Tag: falsifiability

The stimulus to further development

As Max Planck once remarked in a lecture,

A living and flourishing theory does not avoid its anomalies but searches them out, for the stimulus to fur­ther development comes from contradiction, not from confirmations.

The point to keep in mind is that although falsifiability, rather than verifiability, is the most important criterion in determin­ing whether a theory is scientifically meaningful, its usefulness for the greater task of building confidence in a theory is limited. A theory is accepted not simply because it has withstood many attempts at falsification, the need for such tests notwithstanding, but because it leads to predictions that are experimentally verified. After all, the purpose of a theory is to be productive and not just to fail to be wrong. [115]

Kuhn on falsification

A very different approach to this whole network of problems has been developed by Karl R. Popper who denies the existence of any verification procedures at all. Instead, he emphasizes the importance of falsification, i.e., of the test that, because its outcome is negative, necessitates the rejection of an established theory. Clearly, the role thus attri­buted to falsification is much like the one this essay assigns to anomalous experiences, i.e., to experiences that, by evoking crisis, prepare the way for a new theory. Nevertheless, anomalous experiences may not be identified with falsifying ones. Indeed, I doubt that the latter exist. As has repeatedly been emphasized before, no theory ever solves all the puzzles with which it is confronted at a given time; nor are the solutions already achieved often perfect. On the contrary, it is just the incompleteness and imperfection of the existing data-theory fit that, at any time, define many of the puzzles that characterize normal science. If any and every failure to fit were ground for theory rejection, all theories ought to be rejected at all times. On the other hand, if only severe failures to fit justifies theory rejection, then the Popperians will require some criterion of “improbability” or of “degree of falsification.” In developing one they will almost certainly encounter the same network of difficulties that has haunted the advocates of the various probabilistic verifi­cation theories.

Many of the preceding difficulties [Kuhn is referring to inductive reasoning] can be avoided by recognising that both of these prevalent and opposed views about the underlying logic of scientific enquiry have tried to compress two largely separate processes into one. Popper’s anomalous experience is important to science because it invokes competitors for an existing paradigm. But falsification, though it surely occurs, does not happen with, or simply because of, the emergence of an anomaly or falsifying instance. Instead, it is a subsequent and separate process that might equally well be called verification since it consists in the triumph of a new paradigm over the old one. [146-7]

Gould’s view of Popperian falsification

Philosopher Karl Popper has argued for decades that the primary criterion of science is the falsifiability of its theories. We can never prove absolutely, but we can falsify. A set of ideas that cannot, in principle, be falsified is not science.

The entire creationist argument involves little more than a rhetorical attempt to falsify evolution by presenting supposed contradictions among its supporters. Their brand of creationism, they claim, is “scientific” because it follows the Popperian model in trying to demolish evolution. Yet Popper’s argument must apply in both directions. One does not become a scientist by the simple act of trying to falsify another scientific system; one has to present an alternative system that also meets Popper’s criterion—it too must be falsifiable in principle. [256]

Proposals for the scientific method

When verificationism failed, philosophers proposed that science progresses because scientists follow a method guar­anteed to lead to the truth. Proposals for the scientific method were offered by philosophers such as Rudolf Carnap and Paul Oppenheim. Karl Popper put forward his own proposal, which was that science progresses when scientists pro­pose thories that are falsifiable—that is, they make statements that can be contradicted by experiment. According to Popper, a theory is never proved right, but if it survives many attempts to prove it wrong, we can begin to have faith in it—at least until it is finally falsified. [296]

The meagre foundation of science

[E]ver since the seminal work of philosopher of science Karl Popper, for a scientific theory to be worthy of its name, it has to be falsifiable by experiments or observations. This requirement has become the foundation of the “scientific method.” [262]

The recklessly critical quest for truth

With the idol of certainty (including that of degrees of imperfect certainty or probability) there falls one of the defences of obscurantism which bar the way of scientific advance. For the worship of this idol hampers not only the boldness of our questions, but also the rigour and the integrity of our tests. The wrong view of science betrays itself in the craving to be right; for it is not his possession of knowledge, of irrefutable truth, that makes the man of science, but his persistent and recklessly critical quest for truth.

Has our attitude, then, to be one of resignation? Have we to say that science can fulfill only its biological task; that it can, at best, merely prove its mettle in practical applications which may corroborate it? Are its intellectual problems insolu­ble? I do not think so. Science never pursues the illusory aim of making its answers final, or even probable. Its advance is, rather, towards an infinite yet attainable aim: that of ever discovering new, deeper, and more general problems, and of subjecting our ever tentative answers to ever renewed and ever more rigorous tests.[281]

Our method is not to prove how right we were

[T]hese marvellously imaginative and bold conjectures or ‘anticipations’ of ours are carefully and soberly controlled by systematic tests. Once put forward, none of our ‘anticipations’ are dogmatically upheld. Our method of research is not to defend them, in order to prove how right we were. On the contrary, we try to overthrow them. [278-9]

Corroboration and timeless truth

In the logic of science here outlined it is possible to avoid using the concepts ‘true’ and ‘false’. …

Whilst we assume that the properties of physical objects (of ‘genidentical’ objects in Lewin’s sense) change with the passage of time, we decide to use these logical predicates in such a way that the logical properties of statements become timeless: if a statement is a tautology, then it is a tautology once and for all. This same timelessness we also attach to the concepts ‘true’ and ‘false’, in agreement with common usage. It is not common usage to say of a statement that it was perfectly true yesterday but has become false today. If yesterday we appraised a statement as true which to­day we appraise as false, then we implicitly assert today that ; that the statement was false even yesterday—timelessly false—but that we erroneously ‘took it for true’.

Here one can see very clearly the difference between truth and corroboration. The appraisal of a statement as corrobo­rated or as not corroborated is also a logical appraisal and therefore also timeless; for it asserts that a certain logical relation holds between a theoretical system and some system of accepted basic statements. But we can never simply say of a statement that it is as such, or in itself, ‘corroborated’ (in the way in which we may say that it is ‘true’). We can only say that it is corroborated with respect to some system of basic statements—a system accepted up to a particular point in time. ‘The corroboration which a theory has received up to yesterday’ is logically not identical with ‘the corro­boration which a theory has received up to today’. Thus we must attach a subscript, as it were, to every appraisal of cor­roboration—a subscript characterizing the system of basic statements to which the corroboration relates (for example, by the date of its acceptance).

Corroboration is therefore not a ‘truth value’; that is, it cannot be placed on a par with the concepts ‘true’ and ‘false’ (which are free from temporal subscripts); for to one and the same statement there may be any number of different cor­roboration values, of which indeed all can be ‘correct’ or ‘true’ at the same time. For they are values which are logically derivable from the theory and the various sets of basic statements accepted at various times.

The above remarks may also help to elucidate the contrast between my views and those of the pragmatists who pro­pose to define ‘truth’ in terms of the success of a theory—and thus of its usefulness, or of its confirmation or of its corro­boration. If their intention is merely to assert that a logical appraisal of the success of a theory can be no more than an appraisal of its corroboration, I can agree. But I think that it would be far from ‘useful’ to identify the concept of corrobo­ration with that of truth.* [273-5]

* Thus if we were to define ‘true’ as ‘useful’ (as suggested by some pragmatists), or else as ‘successful’ or ‘confirmed’ or ‘corroborated’, we should only have to introduce a new ‘absolute’ and ‘timeless’ concept to play the role of ‘truth’.

Step-by-step approximations to truth

The degree of corroboration of two statements may not be comparable in all cases, any more than the degree of falsi­fiability: we cannot define a numerically calculable degree of corroboration, but can speak only roughly in terms of positive degree of corroboration, negative degrees of corroboration, and so forth. Yet we can lay down various rules; for instance the rule that we shall not continue to accord a positive degree of corroboration to a theory which has been falsified by an inter-subjectively testable experiment based upon a falsifying hypothesis. (We may, however, under cer­tain circumstances accord a positive degree of corroboration to another theory, even though it follows a kindred line of thought. An example is Einstein’s photon theory, with its kinship to Newton’s corpuscular theory of light.) In general we regard an inter-subjectively testable falsification as final (provided it is well tested): this is the way in which the asymme­try between verification and falsification of theories makes itself felt. Each of these methodological points contributes in its own peculiar way to the historical development of science as a process of step by step approximations. [266-7]

Falsifiability and probability statements

How is it possible that probability statements—which are not falsifiable—can be used as falsifiable statements? (The fact that they can be so used is not in doubt: the physicist knows well enough when to regard a probability assumption as falsified.) This question, we find, has two aspects. On the one hand, we must make the possibility of using probability statements understandable in terms of their logical form. On the other hand, we must analyse the rules governing their use as falsifiable statements.

According to section 66, accepted basic statements may agree more or less well with some proposed probability esti­mate; they may represent better, or less well, a typical segment of a probability sequence. This provides the opportunity for the application of some kind of methodological rule; a rule, for instance, which might demand that the agreement between basic statements and the probability estimate should conform to some minimum standard. Thus the rule might draw some arbitrary line and decree that only reasonably representative segments (or reasonably ‘fair samples’) are ‘permitted’, while atypical or non-representative segments are ‘forbidden’. [197]