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Karl Popper by Dr Ray Scott Percival 

Nearly every first-year philosophy student knows that Popper regarded his solutions to the problems of induction and the demarcation of science from pseudo-science as his greatest contributions

The universe is a place filled with wonderful but deeply mysterious structures and processes. Arguably, these can be understood as behaving in accord with universal laws. In any case, what makes for a scientific approach to delving into the mystery that surrounds us, and separates this from practises and theories that are not scientific? What makes Einstein's work scientific, but crystal ball gazing or tea-leaf interpretation unscientific? (The particular examples of pseudo-science that one might choose are irrelevant to the argument. A point missed by many commentators. Presumably there is such a thing as pseudo-science.) Is there a criterion that we can apply to demarcate the scientific method from other approaches to knowledge, and that will help us to adjudicate between competing solutions to these mysteries? The question is not about which practise deserves the noble title "Science", but about the best method for promoting the growth of knowledge and the control of error. There may be a defensible argument that shows that tea-leaf interpretation or disciplined meditation on a candle-flame is the best method for discovering, say, the maximum radius of a black hole with a given mass, but I have yet to see one.

Before David Hume Treatise of Human Nature [1739], all approaches to knowledge had assumed that it was distinguishable from merely true opinion by the provision of some type of positive reason. They all assumed that the problem was to show that and how knowledge could be derived by a process of justification. The empiricists argued that all knowledge was derived from experience; while others argued that knowledge was derived from reason itself. But they all agreed that knowledge was Justified True Belief. The empiricists thought that our knowledge of the regularities and universal structures of the world were derived logically from experience or observations. But Hume pointed out that our experience is limited and that there is in fact no logical or even probabilistic connection between say, the number of times the sun has risen and whether it will rise tomorrow. His point was more general than that of the invalidity of inferring from past to future cases. His point was that one cannot sanction a logical or probable inference from observed cases to unobserved cases. Yet as an empiricist in the wider sense, one who advocates that our preference for a theory over another must take account of experience, Hume had revealed a profound problem with the usual account of how to obtain knowledge and its certification as knowledge. He had revealed a dramatic conflict between:

1. The assumption that there are universal laws and regularities and that we can know these.
2. There can be no valid reasons justifying our belief in a universal law other than those based on experience.
3. There is no valid inference from observed cases to unobserved cases. Yet, universal laws cover an infinite number of possible cases throughout the whole of space and time, and therefore necessarily go beyond all actual and possible experience.
This is the notorious problem of induction.

Popper wished to provide a solution to this problem that retained the respect for experience as adjudicator between competing theories and the assumption that if the world contains universal laws and structures then we can discover what they are. He proposed the complete rejection of the search for justifications and replaced this quest with the search for truth alone by the method of bold conjecture and refutation. Whether intentional or not, his proposal revived a hint in Plato's Meno that the possession of merely true opinion would serve one just as well for the satisfaction of curiosity and all practical purposes as the possession of the ostensively more dignified or useful "knowledge". To elaborate his argument Popper focused on scientific knowledge as the problem could be stated more clearly for this type of knowledge. Popper expressed his wish to characterize a heroic conception of science, a conception that captured the spirit and method of great scientists such as Galileo, Kepler, Newton, Einstein and Bohr. (Popper, [1974], The Philosophy of Karl Popper, Bk.II, Sections 5-8 of Replies to my Critics.) It must be understood that Popper's main concern in his philosophy of science is to account for and to promote the growth of knowledge. So that we may be able to chart better at least the contours of that vast ocean of truth that Newton spoke of. It is Popper's idea that such men made possible a tremendous growth of knowledge by championing bold ideas and subjecting them to severe attempts at refutation. Popper's criterion of demarcation is the outcome of a logical/methodological analysis of what has counted as bold ideas and severe criticism, and thus of what promoted the growth of knowledge.

Popper contrasted these two theories with the theories of Newton and of Einstein which were full of testable (i.e. falsifiable) content. Thus the term "immunizing stratagem" arose in connection with Popper's attempt to solve the problem of distinguishing scientific from pseudo-scientific theories - the so-called demarcation problem. Popper's solution was the methodological rule to allow into science only empirically falsifiable hypotheses, and subject these to severe criticism. In addition, theory development was to proceed from less to more testable, i.e., more informative theories. If a theory is refuted and an alternative sought, it had to be more testable, not less, and the more testable the better. For to reduce testability is to reduce knowledge, but in science we desire the growth of knowledge. An immunizing stratagem is a development in theory that reduces testability.

Popper begins with a rough characterization of bold ideas: a theory is bold if it is a new, daring, hypothesis. It is daring if it takes a large risk in being false. Popper argues that this risk can be analysed ultimately in terms of the amount of possibilities that the idea excludes, the degree to which it forbids states of affairs. Severe attempts at refutation are severe critical discussions and severe empirical tests.

Popper illustrates these ideas by examining the development of cosmology, from the heliocentric theories of Aristarchus and Copernicus to Einstein's general theory of relativity. Popper argues that this development illustrates not only the growth of knowledge but an improvement in method, in which theories become ever more daring and subject to severer tests.

It becomes apparent that riskiness and testability are linked: the greater the former the greater the latter. Aristarchus and Copernicus conjectured that the sun sat at the centre of the universe, in opposition to the prevalent earth-centred view of their own times. The heliocentric theory was exceptionally bold because it clashed with both common sense and the prima facie evidence of the senses. It went beyond the appearances to posit an unobserved reality; the appearances were explained in terms of this unfamiliar reality. This was bold in itself, for it broke with the Aristotelian idea that to explain something is to reduce it to the familiar.

However, Popper says, neither Aristarchus nor Copernicus were fully scientific because neither of them was bold enough to predict new observable appearances and thereby expose their theories to new empirical tests. They explained the known appearances, but did not explicitly suggest the existence of unknown appearances, appearances that might decide between the heliocentric and earth-centred views. If they had made such predictions their theories would have been much more informative, and therefore have taken a larger risk of being false, but they would also have promoted the growth of knowledge.

Kepler comes closer to Popper's idea of good science. Kepler had a bold theory of the world, but he also made detailed predictions of new appearances. Not only that, he abandoned many of his ideas in the light of the observations furnished him by Tycho Brahe. In accordance with a promise he had made Tycho, Kepler tried to fit Tycho's model of the solar system to these observations. Tycho accepted neither Copernicus's nor Ptolemy's model, but like all other astronomers Tycho took for granted their Aristotelian/Platonic assumption that orbits must be circular. Nevertheless, he subjected this idea to empirical testing. Kepler made seventy different trials to fit the model to the data and failed. He then took the bold step of proposing that the orbits of the planets were elliptical. The data fell snugly into place.

Kepler's three laws, though good approximations to the truth, have been refuted. But, Popper says, though false, Kepler's theory is regarded as scientific. Newton's theory is also regarded as false but scientific. Hence it is not truth which decides whether a theory is scientific. Why should this be? Each theory, though false, represented an attempt to increase knowledge, and did so because even though each was false, it had greater truth content than its predecessor and exposed itself to more tests. Popper's answer, then, is that it is a theory's openness to empirical refutation that makes it scientific. But more generally, it is whether the theory is an attempt to expand our knowledge, whether it represents an increase of information on the theory it replaces.

We may infer from this that Marxism or Freudianism would not be counted as unscientific simply because they have been refuted, but because of the way Marxists and Freudians have dealt with refutations. What is most important for the demarcation criterion is a critical attitude and the proposal of increasingly falsifiable theories in response to refutations. Kepler's elliptical orbit hypothesis represented just this sort of increase of information content in response to empirical refutation.

What impressed Popper most about the theory of relativity were the following characteristics:

(1) Like Kepler's and Newton's theories, Einstein's theory was very bold, differing fundamentally from Newton's outlook.
(2) Einstein derived from the theory three predictions of vastly different observable effects, two of which were radically new, all of which contradicted Newton's theory.1
(3) Einstein explicitly declared in advance of the experimental tests of his theory, that they were crucial: if the results did not precisely match his predictions, he would abandon them as false.
(4) Einstein regarded his theory as simply a better approximation to the truth. For a number of reasons he was convinced that it was false. He specified a number of characteristics that a true theory would have to satisfy. (Popper argued that Einstein's attitude to his theory clearly showed that belief in the truth of a theory was unnecessary to working on it as a promising candidate. It is worth noting, though, that Einstein believed that the theory was closer to the truth than its rivals; so it could not warrant the inference that belief is irrelevant to explaining why Einstein worked on the theory.)

Popper's proposal was that science was distinguished from pseudo-science by two things:

1) The boldness of predicting as yet unobserved phenomena; especially phenomena which will pit the theory against its competitors and allow us to decide between them. Einstein was acutely aware of the need to compare his theory with its competitors.
(2) The boldness of looking for tests and refuting instances. (I would also add: the boldness of accepting refuting instances, which is not implied by the boldness of looking for them.)

We may generalize the methodological conclusions of Popper's investigation as follows:

1. Propound empirically testable theories;
2. Aim to refute them;
3.Given any theory T, aim to replace it by another theory T' which is more general and precise (i.e, has higher information content.2 ), one that explains the success of T, explains the refuting evidence of T and is moreover independently testable.

Popper later placed much more emphasis on the importance of non-empirical theories, while retaining empirical content as the ultimate goal of theory development. These are purely methodological rules. But there is also an historical thesis connected with it. It is Popper's conjecture that these ideals are responsible for some of the greatest leaps of man's scientific knowledge. Many commentators have confused Popper's methodological/normative analysis with his historical hypothesis. Kuhn is perhaps mostly responsible for this confusion, and others (for example, Boudon) have been lead astray by relying on secondary sources. Chalmers also makes this mistake.

It is worth emphasizing that there are two aspects to the demarcation criterion: one of attitude and one of pure logic. Firstly, the scientist must try to find falsifying instances to his theories. This is a matter of the correct attitude; the critical attitude. Secondly, the scientist must have at his disposal refutable theories. The possibility then arises of a scientist earnestly following the first injunction without realizing that the theory he is dealing with is empirically irrefutable. Equally, a body of theory may be logically capable of refutation, though its adherents have refused or neglected to look for refuting instances. Since Popper is interested in the growth of knowledge he is most concerned to discourage the use of immunizing stratagems that flout the demarcation criterion, effectively reducing the information content of our theories. (the term "information content" will be defined later.) Kepler, for instance, could have described the planets that did not fit his master's model as not really planets. After all, he might have said, planets do not behave like that: a planet is essentially an object with a circular orbit. This would have been an example of what Popper calls an immunizing stratagem. Such a manoeuvre, Popper would say, saves the theory but at the price of a reduction in information content. As we have seen Kepler's actual response greatly increased the informative content of astronomy, and is rightly admired for that.

Not all evasive moves are on the wrong side of the demarcation criterion. Some auxiliary hypotheses introduced to deflect a refutation from a valuable assumption have added greatly to our knowledge. One such auxiliary hypothesis was the prediction by Adams and Leverier of the existence of the planet Neptune. It had been observed that the orbit of the planet Uranus was not in accord with Newton's core theory (the laws of motion and the law of gravity) plus the then known initial conditions (ie assumptions about the gravitational influence of other planetary bodies). Newton's theory could have been regarded as falsified by this anomaly. However, Adams and Leverier proposed the existence of a previously unknown planet to account for the failure of the predictions, thus saving Newton's theory. But this particular evasion brought increased information content to the Newtonian system as was clear from the fact that the hypothesis was empirically testable by independent means (i.e., not simply by checking whether the hypothesis agreed with the already observed perturbations of Uranus).

My point, contrary to Popper, is that "immunizing stratagems" are auxiliary hypotheses that are on the wrong side of the demarcation criterion and precisely those that while saving the original theory from refutation effectively abandon it, replacing it with another theory. In our hypothetical example, Kepler's redefinition of planets as essentially circular in orbit would introduce a radically new theory and jettison the original claim. I will expand on this point in a later section, after we have seen how Popper deals with the problem presented by metaphysical theories to his demarcation criterion.

Karl Popper:  Stanford Encyclopedia of Philosophy

Karl Popper is generally regarded as one of the greatest philosophers of science of this century. He was also a social and political philosopher of considerable stature, a self-professed ‘critical-rationalist’, a dedicated opponent of all forms of scepticism, conventionalism, and relativism in science and in human affairs generally, a committed advocate and staunch defender of the ‘Open Society’, and an implacable critic of totalitarianism in all of its forms. One of the many remarkable features of Popper’s thought is the scope of his intellectual influence. In the modern technological and highly-specialised world scientists are rarely aware of the work of philosophers; it is virtually unprecedented to find them queuing up, as they have done in Popper’s case, to testify to the enormously practical beneficial impact which that philosophical work has had upon their own. But notwithstanding the fact that he wrote on even the most technical matters with consummate clarity, the scope of Popper’s work is such that it is commonplace by now to find that commentators tend to deal with the epistemological, scientific and social elements of his thought as if they were quite disparate and unconnected, and thus the fundamental unity of his philosophical vision and method has to a large degree been dissipated. Here we will try to trace the threads which interconnect the various elements of his philosophy, and which give it its fundamental unity.

Popper was profoundly impressed by the differences between the allegedly ‘scientific’ theories of Freud and Adler and the revolution effected by Einstein’s theory of relativity in physics in the first two decades of this century. The main difference between them, as Popper saw it, was that while Einstein’s theory was highly ‘risky’, in the sense that it was possible to deduce consequences from it which were, in the light of the then dominant Newtonian physics, highly improbable (e.g. that light is deflected towards solid bodies - confirmed by Eddington’s experiments in 1919), and which would, if they turned out to be false, falsify the whole theory, nothing could, even in principle, falsify psychoanalytic theories. These latter, Popper came to feel, have more in common with primitive myths than with genuine science. That is to say, he saw that what is apparently the chief source of strength of psychoanalysis, and the principal basis on which its claim to scientific status is grounded, viz. its capability to accommodate, and explain, every possible form of human behaviour, is in fact a critical weakness, for it entails that it is not, and could not be, genuinely predictive. Psychoanalytic theories by their nature are insufficiently precise to have negative implications, and so are immunised from experiential falsification.

The Marxist account of history too, Popper held, is not scientific, although it differs in certain crucial respects from psychoanalysis. For Marxism, Popper believed, had been initially scientific, in that Marx had postulated a theory which was genuinely predictive. However, when these predictions were not in fact borne out, the theory was saved from falsification by the addition of ad hoc hypotheses which made it compatible with the facts. By this means, Popper asserted, a theory which was initially genuinely scientific degenerated into pseudo-scientific dogma.

These factors combined to make Popper take falsifiability as his criterion for demarcating science from non-science: if a theory is incompatible with possible empirical observations it is scientific; conversely, a theory which is compatible with all such observations, either because, as in the case of Marxism, it has been modified solely to accommodate such observations, or because, as in the case of psychoanalytic theories, it is consistent with all possible observations, is unscientific. For Popper, however, to assert that a theory is unscientific, is not necessarily to hold that it is unenlightening, still less that it is meaningless, for it sometimes happens that a theory which is unscientific (because it is unfalsifiable) at a given time may become falsifiable, and thus scientific, with the development of technology, or with the further articulation and refinement of the theory. Further, even purely mythogenic explanations have performed a valuable function in the past in expediting our understanding of the nature of reality.

The Problem of Demarcation

As Popper represents it, the central problem in the philosophy of science is that of demarcation, i.e. of distinguishing between science and what he terms ‘non-science’, under which heading he ranks, amongst others, logic, metaphysics, psychoanalysis, and Adler’s individual psychology. Popper is unusual amongst contemporary philosophers in that he accepts the validity of the Humean critique of induction, and indeed, goes beyond it in arguing that induction is never actually used by the scientist. However, he does not concede that this entails the scepticism which is associated with Hume, and argues that the Baconian/Newtonian insistence on the primacy of ‘pure’ observation, as the initial step in the formation of theories, is completely misguided: all observation is selective and theory-laden - there are no pure or theory-free observations. In this way he destabilises the traditional view that science can be distinguished from non-science on the basis of its inductive methodology; in contradistinction to this, Popper holds that there is no unique methodology specific to science. Science, like virtually every other human, and indeed organic, activity, Popper believes, consists largely of problem-solving.

Popper, then, repudiates induction, and rejects the view that it is the characteristic method of scientific investigation and inference, and substitutes falsifiability in its place. It is easy, he argues, to obtain evidence in favour of virtually any theory, and he consequently holds that such ‘corroboration’, as he terms it, should count scientifically only if it is the positive result of a genuinely ‘risky’ prediction, which might conceivably have been false. For Popper, a theory is scientific only if it is refutable by a conceivable event. Every genuine test of a scientific theory, then, is logically an attempt to refute or to falsify it, and one genuine counter-instance falsifies the whole theory. In a critical sense, Popper’s theory of demarcation is based upon his perception of the logical asymmetry which holds between verification and falsification: it is logically impossible to conclusively verify a universal proposition by reference to experience (as Hume saw clearly), but a single counter-instance conclusively falsifies the corresponding universal law. In a word, an exception, far from ‘proving’ a rule, conclusively refutes it.

Every genuine scientific theory then, in Popper’s view, is prohibitive, in the sense that it forbids, by implication, particular events or occurrences. As such it can be tested and falsified, but never logically verified. Thus Popper stresses that it should not be inferred from the fact that a theory has withstood the most rigorous testing, for however long a period of time, that it has been verified; rather we should recognise that such a theory has received a high measure of corroboration. and may be provisionally retained as the best available theory until it is finally falsified (if indeed it is ever falsified), and/or is superseded by a better theory.

Popper has always drawn a clear distinction between the logic of falsifiability and its applied methodology. The logic of his theory is utterly simple: if a single ferrous metal is unaffected by a magnetic field it cannot be the case that all ferrous metals are affected by magnetic fields. Logically speaking, a scientific law is conclusively falsifiable although it is not conclusively verifiable. Methodologically, however, the situation is much more complex: no observation is free from the possibility of error - consequently we may question whether our experimental result was what it appeared to be.

Thus, while advocating falsifiability as the criterion of demarcation for science, Popper explicitly allows for the fact that in practice a single conflicting or counter-instance is never sufficient methodologically to falsify a theory, and that scientific theories are often retained even though much of the available evidence conflicts with them, or is anomalous with respect to them. Scientific theories may, and do, arise genetically in many different ways, and the manner in which a particular scientist comes to formulate a particular theory may be of biographical interest, but it is of no consequence as far as the philosophy of science is concerned. Popper stresses in particular that there is no unique way, no single method such as induction, which functions as the route to scientific theory, a view which Einstein personally endorsed with his affirmation that ‘There is no logical path leading to [the highly universal laws of science]. They can only be reached by intuition, based upon something like an intellectual love of the objects of experience’. Science, in Popper’s view, starts with problems rather than with observations - it is, indeed, precisely in the context of grappling with a problem that the scientist makes observations in the first instance: his observations are selectively designed to test the extent to which a given theory functions as a satisfactory solution to a given problem.

On this criterion of demarcation physics, chemistry, and (non-introspective) psychology, amongst others, are sciences, psychoanalysis is a pre-science (i.e. it undoubtedly contains useful and informative truths, but until such time as psychoanalytical theories can be formulated in such a manner as to be falsifiable, they will not attain the status of scientific theories), and astrology and phrenology are pseudo-sciences. Formally, then, Popper’s theory of demarcation may be articulated as follows: where a ‘basic statement’ is to be understood as a particular observation-report, then we may say that a theory is scientific if and only if it divides the class of basic statements into the following two non-empty sub-classes: (a) the class of all those basic statements with which it is inconsistent, or which it prohibits - this is the class of its potential falsifiers (i.e. those statements which, if true, falsify the whole theory), and (b) the class of those basic statements with which it is consistent, or which it permits (i.e. those statements which, if true, corroborate it, or bear it out).

Probability, Knowledge and Verisimilitude

In the view of many social scientists, the more probable a theory is, the better it is, and if we have to choose between two theories which are equally strong in terms of their explanatory power, and differ only in that one is probable and the other is improbable, then we should choose the former. Popper rejects this. Science, or to be precise, the working scientist, is interested, in Popper’s view, in theories with a high informative content, because such theories possess a high predictive power and are consequently highly testable. But if this is true, Popper argues, then, paradoxical as it may sound, the more improbable a theory is the better it is scientifically, because the probability and informative content of a theory vary inversely - the higher the informative content of a theory the lower will be its probability, for the more information a statement contains, the greater will be the number of ways in which it may turn out to be false. Thus the statements which are of special interest to the scientist are those with a high informative content and (consequentially) a low probability, which nevertheless come close to the truth. Informative content, which is in inverse proportion to probability, is in direct proportion to testability. Consequently the severity of the test to which a theory can be subjected, and by means of which it is falsified or corroborated, is all-important.

For Popper, all scientific criticism must be piecemeal, i.e. he holds that it is not possible to question every aspect of a theory at once. More precisely, while attempting to resolve a particular problem a scientist of necessity accepts all kinds of things as unproblematic. These things constitute what Popper terms the ‘background knowledge’. However, he stresses that the background knowledge is not knowledge in the sense of being conclusively established; it may be challenged at any time, especially if it is suspected that its uncritical acceptance may be responsible for difficulties which are subsequently encountered. Nevertheless, it is clearly not possible to question both the theory and the background knowledge at the same time (e.g. in conducting an experiment the scientist of necessity assumes that the apparatus used is in working order).

How then can one be certain that one is questioning the right thing? The Popperian answer is that we cannot have absolute certainty here, but repeated tests usually show where the trouble lies. Even observation statements, Popper maintains, are fallible, and science in his view is not a quest for certain knowledge, but an evolutionary process in which hypotheses or conjectures are imaginatively proposed and tested in order to explain facts or to solve problems. Popper emphasises both the importance of questioning the background knowledge when the need arises, and the significance of the fact that observation-statements are theory-laden, and hence fallible. For while falsifiability is simple as a logical principle, in practice it is exceedingly complicated - no single observation can ever be taken to falsify a theory, for there is always the possibility (a) that the observation itself is mistaken, or (b) that the assumed background knowledge is faulty or defective.

Popper was initially uneasy with the concept of truth, and in his earliest writings he avoided asserting that a theory which is corroborated is true - for clearly if every theory is an open-ended hypothesis, as he maintains, then ipso facto it has to be at least potentially false. For this reason Popper restricted himself to the contention that a theory which is falsified is false and is known to be such, and that a theory which replaces a falsified theory (because it has a higher empirical content than the latter, and explains what has falsified it) is a ‘better theory’ than its predecessor. However, he came to accept Tarski’s reformulation of the correspondence theory of truth, and in Conjectures and Refutations (1963) he integrated the concepts of truth and content to frame the metalogical concept of ‘truthlikeness’ or ‘verisimilitude’. A ‘good’ scientific theory, Popper thus argued, has a higher level of verisimilitude than its rivals, and he explicated this concept by reference to the logical consequences of theories. A theory’s content is the totality of its logical consequences, which can be divided into two classes: there is the ‘truth-content’ of a theory, which is the class of true propositions which may be derived from it, on the one hand, and the ‘falsity-content’ of a theory, on the other hand, which is the class of the theory’s false consequences (this latter class may of course be empty, and in the case of a theory which is true is necessarily empty).