no way characteristic of philosophy. They are no more characteristic of philosophy than of any other scientific or rational inquiry.

It may perhaps be asked what other ‘methods’ a philosopher might use. My answer is that though there are any number of different ‘methods’, I am really not interested in enumerating them. I do not care what methods a philosopher (or any­body else) may use so long as he has an interesting problem, and so long as he is sincerely trying to solve it. [xix-xx]