1. Introduction

In the early 1930s Popper's Logik der Forschung (Reference Popper1935, actually published in November 1934) came to solve two traditional philosophical problems: the problem of demarcation between science and non-science (by what criterion do we decide which hypothesis is scientific?) and the problem of induction (that has many formulations and variants, among which Popper chose the following: how do we learn from experience?).

The traditional answer to the first question is that all—and only—established theories belong to science, while the traditional answer to the second is that experience leads to the adherence to established theories. Popper's answers were different. First, he said that those hypotheses are scientific which are capable of being tested experimentally, where tests of a hypothesis comprise attempts to refute it. Second, he argued that learning from experience is the very act of overthrowing a theory with the help of that experience: we learn from experience by repeatedly positing explanatory hypotheses and refuting them experimentally, thus approximating the truth by stages.

This conclusion took a long elaboration, which I think is very interesting both from the historical and the philosophical point of view. Historically, it is interesting to see how Popper came to his original solutions, while philosophically it is interesting to understand why he changed his views—and quite radically, as we shall see.

In this paper I explore both paths, albeit very briefly. In order to do that, we will have to consider some of Popper's very first philosophical writings.Footnote ¹ Of course, Die beiden Grundprobleme der Erkenntnistheorie (together with Logik der Forschung) is of fundamental importance for an understanding of Popper's philosophy, but if we want to understand its background and get a grasp of the difficult path he had to struggle through in order to conceive and elaborate his ideas, we must consider also his early—and largely still unpublished—German works.Footnote ²

2. Popper's Early Inductivism

“The present work, although highly theoretical in its main parts, has arisen out of practical experiences [with pupils], and has eventually to serve practice again. Its method is therefore essentially inductive” (Popper Reference Popper1927, 3) Surprising as it may sound, these words appear at the very beginning of a long typescript which constitutes Popper's first philosophical work.Footnote ³

Indeed, in his 1927 thesis, “Gewohnheit” und “Gesetzerlebnis” in der Erziehung (“Habit” and “Experience of Law” in Education)Footnote ⁴ Popper clearly holds induction as the characteristic feature of empirical science. Contrary to Freud's, Adler's and others’ psychological theories, which often go beyond what is factually verifiable, the theories of natural science, he says, only abstract from empirical data, never asserting something beyond the facts (Popper Reference Popper1927, 19–21).Footnote ⁵ Here Popper is clearly an inductivist (in the style of Ernst MachFootnote ⁶)—something which, in his later accounts of the early development of his own thought, is totally absent and even implicitly denied. In fact, contrary to what he later reports (Popper [Reference Popper1935] 1959, 311–312; see also Popper Reference Popper and Mace1957, [Reference Popper and Schilpp1974a] 1976, 31–44), he did not arrive at his criticism of induction in the years between 1926 and 1928, nor did he formulate his famous criterion of demarcation in those years. “Instead of being involved in abstract epistemological and methodological problems, Popper in this period attempted to find his way in the different fields of psychology” (ter Hark Reference ter Hark2002, 80; Reference ter Hark1993).Footnote ⁷

In order to be empirical, a theory “may only be formed inductively, through abstraction from empirical facts, and may never be projected into them” (Popper Reference Popper1927, 20).Footnote ⁸ The inductive process follows three steps:

1. a. an “unprejudiced description (phenomenology) of empirical facts”Footnote ⁹ (no reference to Husserl), that is, a comprehensive description of the psychology of lawfulness among children (Popper Reference Popper1927, 20);

2. b. an “attempt at abstraction” (Reference Popper1927, 20);Footnote ¹⁰

3. c. an “ordered representation (from a theoretical perspective)” (Reference Popper1927, 20),Footnote ¹¹ so as to offer an explanation of the phenomena taken into consideration (19).

Interestingly, Popper also points out an intrinsic danger in the inductive method, which threatens particularly psychoanalysis. The first (phenomenological) stage will always receive a feedback from the third (theoretical) one, so that the facts are selected to fill certain gaps in the theory: “As time goes by, systematics penetrates deeper and deeper into phenomenology; this entails the danger that phenomenology, the description, which must be purely empirical and unprejudiced, gets influenced by the theory itself. As a consequence, it [phenomenology] presupposes the theory for which it should provide the inductively based empirical evidence in the first place; this would clearly be a so-called circular reasoning, a petitio principii” (Reference Popper1927, 20).Footnote ¹² Clearly, Popper is very far from his later and well known deductive view that there is no observation that is not theory-laden.Footnote ¹³

Consider also the following passages:Footnote ¹⁴

In 1927, then, Popper feels the necessity to justify the scientific character of psychology comparing it to natural sciences, which are founded (as Popper himself thinks in those years) on induction. At this stage, thus, there is no such a thing as a “problem of induction”: induction is to Popper no problem at all— without any qualms, it is taken to be the criterion for empirical science.

3. The Problem of Demarcation

In his first thesis Popper states some “general methodological presuppositions” (Reference Popper1927, 18)Footnote ¹⁸ about the problem of the scientific character of pedagogy, defending its scientific status against the sceptics on the basis of the “objective-scientific decidability of pedagogical problems properly put” (7):Footnote ¹⁹ these remarks, as ter Hark also notices (Reference ter Hark2002, 88), are Popper's first steps in methodology, or the philosophy of science. Such a treatment should deal primarily with the “delimitation of the empirical part of pedagogy from its non-empirical part” (7, my emphasis)Footnote ²⁰ since Popper holds it to be true that “pedagogy as a modern science must first be purely empirical” (7).Footnote ²¹ Complementarily, it is more important “to delimit the rational, speculative part” (7).Footnote ²² These first methodological remarks do not show any sign of Popper's deductive method of trial and error: Popper's stance is thoroughly traditional, that is, inductive (see ter Hark Reference ter Hark2002, 88).

We must also notice that the term Abgrenzung (which we might translate with “delimitation”) does have a different meaning from the standard one, usually translated with “demarcation.” In fact, it is crucial that in 1927 Popper is not relying on a deductive method (falsifiability) as a criterion of demarcation: as we have seen, he takes inductive method for granted. In 1927 Popper's problem is actually to verify the point to which general theoretical assertions are supported by empirical facts, and are consequently valid: he is simply delimiting the science which intends to relate to reality (logic and mathematics excluded, then) through the integral and concrete support of empirical evidence. Only empirical theories—that is, theories whose assertions are covered by empirical facts—share the true scientific method (that is, of course, induction). Moreover, this early discussion of Abgrenzung is a discussion within the field of psychology, while Popper's later discussion of the demarcation problem is framed in terms of a sharp distinction between scientific disciplines (such as physics) and non-scientific ones (such as psychoanalysis and Marxism):Footnote ²³ in 1927 Popper speaks only of the boundary between Adler's theory and empirical psychology (Külpe's and Bühler's Denkpsychologie). This does not mean that Popper's Hausarbeit is to be regarded as an early attempt to solve a problem of demarcation between science and non-science:Footnote ²⁴ in fact, Popper has by no means in mind the concept of demarcation (or the solution to the problem of demarcation) as we know it from his published works (see Popper [Reference Popper1935] Reference Popper1959, 34–35; and [Reference Popper1979] Reference Popper1994, XXVII and 3–5). In his 1927 thesis the problem of demarcation is as absent as the problem of induction.Footnote ²⁵

In his Reference Popper1928 doctoral dissertation, Zur Methodenfrage der Denkpsychologie (The Problem of Method in Cognitive Psychology)Footnote ²⁶ Popper holds an inductivist position and works on the theory, rather than on the psychology, of knowledge. For in his second thesis Popper discusses scientific method in psychology, taking as his starting point Schlick's Allgemeine Erkenntnislehre and Bühler's Die Krise der Psychologie.Footnote ²⁷ Bühler defends a “pluralism of aspects”(Popper Reference Popper1928, 5)Footnote ²⁸ in psychology and establishes his methodology as a prerequisite for a theory of language. Psychology is possible if and only if the aspects of experience, of behaviour and of ideas in the objective sense (“Gebilde des objektiven Geistes”) find an equal place. Popper applies this pluralistic methodology first to the mind-body problem and next to cognitive psychology (Denkpsychologie). He aims first at defending Bühler's pluralistic methodology against the objections of physicalism,Footnote ²⁹ and then at showing that Bühler's pluralistic methodology “will display itself also as inevitable in cognitive psychology” (Popper Reference Popper1928, 5).Footnote ³⁰ As to Schlick, Popper discusses, in particular, the setting out of the psychophysical analogy, according to which the series of psychical and physical phenomena of the nervous system run in parallel, with none being the cause or the effect of the other. Schlick regards such a parallelism as a hypothesis which we have to accept in order to remedy several problems faced by the theory of the reciprocal action of mind and body. He therefore accepts the parallelism as a necessary postulate if we want to explain reality. But postulates such as these remain outside empirical science, and the same holds for the reciprocal causality which “neo-vitalists” require (see Popper Reference Popper1928, 42). Popper objects to both physicalism and the psychophysical parallelism. He concedes that the choice between Bühler's pluralism (which recognizes the interaction of body and mind) and Schlick's physicalism can not be logically decided. However, he argues, a methodological separation between physics and psychology is essential. Schlick's physicalism offers no working hypothesis for psychology. The positivist ideal of the methodological unity of the sciences is logically problematic and methodologically not viable. Scientific procedures are logical and autonomous: the task of epistemology is to determine them. In contrast, pre-scientific thinking reflects psychological experience. Epistemological and psychological issues must be kept separated (see Hacohen Reference Hacohen2000, 158–161).

However, it is only with his third, Reference Popper1929 thesis, Axiome, Definitionen und Postulate der Geometrie,Footnote ³¹ that Popper sets himself on the path towards a satisfactory solution of the problem of demarcation. Indeed, here Popper follows three steps (see Hansen Reference Hansen, Jarvie, Miller and Milford2004):

1. 1. he shifts the focus of his work from the psychology of knowledge to the theory of knowledge (Popper Reference Popper1929, 25–36): he is no longer interested in the “experience of law” (Gesetzerlebnis), but in the logical status of natural laws: indeed, he speaks of such things as the “validity of foundations” (“Geltung der Grundsätze”, 25);

2. 2. he distinguishes between strictly universal statements and numerical universal statements (or, what is the same, between strictly universal statements and singular statements);

3. 3. he solves the problem of induction—a problem that “can not even be formulated” without the distinction between strictly universal statements and singular statements.Footnote ³²

These three steps take Popper to his philosophical breakthrough, allowing his revolutionary solution to the problem of rationality. Let me put this into context.

4. Popper's Philosophical Breakthrough

At the very beginning of his philosophical development, Popper was an inductivist; then he radically changed his mind. The break that marks Popper's philosophical development dates, I suggest, to 1929 (ten years after the year Popper identifies as crucial for his views).Footnote ³³

As I see him, Popper is the philosopher of revolution. He said that we learn from experience by the very act of overthrowing a theory with the help of that experience. We learn from experience, that is, by repeatedly positing explanatory hypotheses and refuting them experimentally, thus approximating the truth by stages. In other words, we gain theoretical knowledge when and only when revolutions occur.

And I think that one of the most important lessons we could learn from him resides precisely in the revolutions Popper's thought went through in his early and most creative years. The first revolution was political: in his youth he was a communist and then a socialist, but eventually renounced both these ideas since he found them mistaken. The second revolution was epistemological: Popper was a committed inductivist and then became a deductivist. While the first revolution took place in 1919, as Popper himself says in his autobiography ([Reference Popper and Schilpp1974a] Reference Popper and Schilpp1976, 31–38), it is 1929 that marks the turn in Popper's philosophy.Footnote ³⁴ For, I suggest, in Axiome, Definitionen und Postulate der Geometrie we notice a significant break (maybe due to very practical reasons, given Popper's new job as a teacher of mathematics and physics) from the subjects he had been studying and which had a pedagogic-psychological character. Up to 1929 epistemology enters as far as the problem is that of the justification of the scientific character of these fields of research. In 1929 Popper explicitly discusses the cognitive status of geometry without referring to psycho-pedagogical aspects. This thesis first formulates the problem of scientific rationality, enabling Popper's future philosophical progress. It reflects Popper's turn from cognitive psychology to the logic and methodology of science.

In the thesis Popper presents a scholarly survey of the problems connected to geometrical axioms, postulates and definitions in Euclidean geometry. As is well known, Euclid's fifth postulate (the parallel postulate) proved very problematic: the dissatisfaction with it stemmed from its complicated and somewhat contrived nature, when compared with other postulates; it was considered true, but not sufficiently self-evident to justify its status as a postulate.Footnote ³⁵ Since its appearance, then, non-trivial attempts were made to prove it from the other axioms. Failures to do this culminated in the various non-Euclidean geometries first devised by Gauss, Bolyai, Lobatchevskij and Riemann, who gave up the parallels postulate and developed a geometry independent of it. Non-Euclidean geometries were purely conceptual. They were not grounded in experience or perception, and thus epistemology was irrelevant to them (see Popper Reference Popper1929, 61).Footnote ³⁶

For the first time, theoretical physics faced a choice among competing geometries: all of them were internally consistent, offered alternative space-conceptions and were always unconditionally true. There arose the problem of their application to reality. Logic (as well as mathematics) is never involved in questions of conformity to reality, since the relationships it establishes among objects are conceptual, not real: the only thing at issue is its internal consistency.Footnote ³⁷ The same holds for pure geometry: all geometric theorems are analytic, derived from axioms. As long as the axioms are accepted, the theorems are valid a priori. Applied geometry, however, is different: it establishes real, not conceptual, relationships among objects. Its theorems are, at least in part, synthetic and valid a posteriori. Their proof requires observational verification. Therefore, applied geometry involves scientific procedure and raises epistemological as well as methodological issues (see Hacohen Reference Hacohen2000, 176–177).

The most striking applications of geometry are in the field of theoretical physics, where divergent concepts of geometrical-physical space compete. Popper agrees with Poincaré (against Helmholtz): our choice of geometry for physical space is free and physical theories can always be reinterpreted in the light of geometry—but such reinterpretation often requires introducing too many ad hoc hypotheses. Therefore, Popper adopts the methodological proposal that scientific theories require the greatest economy in the use of hypotheses (see Popper [Reference Popper1935] Reference Popper1959, 82–83). Our choice among competing geometrical metrics to describe our space can be methodologically decided. It is Popper's first statement on the methodology of natural science. The methodological path he sets himself to take is clear; while accepting a strong conventionalist component in methodology, Popper chooses to make tests express the final verdict upon our decisions (Hacohen Reference Hacohen2000, 177–178). For sure, the acceptance of these results is conventional, but our decision bears an epistemic value. Together with the idea of simplicity, the metaphysical assumption of realism paves a new way, rigorously deductive, far both from Poincaré's conventionalism and Helmholtz's inductivism.

Thus, applied geometry sets the context for Popper's discussion of scientific rationality. In the following years, he will be applying the hypothetico-deductive model to all natural sciences (which, unlike geometry, are not axiomatic): “whenever we are doubtful whether or not our statements deal with the real world, we can decide it by asking ourselves whether or not we are ready to accept an empirical refutation. If we are determined, on principle, to defend our statements in the face of refutations …, we are not speaking about reality. Only if we are ready to accept refutations do we speak about reality” (Popper Reference Popper1946, 212).

Consider the closing paragraph of the 1929 thesis:

To sum up, then, it is the problematic relationship between geometrical-mathematical constructions and physical reality which triggers Popper's philosophical revolution. As a consequence, he gets over a too direct notion of such relationship, casting doubts on inductive inference, and starts conceiving in a new (non-inductivist) manner the problem of the relationship between axiomatized theories and reality, between theoretical and observational propositions. It is only in 1929 that Popper sees induction as a problem—and, given its close interdependence with the solution of the demarcation problem, 1929 marks the first step towards such a solution. Here lies Popper's philosophical breakthrough, the insight that might allow us to bridge the gap in our reconstruction of the decisive developments of his thought, from the early inductivist position to the one he adopts in Die beiden Grundprobleme der Erkenntnistheorie.

5. Popper's Later Fall Back into Inductivism

In Logik der Forschung Popper proposes that a theory is scientific if and only if it can be overthrown with the help of experience, and that we gain theoretical knowledge from experience when and only when revolutions occur. There is nothing explicit about corroboration, namely about the failure to refute hypotheses.Footnote ⁴⁰ Therefore, Popper tried to solve the problem of induction not by his theory of corroboration, which came later,Footnote ⁴¹ but by his theory of gradual approximation to the truth by repeatedly making explanatory hypotheses and refuting them experimentally. It is important to stress how Popper's original solution of the problem of induction, as stated in the early 1930s, offers a model of the progress of science and of the growth of knowledge by a never-ending process of conjectures and refutations—of bold scientific hypotheses which we must do our best to criticize and refute.

In Logik der Forschung Popper declares learning from experience to be not by positive evidence but by negative evidence. For, if we search for positive evidence, the evidence will not be scientific, the only way to find positive evidence recognizable by science is by looking for negative evidence.Footnote ⁴² If we look for negative evidence, says Popper, we may find it, or else we will find positive evidence; but if we look for positive evidence we will find only positive evidence, which is of no scientific value (see Agassi Reference Agassi1961, Reference Agassi, Cohen and Wartofsky1968Reference Agassi).

Science, then, is to Popper a special case of Socratic dialogue, with experiments and observations offering new arguments, or new empirical criticisms. And when an attempt at empirical criticism misfires the result is positive evidence. Whatever role positive evidence may play, it can not play any role qua positive evidence. It may stimulate the invention of a conjecture and it may be not only a positive support of one conjecture, but also a refutation of another. This, and no more: the corroboration of a theory is enlightening, though less enlightening than its refutation—but it is not really necessary.

However, in his later works Popper claimed that corroboration is important, and not only enlightening as discovery and increasing of explanatory power of a hypothesis. Corroboration became even essential to science, since it constitutes an encouragement to our research: a good theory should be not only capable of being refuted, but also it should not be refuted too soon. We want positive evidence before we get negative evidence, so as to be assured that knowledge grows. With that, Popper changed his view of science from a theory of conjectures and refutations to a theory of conjectures, corroborations and refutations. Indeed, in 1963 Popper introduced a “third requirement” to be satisfied by a new scientific theory for it to be a major advance on its predecessors. His first two requirements were: (1) “The new theory should proceed from some simple, new, and powerful, unifying idea about some connection or relation … between hitherto unconnected things … or facts … or new ‘theoretical entities’ …”; and (2) “the new theory should be independently testable” (Popper Reference Popper1963b, 241; see also 240–248). The third was: “the theory should pass some new, and severe, tests” (Popper Reference Popper1963b, 242). It may be divided into two parts: “first we require of a good theory that it should be successful in some of its new predictions; secondly we require that it is not refuted too soon—that is, before it has been strikingly successful” (Popper Reference Popper1963b, 247; see also Watkins Reference Watkins1984, 288–304).Footnote ⁴³

But if our aim is to learn from experience all this is redundant. We learn from experience by repeatedly positing explanatory hypotheses and refuting them experimentally, thus approximating the truth by stages. From this point of view corroborations are entirely irrelevant. On the contrary, testing matters, and it has an undeniable epistemological significance. “Testing is important because it is only by subjecting our theories to tests that we have any opportunity of eliminating those that are false; and the more severe the test, the more generous the opportunity” (Miller Reference Miller1994, 120).Footnote ⁴⁴ Corroborations are needed if science is to exist, but they make no contribution to the progress of science or to the growth of knowledge.

How do we learn, then? Popper's answer is: by criticizing our errors. The idea that anything we say can be subjected to critical examination is the core of Popper's philosophical attitude, his solution to the problem of rationality. Popper takes the critical attitude as fundamental: corroboration is just one sort of happening in the history of science which results from this attitude and to which, in turn, this very attitude should be applied.Footnote ⁴⁵ Practically all rational philosophers have stressed the value of criticism, yet they almost all viewed criticism—that is, the elimination of error—as a preliminary to the positive advancement of the understanding. Popper almost alone, and alone in the twentieth century, claimed that criticism constitutes the very engine of the advancement of our understanding of the world and of our place in it.Footnote ⁴⁶

Rationality is critical debate, said Popper. As Joseph Agassi remarked, “rationality is not any critical debate, but only that which is oriented towards a specific goal as well as might be reasonably expected” (Agassi Reference Agassi, Cohen and Wartofsky1968, 34). And this goal, I suggest, must be truth (see also Gattei Reference Gattei2002a, 249–252, and Reference Gattei2002b, 449–451). The appropriate standards of criticism are not those that appeal to justification, but those that appeal to truth. While traditional philosophy regarded the justification of beliefs as the goal, and the critical method a way of reaching it, for Popper the goal is truth, and it is the method of investigation itself that is rational.Footnote ⁴⁷ This is the core of the revolution Popper marked in twentieth century philosophy of science—rationality requires no foundation, only critical dialogue: it is the end of foundationist philosophy.

From the philosophical point of view, the twentieth century was characterized by the crisis of foundationalism. Philosophers were confronted with the problem of how to respond to it. Some have concluded that scientific knowledge is unjustified and hence irrational after all. Others—indeed, the majority—have opted for retaining the idea that scientific knowledge is justified belief, while weakening either the idea that truth is correspondence with reality or the idea that justification shows that a statement is true. Each of these responses retains the foundationalist theory of rationality, according to which it is irrational to accept a belief that has not been justified and obligatory to accept one that has. But the failure of foundationalism has no implication whatsoever for truth. It does not belittle the truth, and it does not reduce it to solidarity and consensus (Wittgenstein, Kuhn). It only shows that—as Socrates beautifully said—we are living in the twilight zone between knowledge and ignorance, where the views that we hold may be true, but where we are unable to know that they are. The failure of foundationalism does not drag epistemology with it. The twilight zone between knowledge and ignorance is an ideal well worth holding on to.