2 Theory of science

Two problems structure Popper’s theory of science: he calls them ‘the problem of induction’ and ‘the problem of demarcation’. The problem of induction can be formulated: what relation holds between theoretical knowledge and experience? The problem of demarcation can be formulated: what distinguishes science from metaphysics as well as from logic and mathematics?

The received answers to these problems are: we get knowledge from experience by means of induction, that is, by inferring universal theories from accumulations of particular facts; and the inductive method demarcates science from metaphysics as well as from logic and mathematics. However, Hume showed that inductive inferences are invalid, hence the problem of induction: either we get knowledge from experience by invalid means (irrationalism) or we do not get any at all (scepticism); and induction collapses as a demarcation criterion (see Demarcation problem §1; Induction, epistemic issues in ).

In Part I of The Logic of Scientific Discovery, Popper’s solutions to these two problems are set out and shown to converge: knowledge results when we accept statements describing experience that contradict and hence refute our hypotheses; thus a deductive rather than an inductive relation holds between theoretical knowledge and experience. Experience teaches us by correcting our errors. Only hypotheses falsifiable by experience should count as scientific. There is no need for the inductive leap that Hume thought illogical but unavoidable; and the Hobson’s choice between irrationalism or scepticism is avoided. To the question, ‘where do hypotheses come from, if not inductively from experience?’, Popper answers, like Francis Bacon, that they come from our propensity to guess (see Bacon, F. §6 ); in any case they cannot come from observation alone because there is no observation without hypotheses. Hypotheses are both logically and psychologically prior to observation. We are theorizing all the time in order to navigate in the world, and our encounters with negative evidence are the bumps that deliver information about the shape of reality.

The Logic of Scientific Discovery is dialectical in style, dealing with the traditional alternatives and the objections to each idea as it goes along. It is remarkable how frequently critics rediscover objections set out and answered in the book. The commonest objection is that, just as no amount of experience will conclusively verify a statement, so no amount of experience will conclusively falsify it. To answer this objection Popper points to a logical asymmetry. A universal statement cannot be derived from or verified by singular statements, no matter how many are marshalled. It can, however, be contradicted by one singular statement. The logic of falsification is the issue; conclusiveness is a red herring. Another argument, to the effect that the force of falsifying evidence can always be evaded by ad hoc definition or simple refusal to countenance it, Popper finds insuperable. The way to proceed, he concludes, is to entrench falsifiability in a methodology.

For Popper, a methodology is a policy decision governing action and embodied in norms or ‘methodological rules’. Our decisions concern which course of action will best foster our aims. Thus falsificationism is made into a supreme rule to the effect that the ‘rules of scientific procedure must be designed in such a way that they do not protect any statement in science against falsification’ ([1935] 1959: 54). The rule for causality is typical of the small number offered: ‘we are not to abandon the search for universal laws and for a coherent theoretical system, nor ever to give up our attempts to explain causally any kind of event we can describe’ ([1935] 1959: 61). A broad epistemological ambition is revealed when Popper generalizes: ‘It might indeed be said that the majority of problems of theoretical philosophy, and the most interesting ones, can be reinterpreted…as problems of method’ ([1935] 1959: 56) (see Scientific method §2 ).

Throughout The Logic of Scientific Discovery, Popper defines his position by debate and contrast with logical positivist positions regarding meaning, and with two traditional views regarding science, inductivism and the conventionalism of Poincaré and Duhem (see Conventionalism §1; Logical positivism §4 ). It is notable that, like the logical positivists, Popper expresses unbounded respect for science. Unlike them, he grants a constructive (historical) role to metaphysics in science, seen as directly descended from the earliest Greek speculations about the nature of the world. The demarcation between science and metaphysics is thus a matter for decision, not a discovery about the nature of things. Popper’s attacks on central logical positivist contentions contributed to the demise of that movement.

Popper respects conventionalism as self-contained, defensible and most likely consistent. His objection is that it risks treating obsolete or floundering science as incontrovertible truth. Yet Popper is a conventionalist in one respect: methodology. As opposed to the ‘methodological naturalism’ of the logical positivists, who treat the demarcation between science and metaphysics as a difference existing in the nature of things, or rather, in the nature of language, Popper is a ‘methodological conventionalist’, proposing rules that embody choices or decisions – which are in turn governed by aims. His demarcation should be judged, Popper maintains, by whether it proves fruitful in furthering the aims of discovering new ideas and new problems.

Part II of The Logic of Scientific Discovery consists of chapters on theories, falsifiability, the empirical basis, testability, simplicity, probability, quantum theory and corroboration. Each is an expansion, development and defence of the ideas briefly stated in Part I and parries a particular cluster of critical objections. The chapters on probability and corroboration, for example, deal at length with the objections that the pervasive probability statements of modern science are not falsifiable, and that they measure the strength of our inductive evidence. The chapters endeavour to show how probability statements can be falsified in relevant ways, and how they are better interpreted as statements of frequencies rather than as measures of inductive support.