The purpose of this paper is to analyze and criticize what seem to me to be some controversial aspects in Popper’s solution to the problem of demarcation in the philosophy of science. The idea that there is something flawed about Popper’s famous criterion of falsifiability is not new – in a way or another Popper’s methodology has been criticized for more than 50 years. However, I do not attempt at devising arguments to the effect that Popper’s account of the dynamics of science is not faithful to the actual history of science, or that the concept of science that he provides is incompatible with the common-sense intuition about science . Such arguments may be countered on the grounds that they fail to meet their intended target: Popper’s aim was not to describe the actual dynamics of science, nor to clarify the commonsense intuitions about what it is to be scientific, but to provide a methodology, an ethics of scientific research. (It is true that Popper sometimes speaks of his methodological criterion as if it were an attempt to clarify common intuitions; for example, “My reason for proposing my criterion of demarcation is that it is fruitful; that a great many points can be clarified and explained with its help…It is only from the consequences of my definition of empirical science, and from the methodological decisions which depend upon this definition, that the scientist will be able to see how far it conforms to his intuitive idea of the goal of his endeavours. The philosopher too will accept my definition as useful only if he can accept its consequences.“. (LSD, p. 55). (It does not become automatically clear, however, when and why the scientist or the philosopher should accept the definition of science – if no requirements are provided for when and why they should be accepted, Popper’s methodology may become closer to the naturalism which he opposes than it seems). Leaving aside this complication, let us note that, in principle, any attempt to say that Popper’s definition of science is not a faithful reconstruction of the historically constituted or intuitive meaning of science could be labeled by Popper as a naturalist attack and thus as a misunderstanding of his attempt to provide a methodology, that is an ethics, of scientific research.

However, if it could be proven that Popper’s criteria for scientificity are actually inconsistent and impossible to follow, then his methodology would be attacked in a far more drastic way. What I aim at in this paper is to argue that Popper’s methodology is in principle inconsistent. I will point to the fact that his criterion of falsifiability cannot tell apart between science and pseudo-science; that it cannot provide for closeness to truth and that it cannot exclude ad-hoc hypotheses. In the first section of my essay I will suggest that the criterion of falsifiability is wrong if it is interpreted in a "Platonic" way, i.e. as characterizing theories and not attitudes towards theories. In the second section, I will argue that, despite his realist intentions, Popper's methodology is actually suited for valuing the rapidity of scientific change, rather than the pursuit of objective truth and that it should be supplemented by a methodology of advancing hypotheses. Thus, while Popper claims that his methodological rules apply only to the context of justification, there should be rules applying to the context of discovery. Such a methodology of discovery is implicit in Popper's work, but it is unsatisfactory. Part of the reason why it is unsatisfactory consists in Popper's flawed theses about probability. A methodology of discovery is needed, that will not be obstructed by Popper's views of probability.

1. Platonic Falsifiability and Constructed Falsifiability

I take Popper’ s famous criterion of falsifiability to be a property of hypotheses or theories. This is how the hope for a logical criterion of falsifiability can have any chance of being understood: a theory, once advanced, is either fallible (and scientific) or unfallible (and unscientific). Popper subsequently attempted to give a formalization of the idea of falsifiability in probabilistic terms: thus, falsifiability becomes a gradual matter, since the more probable a theory is, the less potential falsificators it has. The degree of falsifiability is the class of potential falsifiers of a theory : since the empirical content of a theory is defined as the class of its potential falsifiers, a theory is the more falsifiable, the more scientific when it has a higher empirical content and its probability is lower. Natural laws can thus be regarded as prohibitions. (LSD p. 69).

These requirements on a scientific theory may appear questionable, however, if we pay attention to the “hidden agenda’ of Popper’s program of distinguishing science from pseudo-science. As it is known, the intended targets of Popper’s attack were mainly psychoanalysis and Marxism. It is these theories that, by their claim to explain everything and interpret everything in their categories, should appear unscientific on Popper’s criterium: they are unfalsifiable, unprohibitive and devoid of empirical content. It is, however, a historical fact that psychoanalysis and Marxism are now regarded as being largely discredited and abandoned. (another question, which I defer for the moment, is whether – and how – they were rightly rejected). At any rate, I presume they were not rejected on the grounds that “a counterexample was discovered”. I suppose that psychoanalysis was rejected on such grounds as the implausibility of the claim that all conflicts are repressed desires; that it proved too ineffective or difficult a therapy (as compared with modern psychiatry); that its moral assumptions are questionable. Likewise, Marxism is discredited because of the economical and political failure of the Communist regimes and, perhaps, by the realization of the immorality of the methods advocated by its proponents (such as the use of violence, repression, censorship and the like). However, the fact that psychoanalysis and Marxism were rejected is not by itself an argument against Popper’s methodology. What Popper could reply is that such theories should have been rejected once their unfalsifiable status has been discovered, and that it is a rather wrong (or less good) fact that they were rejected on other grounds.

For a theory’s being falsifiable or not is, according to Popper, a property to be discovered, a property that intrinsically characterizes a theory. Falsifiability can be formalized in probabilistic terms, by saying that the higher the logical probability of a theory, the lower its degree of falsifiability. (LSD, p. 119). Thus, the degree of scientificity of a theory is complementary to its logical probability. The consequence is that it is possible to decide, once a theory is advanced, whether it is scientific (falsifiable) or unscientific (unfalsifiable). Scientificity is, so to speak, written on the face of a theory. Falsifiability is a Platonic notion: a theory is falsifiable or not regardless on whether we discover its being falsifiable or not. In order to learn whether a theory is falsifiable or not, we don’t need to look at its historical destiny. It follows that a theory may be falsified, without our recognizing or admitting its being falsified.

But if this is so, it follows that pseudo-scientific theories are such that it should be impossible to specify any circumstance, any moment when they should be abandoned. They are such that it would have been better not to have been proposed at all. Rather than saying, as we would be inclined to say, that “Marxism was falsified by the economical and political failure of Communism” or - as Popper writes in “Realism and the Aim of Science’ – that the (Freudian) psychoanalytic hypothesis that all dreams are repressed desires was falsified by the negative evidence of nightmares, we should say that Marxism and psychoanalysis should have been rejected once they were advanced, since they were unfalsifiable and prone to be maintained in the face of recalcitrant evidence. The very attempt to falsify or corroborate them was pointless since – isn’t it – they were unscientific.

It is this point that I want to criticize. If it could be maintained that a theory’s being falsifiable or not is an intrinsic property of it, one that should be specified in its birth certificate, then not only that it is not true that a recalcitrant experiment did not lead to its being abandoned. (Unfalsifiable theories are prone to ad-hoc modifications and to reinterpretation of their terms, although Popper is less specific about the latter point). It is, moreover, impossible to specify a recalcitrant experiment that should have led to the theory’s being abandoned. But it so, then what is the reason of Popper’s pointing to the evidence that should have falsified Freud’s hypothesis that dreams are repressed desires? (As Popper presents the situation, the negative instance of nightmares falsified de iure, but not de facto, Freud’s hypothesis). Popper is simply contradicting himself by pointing to such evidence. For, by admitting that there were precise circumstances when Freud’s theory should have be abandoned, he is implicitly countenancing its scientific status. Thus, the reasons (better to say: the causes) why it was not abandoned are psychological and sociological ones, consisting in the stubbornness or lack of imagination of its proponents; in the timidity of its adversaries. In short, if we belive that falsifiability or lack thereof is an intrinsic property of theories, there is a distinction between a theory’s being falsifiable and a theory’s being abandonable; between a theory’s being unfalsifiable and between a theory’s being retained in face of recalcitrant evidence. The first properties are logical, the latter are psychological or sociological. If so, then from the mere historical evidence that a theory was not abandoned when it should have been it does not follow that the theory was unfalsifable or unscientific. On the contrary, such theories were scientific, they were falsifiable – precisely because there is a moment when they should have been abandoned, when they were de iure falsified. It only follow that, unfortunately, its proponents were unwilling to abandon it.

If this is in general true, then the claim that being unscientific or unfalsifiable is an intrinsic property of theories should at least be qualified. Psychoanalysis, Marxism and perhaps astrology should be accepted, on Popperian lines, as bona fide scientific theories: namely false, falsified, ought-to-be rejected but nevertheless genuine scientific theories. The fact that they were not abandoned when they should have been does not prove their unscientific status; quite to the contrary.

I feel attracted towards a more radical conclusion: namely, that no theory is itself falsifiable or unfalsifiable, scientific or unscientific. Rather, theories become scientific or unscientific in the hands of their proponents and adversaries. I think such a conclusion is mainly correct, although it should be qualified. I am ready to admit that there are tautological hypotheses, such that tomorrow it will rain or it will not rain, or hypotheses whose terms are hopelessly ambiguous. (The point about ambiguity needs however further elaboration). The reason why I am inclined to think that no theory is intrinsically scientific or unscientific is that believing in the opposite thesis, that of the Platonic status of falsifiability, invites an exaggerate optimism about our knowledge of the future. If some theories were ab initio unscientific, this would mean that noone, never in the future, will be able to devise an experiment that will justifiably lead us to reject a theory, or to maximize our justified belief in it. According to this view, it is possible, in principle, to realize that some theories are such that they are not even worth testing.

As I will try to prove in the next section of this paper, it is wrong to believe this. If, on the other hand, it is true that falsifiability is not a Platonic notion, but rather a property that theories acquire in the course of their being debated, then Popper cannot be justified in condemning some theories as scientific and others as unscientific. Being fallibilist is not a virtue of theories, but of people. Or – if we continue to say that falsifiability characterizes theories, we will have to say rather that theories become falsifiable. Thus, it is incorrect to say that some theories are falsifiable and others are unfalsifiable. The consequence of this view is that – if we continue to believe that closeness to truth is somehow related to the ability of passing severe tests – a theory may become closer or farther from truth. I will try to bring several arguments that this view of falsifiability is correct.

2. The need for a methodology of discovery

If it is wrong to say that some theories are falsifiable while others are not, we may no longer retain the idea that the criterion of falsifiability constitutes an acceptable criterion for distinguishing hypotheses that are worth testing from hypotheses that should be dismissed. If so, then the question may legitimately be raised: what other criterion, besides falsifiability, can we have for this distinction? Indeed, it seems that we do need such a criterion: in the absence of it, we may simply not know which hypothesis – among the many possible hypotheses that may come to our minds – do deserve to be tested. I believe that, to some extent, Popper implies the idea that we do not need any criterion to distinguish between theories that are worth testing and those that are not; to some extent, he suggests unacceptable proposals for such a criterion.

Popper is specific about the point that theories that are corroborated in a high degree should be accepted at the expense of those which cannot satisfy the requirement of “severe tests”. Unlike probability, the degree of corroboration is a measure of the worthiness of maintaining a theory, of its closeness to the truth. That’s why Popper is careful about defining the degree of corroboration not in terms of the number of corroborating instances, but in terms of the diversity and severity of the tests to which it has been subjected. But it is hard to see how to find a theory that should meet this requirement after a rival theory was falsified. Since Popper does not give any precise indication about what to do after rejecting a theory – except the maxim that adhoc modifications should be avoided and that new theories that should be amenable to severe tests should be advanced – we may note that whether a theory can be severely tested and thus corroborated depends on the availability of tests and on the creativeness of scientists.

Indeed, it may happen that new, severely testable and thus highly corroborable theories will not be available simply because of the lack of imagination of scientists. Popper was emphatic against the doctrine of the manifest truth (i.e., the thesis that truth may come easily and in such a way that it could be recognizable by any sane person). On the other hand, he believed in the manifest status of falsifiability and corroborability. This is the only way he could explain why the rejection of a falsified theory followed by the proposal of a new theory (which is corroborated by all the evidence that corroborated the old theory plus the evidence that falsified it) can be an instance of progress. It can be an instance of progress only if the newer theory is able to be better corroborated and at least as severely tested as the old (rejected) theory. But if such a theory is actually found, this is a psychological fact. In the absence of finding such a meritorious alternative, the only thing that remains available is believing in a disjunctive theory, i.e. in one that is much more probable than the old, rejected theory. That is, the hypothesis "All Fs are Gs", once rejected, will be replaced by the hypothesis "All Fs are Ds or Es or Hs or Is or Js… ". Such a proposal could hardly be accepted on Popperian lines – since a disjunctive theory is obviously more probable and less falsifiable, less "risky" than a non-disjunctive theory.

Secondly, the corroborability of a hypothesis is not only a psychological matter. It may also be a technical one. For, whether a theory can be tested (and thus corroborated) depends on the availability of instruments fit to test it. (in LSD VI 37, Popper stressed that theories that are able to be expressed in precise terms are more severly testable and thus that techniques of measurement should be improved in order to make a theory better corroborable. But this leaves us with the question: what if instruments of measurement are simply not available and cannot be devised because of technical (or, even worse, economical reasons)? Popper would recommend that theories whose testability depends upon not-yet-available instruments should be abandoned – they cannot be corroborated to a satisfactory degree. But it is implausible to try to define the closeness-to-truth (or at least distance from falsity) in terms of the availability of technical means. If our notion of truth depended on psychological creativeness or availability of technical resources, then we would be left – in the best case – with an antirealist concept of truth. Truth would depend on what people can think, on what people have at their disposal to ground their beliefs. But this is not the concept of truth that Popper wanted.

I can illustrate this point by means of a metaphor. Imagine we are at the South Pole of an unknown planet and our task is to get as close as possible to the North Pole. There may be strong magnetic fields so that the reliability of our compasses is questionable, and the weather is misty. All we could do is to try to progress northwards and to build long roads and highways. It will happen that, after a long time, we reached a point from where the return to the South Pole would be difficult – indeed, we would need to go a long way back on the highways we built if we wanted to get to the South Pole. But we would have no guarantee that we got closer to the North Pole in terms of absolute distance – perhaps the absolute distance from the South Pole is small. Whether such a circumstance should count as getting farther and farther from the South Pole or not, it depends on whether we can imagine alternative, counterfactual possibilities of where we could have built our highways. We can also say that, since our compass is unreliable and we have no way of measuring our closeness to the North Pole in terms of absolute distance, there is no such thing as absolute distance and progress and closeness to truth in terms of elimination and replacement of falsified hypotheses. If this can be a measure of our getting closer to the truth, then we should be satisfied with a concept of truth that is relative to our powers of understanding. If we want an objective concept of truth, i.e. of the Truth that precedes our building of any theory, then successive falsification of theories is not an adequate measure of it.

This may also be illustrated by the example of theories that were dismissed in the past then revived. (Call this “anachronic progress”). In geology, the theory of continental drift is now largely accepted (and has been so since the sixties). It was initially proposed by Wegener at the beginning of the 20th century, but it was initially ridiculed and dismissed because it made no empirical difference; the postulation of forces that should be responsible for the drift of continents we can define the North Pole as the point where can no longer continue building the highway in such a way that it will not intersect its past sections. At any rate, the mere fact that we built a long highway starting from the South Pole does not authorize us to believe that we got closer to the North Pole. The same could be said about Popper’s account of seemed implausible; it was belived that a body with the mass of a continent cannot move without breaking. The theory was revived and accepted in the 60ies following the availability of adequate (severe) tests, that refuted the rival hypothesis (that continents are at rest). These tests were not available, however, at the time of Wegener. Another famous example is that of Ancient heliocentrism. Aristarchus explicitly proposed the theory that the planets and the Earth revolve around the sun. this theory had no success at the time and it was dismissed in favour of the Ptolemaic geocentrism. Heliocentrism was then revived in the 17th century following the dissatisfaction with the increasing complication undergone by the Ptolemaic system. Should we say that, according to Popperian methodology, the theory of continental drift and Aristarchus’ heliocentrism were rightly rejected at the time when they were first proposed? Popper is committed to answer both in the affirmative and in the negative. On the one hand, these theories were not severely tested (actually they made no difference to observations). So they were rightly dismissed: entertaining them at the time of their proposal would have been a metaphysical attitude, an article of faith and not of critical spirit. On the other hand, as we today know (or at least we believe we know) these theories are closer to the truth than their rivals. The theory of continental drifts ended by defeating the hypothesis of the immobility of continents, and heliocentrism ended by defeating geocentrism; it was right that this happened. Thus, Popper is committed to holding (as a typical rationalist) that these theories should have been accepted in the past. (Rationalists usually take pride in, and are blamed by their rivals for, judging the past from the standards of the present; Popper is no exception). On the premises of Popper’s rationalism, it is a regrettable fact that theories that are now accepted were once rejected in favour of theories that we know to have been falsified. But this legitimation of counterfactual progress conflicts with Popper’s claim that only theories that can be severely enough tested should be accepted and considered as corroborated.

I guess that Popper could retort to this accusation by saying that these theories (Wegener’s theory of continental drift and Aristarchus’ heliocentrism) should have been tested once they were advanced; that people were wrong for not having done so. After all, these theories could have been subjected to severe tests and appropriate instruments should have been devised. Popper required that instruments should be adjusted in order severely to test our theories. However, I hold that this answer is wrong.

Claiming that we should devise appropriate instruments to test our theories is a vacuous claim, insofar as it provides us with no criterion to distinguish between those theories that are worth testing and those that are not worth testing. In principle – at least this is the conclusion of the first section of this essay – all theories are amenable to severe tests, all are corroborable or falsifiable. (If one denied this thesis, one would be committed to holding that some theories ab initio less falsifiable than others). At any rate, I believe that it is highly plausible that there are an infinite number of theories that could be tested in an equally severe way, given the instruments available at a certain historical time and, evne more so, given the instruments that could have been devised at a certain historical time. Popper’s methodological rules would ask us to devise such instruments as to test, as severely as possible, all the hypotheses that may come to anyone’s mind, in any given or in no order. But this requirement is plainly irrational. It is irrational to require severe tests and instruments as precise as possible without specifying the theories which should be subjected to these tests. As I showed, we cannot be justified in dismissing some theories before testing them and before devising instruments able to severely test them: one cannot invoke the criterion that some theories are falsifiable and others are unfalsifiable: I tried to argue that no theory is doomed to be one way or another. On the other hand, it is irrational to proceed to test all hypotheses that may happen to come to anyone’s mind. We seem to need a methodological criterion which should tell us not only which theories should be accepted and which rejected; but which should tell us which theories should be entertained (and subjected to tests) and which should be dismissed. In other words, the logic of science cannot do without a psychology of discovery of relevant hypotheses.

The same problem, of how to select hypotheses that are worth testing from those that are not arises in connexion with the status of the singular existential statements. Popper’s criterion of falsifiability has been attacked for not accommodating these sentences into science. Popper’s reply was that an existential statement may be considered scientific to the extent at which there is a method of testing it; thus, “there are atoms” may be considered scientific, while “there is a fountain of youth” is unscientific, at least as long as we have no idea about how to look for it. It is, however, obvious (at least to me) that whether we have a method for testing an existential statement or not, this depends on a historically contingent situation. We should expect to be told how to identify those existential statements that are really worth testing. In other words: methods of testing statements – be they universal or existential – need to be built by us; they need our decision. But if the closeness to truth depends on such decisions, then there is little that remains from Popper’s claim to rationalism or realism. Truth becomes dependent on our decisions, and on the possibility of carriying them out.

In my opinion, the moral that results from the above remarks is that Popper was more interested in the rapidity of the process of advancing and eliminating hypotheses than in the process of rapprochement to the truth. This is the only way I can understand his insistence that theories which are less probable should be advanced, as formulated in LSD and in Realism and the Aim of Science.

Therefore, the fact that the criterion of falsifiability cannot be interpreted as a tool of rapproachment towards truth has the consequence that what Popper offers – if he is to remain consistent with his methodological desire for falsifiability as a criterion of telling apart "good" theories from "bad" theories (i.e., worth testing from not-worth testing) and with the preference for theories with a low logical probability, he offers rather guidelines for achieving rapid scientific change. But the ideal of rapidity of scientific change – which is implicitly Popper's ideal – is not necessarily identical with the ideal of truth – which is Popper's self-declared ideal. Indeed, pursuing the two ideals may lead to contradictions.

Moreover, to pursue any of these ideals it is necessary to supplement the methodology of evaluation and rejection of theories with a methodology of discovering, i.e. advancing them. The remaining of this essay will deal with the problem whether Popper really offered at least methodological guidelines for rapidity of scientific change.

Popper was firmly convinced that the process of advancing successive hypotheses, each of them being able to resist the tests (all the tests) that falsified its predecessors, is necessarily the road to truth. (I can only understand by “Truth” a theory - The Theory – which is such that it has no negative instances and is the simplest among all theories that are so. But this assumption is dogmatic and wrong: according to Popper’s methodological rules, one may discover a theory that is closer to the Truth than all our present and past theories, yet not be able to test and corroborate it. That’s why we need to choose between the desire to have theories as close to the truth as possible, and theories that are the product of a scientific change pursued at a rate as quick as possible.

The imperative to always look for counterexamples and negative instances is dogmatic insofar as it unconditionally favours a rapid abandonment of existing theories. But there is no compelling reason to suppose that the newer theories will necessarily be better than the old ones. This holds true even if the newer theories are corroborated by all the tests that corroborated the old theories and the test that falsified it. As Newton-Smith pointed out, it may happen that the new theory will be falsified in the future by several tests, that the old (abandoned) theory would have passed and thus it may come to be closer to the truth than it. (To this it may be replied that it makes no sense to classify theories that are already falsified in terms of their closeness to truth. But such a reply would be wrong, since, according to Popper, all theories are false – perhaps with the exception of the Ultimate True Theory – yet we want to compare theories in terms of their closeness to the truth). This story may have a political counterpart: Popper urged us to replace the question "How to choose the best leaders?" by the question "How can we choose the less evil leaders and how to correct their mistakes?". But if this is all that can be said about investing leaders with power, then there is nothing that will inherently prevent the possibility of replacing bad leaders with even worse ones. Even if we devise mechanisms to prevent the new leaders from making the same mistakes that the old, bad leaders did, it is still possible that the new leaders will make even more, and more grave, mistakes – that perhaps the old leaders would not have made. Popper did not seem to pay attention to this objection, and the reason why he did so is, in my opinion, that he tacitly assumed that there is a finite number of possible mistakes that can be made; that there is a finite number of negative, falsifying instances of any possible theory. If this assumption were true, then it would indeed be the case that devising mechanisms to avoid the mistakes made in the past – be they political or epistemological – will indeed count as a progress towards truth. But I see no reason to accept this assumption as true. If the assumption of the finite number of possible mistakes is wrong, then the successive replacement of falsified theories by not-yet-falsified ones is not necessarily a progressive step.

As a parenthetical remark: The problem “if we reached the truth, how would we select the simplest theory that is compatible with the truth?” I take to be a genuine problem for Popper. It is obvious that several theories are compatible with the totality of facts (and corroborable by them). Even a committed realist like Popper should (and does) acknowledge this fact. How could we decide that we reached The Ultimate True Theory, even if we found it? An obvious answer is that we should select the simplest among the competing rival theories. But the only place where, to my knowledge, Popper discusses the concept of simplicity is LSD, where he equates it with that of low logical probability. Aside from the various problems that may face the preference for theories that have a low logical probability (which I will briefly discuss below) it is obvious that The Ultimate True Theory – if we reasonably hope to find it and if we want it to be the simplest ultimately true theory – cannot be the one among them with the lowest probability. Or – if Popper still insists that we should strive to advance theories that are as improbable as possible – then this requirement prevents us from reaching the Ultimate True Theory. This is another reason why I believe that valuing the rapidity of scientific change is incompatible with valuing Truth, and that Popper actually offers methodological guidelines for a rapid rate of scientific change, rather than for rapprochement to the truth.

3. The Ideal Identity between the Context of Discovery and the context of Justification.

The idea that I will advance in this section is that the methodology that is needed for the context of discovery is the (ideal) identity between it and the context of justification. This means that those theories should be advanced that have the higher chances of being corroborated. In order to make more explicit this idea, we only need to understand "the probability of a hypothesis" as "the probability of the event that it will be corroborated". (Popper was adamant against reducing the probability of theories to probability of the events predicted by the theory; but the identification of the probability of a theory with the probability of the event of its being corroborated is a different proposal). Since "being corroborated" is a normative notion, it would be superfluous to define the probability of a hypothesis as the probability of its being rightly retained (corroborated). The probability of a theory is thus not merely the probability of a historic event: being corroborated for a certain time is a right historic event.

The ideal identity between the context of discovery and the context of justification means that those theories should be advanced, that are discovered in a context as close as possible to the context of their corroboration/falsification. This may favour rapidity of scientific change – and we saw that this is Popper's ideal, since we will not choose to advance theories that will be impossible to falsify. But this proposal may rehabilitate induction: Popper was constantly opposed to the idea that induction may serve as a justification of a theory, claiming that we never learn by being exposed to repeated occurrences; he opposed the model of learning by trial and error to the model of learning by being exposed to repeated occurrences; Popper wrote that the fact that some scientists discover their ideas after observing repeated occurrences of an event is no more important as a justification than the fact that some scientists discover their ideas after smoking or drinking. I dare to say that this view is mistaken: repeated observations of a certain kind may play a role in the corroboration of a theory and in its being retained in the future, while smoking or drinking cannot play any such role. In the light of this, I believe it is rational to advance those ideas that have a high chance of being corroborated, of standing to severe tests.

A moral can be drawn from these lines. The methodology of rejecting-or-not-rejecting the scientific theories should be supplemented by a methodology of discovering the hypotheses that are worth testing. Popper actually does try to provide rules for such a methodology , by his criterion of falsifiability of hypotheses. But I argued in the first section of this paper that this attempt was wrong: falsifiability is not an intrinsic property of theories, but of the attitudes of people about theories. If indeed we need a methodology of discovery, it seems to me that the context of discovery should be ideally identical with the context of justification.

Scientific rationalism is usually associated with the sharp distinction between the context of discovery and the context of justification, and Popper is no exception. If this distinction could be taken seriously, it would oblige us to take seriously and test all hypotheses, no matter how bizarre, that happen to occur to anyone’s mind. As this already has been proven (by Newton-Smith), the succession of theories that would be considered for testing, rejected and then conjectured, could be chaotic and have nothing to do with progress towards truth. But if a methodological recommendation were made – and followed – to the effect that the context of discovery should resemble as much as possible the context of justification, this situation could be emended. It would ensure both the possibility that theories should be selected in such a way that they could be easily corroborated and/or falsified, and would rehabilitate the status of induction (which Popper constantly abhorred as a method of justification). By the “ideal identity between the context of discovery and context of justification”, I mean that those theories should be selected that have a high chance of becoming probable in the light of the tests to which they will be subjected.

The distinction between “acceptance of a theory” in the sense of considering it worth testing and “acceptance of a theory” in the sense that it should be retained after being tested was made by Bar Hillel in “Popper`s theory of corroboration”, in “The Philosophy of Karl Popper, edited by Paul Arthur Schlipp, vol I, 1974, LaSalle, Illinois, the library of living philosophers): “The term ‘acceptance’ has in fact two different meanings for Popper alone: … acceptance-1, in which a theory is accepted-1 when it is, at the time of its acceptance-1 , the preferred candidate among its competitors for undergoing severe tests, and acceptance-2, in which a theory is (tentatively) accepted-2 when it has passed with flying colors the severe tests undergone, after having been accepted-1 at some prior time. It is only for acceptance-1, of course, that Popper would like all competing theories to be rank-orderable , at least in principle, so that at each time one and only one theory would turn out to be accepted-1 and such that, if the theory passes the severe tests it is supposed to undergo after its acceptance-1, it becomes accepted-2 and, if it fails those tests, the next theory in line will be accepted-1 etc. at no time would two theories compete for acceptance-2” (Bar-Hillel, p. 335). However, Bar-Hilel, if I understood him rightly, reaches a relativist conclusion, namely that there are several criteria, each of them equally justified for accepting (in whatever sense) a theory. (He mentions “probability, corroboration and corroborability, but also simplicity, teachability, impact of the beliefs in their truth within some community” (p. 342, ibidem).

In the light of the proposal that the context of discovery should be ideally identical with the context of justification, those theories should be selected to undergo severe tests that are likely to become very probable after undergoing such tests In LSD, Popper distinguishes between logical probability and probability of events (LSD, VII, 34), writing that “the logical probability of a statement is complementary to its degree of falsifiablility… The better testable statements, i.e. the one with the higher degree of falsifiability, is the one which is logically less probable; and the statement which is logically less well testable is the one which is logically more probable" (p. 119).

It would be wrong to identify the probability of a hypothesis as the truth frequency of those singular statements which agree with it, for then a hypothesis would have a probability of 1/2 if, on the average, it is refuted by every second singular statement of this sequence. Popper thought that the requirement that the logical probability of hypotheses should be as low as possible can be used as a weapon against pseudo-scientific theories: see, for example, LSD p. 269: "One of the reasons why we do not accord a positive degree of corroborateion to the typical prophecies of psalmists and soothsayers is that their predictions are so cautious and imprecise that the logical probability of their being correct is extremely high". He was convinced that there is an incompatibility between the requirement to obtain a high probability and the requirement to obtain a high degree of universality and the greatest possible diversity of instances (p. 271). In other words, if we strive to obtain a high probability, our theories will be uninformative: "If what we value is the securest knowledge available, and if predictions as such contribute nothing towards corroboration, why then may we not rest content with our basic statements?" (LSD, p. 272). Later, on in Realism and the aim of science, he distinguished between the probability of a scientific law in the light of the tests and the probability of an event (Realism…, p. 226), while continuing to insist that the desideratum of corroboration should not be confused with the desideratum for a high degree of probability. "Corroboration cannot possible be a probability – it is more closely related to the improbability of a theory than to its probability: a strong theory (such as Maxwell's electromagnetic theory of light) can be tested more widely and more severely than a weaker theory entailed by it (such as Fresnel's wave theory of light).

However, this preference for improbable theories violates two obvious intuition about rationality: namely that we should try to believe hypotheses as probable as possible; and that the degree of corroboration of a theory raises its probability. The better corroborated a theory is, the more probable it becomes and the more it deserves to be retained and believed. Of course, Popper himself believed that a theory is the more deserving to be retained, the better corroborated it is; but he refused to admit that a high probability has anything to do with these. The reason is, in my opinion, his static view of the probability of theories: he believed that the probability of a theory is given once for all, remaining constant. On the contrary, I believe that a hypothesis may become more or less probable in light of the tests to which it is subjected. (If it is corroborated by many, severe and diverse tests, it becomes more probable; if severe and diverse tests are imagined but they are not available, the hypothesis may become less probable. Moreover, a theory's probability may decrease simply for the reason that the probability of other theories that compete for explaining-predicting the same domain increases).

Popper condemns the attitude (which he regards as following from verificationism) which looks for confirmation everywhere. This is an uncritical attitude. But is not the reverse of this attitude, that of looking for counterexamples everywhere, an equally dogmatic and uncritical attitude? I dare to say that it is a dogmatic attitude, which reflects an irrational bias in favour of new theories. Looking for negative instances and severe tests is an uncritical attitude when we are left with no criterion – except our imagination – for knowing which theories are worthy of being tested. There is no guarantee that the theories that will be advanced (and corroborated) will be “less false” than the rivals which they replaced. If it were replied that it is wrong to speak of a gradation of falsity among the theories that are rightly rejected, and that all false theories belong to a trash can of the history of science, occupying, so to speak, the same level of falsity, this reply would be wrong. It would be wrong since we know, from Popper, that all scientific hypotheses are ultimately false with the exception of the ultimate, ideal, true theory which, most probably, will never be discovered. Since there is nevertheless a gradation between theories in terms of their closeness to truth and since all theories are ultimately false, it follows that a gradation among false theories is necessary.

Popper's preference for theories with a low logical probability seems to me based on the following reasoning: If theories have a high probability, then our corroborating them (after the strongest tests), then gain of information about the world is minimal. But if we succeed in falsifying them, the informational gain would be very high. On the other hand, low-probability hypotheses – if corroborated – provide considerable informational gain. But their falsification would result in low informational gain. It results that what we need for scientific progress is to have our low-probable hypotheses corroborated and our high-probability hypotheses falsified. That's why we seem to need both probable hypotheses (in the hope that we will falsify them) and improbable hypotheses (in the hope that we will corroborate them). (It could be held that the two are equivalent, since any time a low-probable hypothesis is corroborated, a high-probability one is falsified and vice-versa. Even so, it remains unintelligible why advancing low-probability hypotheses should be preferred against high-probability hypotheses).

Moreover, the probability of a hypothesis can only be evaluated, if I understand correctly the issue, only comparatively with other hypotheses. If several hypotheses compete for predicting a certain domain, some of them are more probable, others are less probable. (Via the connexion between high universality and low probability, it follows that those hypotheses that those hypotheses that have a high degree of universality are less probable, although I do not believe this is not necessarily so).

Popper urged the adoption of only low-probability hypotheses: as I understand him, his rationale was that corroborating such hypotheses could result in much more considerable informational gain than corroborating high-probable hypotheses. (Of course, another rationale was the connexion he saw between low probability and degree of universality: the more probable a hypothesis, the less universal it is. I am not sure that the converse is correct: it seems intuitive that we can have very improbable hypotheses that claim to explain a very limited domain, i.e. to have a low degree of universality).

But advocating low-probability hypotheses is only half of the picture: this can be realized since falsifying such hypotheses results in negligible informational gain. On the contrary, falsifying very probable hypotheses results in great informational gain. This is why trying to advance only those hypotheses that have a low logical probability is an irrational methodological requirement. (This is, in my opinion, Popper's imperative for the context of discovery).

If we substitute this imperative by the imperative of the ideal identity between the context of discovery and the context of justification, the correct answer to the question "How probable should the hypotheses we advance be, if our aim is the maximal informational gain?" is, in my opinion: our hypotheses should have a low probability but should acquire a high probability. Thus, in the context of discovery those hypotheses should be selected that have a high chance of standing the severe tests to which they are to be subjected;

If the context of discovery is ideally similar with the context of justification, then we can accommodate the intuition that the hypotheses that are corroborated become more and more probable. What is true, however, is that this ideal identity between the context of discovery and the context of justification cannot accommodate the question "When and how should we modify one of the contexts so as to be more resemblant of the other?". If the context of justification is chosen so as to accord with the context of discovery, this is wrong, since the justification may become circular; if the context of discovery is chosen so as to resemble the context of justification, this may lead to the objection which I raised, namely that we may unjustifiable dismiss those theories that cannot be justified because of technical reasons. But this is all we need for an anti-realist concept of truth, or at least for a concept of truth so understood as the truth should necessarily be accessible to us.

We may thus remain from Popper with the requirement that theories should be presented in such a form as to be easily falsifiable, i.e. to specify in advance the circumstances in which their proponents are ready to abandon them. But this is, at least partly, a psychological requirement, as we saw. Likewise, from Popper’s definition of corroborability as a mark of truthlikeness we may remain with the requirement that as many and as diverse instruments of testing should be available in order more accurately to realize the closeness to truth of our theories. But this is a technical imperative. Likewise, whether a theory ca be corroborated (and how severely it can be tested), this is a question about the availability of technical instruments. Whether a theory is falsifiable or not, this is a problem about the people arguing over the merits of that theory or (pace Popper) about the language of the theory (i.e., its degree of ambiguity). It is not a question about the theory itself, at least not about the theory as a semantic entity. No matter how we try to devise our criteria for appreciating truth or closeness to truth, we cannot escape from psychological or technical factors.