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Karl Raimund Popper’s The Logic of Scientific Discovery, one of the most important books ever written on the philosophy of science, begins with the problem of induction. An inference is inductive, Popper explains, if it moves from a singular statement (roughly, a statement whose subject term refers to some particular concrete thing) to one or more universal statements (roughly, statements whose subject terms refer to all the members of a class of things). In science, such inferences occur when one passes from descriptions of particular experimental results to hypotheses or theories alleged to be justified by these results. “All observed swans have been white” sums up a set of particular statements that report observations of concrete particular items. “All swans are white” expresses a universal statement one might inductively infer from that summary.

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The Problem of Induction

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Notoriously, Popper notes, such inferences are not deductively valid, and the problem of induction is the question of whether such inferences are ever rationally legitimate, and if so, under what conditions. One widely held view, Popper notes, is that the universal statements that express natural laws, or laws of science, or well-confirmed scientific theories, or the like, are known by experience; that is, singular statements are statements known by experience from which the natural-law-expressing universal statements may somehow legitimately be derived. Hence, in this view, the problem of induction has some proper solution.

This alleged solution, Popper continues, is often expressed in terms of a principle of induction—a proposition known to be true that can be placed in inferences from singular to universal scientific statements and whose presence in such inference renders the inference rationally compelling. Some philosophers have held that, without some principle of induction, science would be without a decision procedure and could no longer distinguish solid theory from superstition.

This alleged principle of induction, Popper notes, cannot be a logical truth or a statement true by virtue of its very form or structure because no such proposition would legitimately lead one from “All observed A’s are B” to “All A’s are B,” or from singular to universal statements in any other case. It must rather be synthetic or not contradictory to deny. How, though, Popper asks—consciously restating an argument offered by Scottish philosopher David Hume—should one rationally justify one’s acceptance of this principle? The principle must be not a singular but a universal statement. One cannot certify its truth by logic alone. If, then, one tries to justify it from experience, one will again face the very sort of derivation of universal from singular statements the principle itself was meant to sanction, and so on ad infinitum if one appeals to a higher-order inductive principle. Perhaps, an inductive principle is accepted by “the whole of science”; however, Popper asks, cannot “the whole of science” err? It will not do to say that singular statements, while they do not entail universal conclusions, nevertheless render such conclusions probable, for then one would need some principle of probability, and while perhaps this would differ in content from a principle of induction, its justification would present similar difficulties.

Popper completely rejects the familiar inductivist view that, while not rendering universal statements certain or providing conclusive justification for them, true singular statements can provide good reason for universal statements or render them (at least to some degree) probable. Popper argues that, if some degree N of probability is to be assigned to statements based on inductive inference, then some sort of principle of induction must be somehow justified. How this is to be done remains utterly problematic, even if one weakens the alleged relationship between singular premise and universal conclusion (“providing some degree of reliability” replacing “inductively justifies”) or the alleged status of the conclusion (“probable” replacing “true”). Other attempts to shore up induction, Popper feels, are equally unsuccessful.

Popper also rejects the views that induction needs no justification and that universal statements are merely, albeit perhaps infinite, conjuncts of singular statements. In this respect, Popper’s view agrees with a remark by philosopher Bertrand Russell to the effect that there are two kinds of reasoning: deductive and bad.

Rejection of inductive reasoning, Popper holds, involves much gain and no loss. Obviously, however, if he rejects inductive inferences and hence inductive confirmation of theories, Popper must replace this account of scientific method by some other. It is this positive, constructive task that is the central topic of The Logic of Scientific Discovery.

Testing Theories

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The basic task of the scientist, Popper contends, is to put forward, and then test, theories. Part of this task, of course, is the invention of theories, a matter Popper holds “neither to call for logical analysis nor to be susceptible of it.” Study of the conditions, activities, and stages included in the invention of theories, he holds, is a matter for psychology, not philosophy. Philosophy, the logic of knowledge as opposed to the psychology of knowledge, is concerned with the testing part of the scientist’s task.

This testing procedure, Popper says, begins by deducing consequences from the theory being tested; the theory, in effect, becomes a premise from which conclusions are deductively derived. This done, Popper continues, four lines of testing may be distinguished. First, the conclusions may be compared among themselves; this provides something of a test as to the internal consistency of the theory. Second, the conclusions may be examined to see if the theory has any empirical consequences, and so is scientific as opposed to tautological. Third, the conclusions may be compared with those of other theories to see whether the theory, if it survived empirical tests, is such that its acceptance would mean scientific advance. Fourth, the empirical conclusions or predictions, if any, are applied to experimental results to see if what the theory tells us will occur really does occur.

It is this fourth line of testing that is central for Popper. It is the new empirical consequences of a theory—empirical conclusions that follow from it but not from hitherto-accepted theories—that gain the assessor’s attention. These predictions are compared with the results of relevant experiments, old or new; if the predictions of what would happen under certain circumstances are not correct descriptions of what happened under those conditions, the theory, Popper notes, is falsified. (The form of deductive inference involved here is the simple and standard modus tollens: if p entails q, and q is false, then p is false.) If the predictions are correct, then the theory is (so far) verified. A theory that after numerous tests is not falsified is corroborated, although this is fundamentally a matter of not having been falsified. This doctrine of testing procedure raises various questions. What Popper emphasizes most, however, is that the procedure outlined above contains no inductive procedures whatever and yet does not leave the scientist, or the philosopher of science, without a rational decision procedure when faced with a choice between incompatible theories.

Science and Nonscience

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Popper’s “criterion of demarcation” requires that a genuinely scientific hypothesis must be (in principle) empirically falsifiable. Popper regards distinguishing the nonscientific (including what is logical, mathematical, or metaphysical) from the scientific—a task he designates “the problem of demarcation”—as an epistemological problem, perhaps the most basic one. He holds that appeal to inductive reasoning provides no solution to this problem and that his own testing-through-attempting-to-falsify account of scientific decision procedure solves it.

In contrast to traditional (for example, Humean) empiricism, which recognized as scientific only concepts analyzable in terms of sensory phenomena, Popper holds that statements, not concepts, are the basic elements of scientific theories. In contrast to later empiricism, which at least to some degree replaced analysis of concepts by analysis of statements but recognized as scientific only statements derivable from (or reducible to) elementary perceptual claims, Popper holds that any statement that entails a proposition that describes a possible experimental or observational result is scientific, whether or not it is itself entailed by some set of elementary perceptual claims. (“Scientific” here does not mean “part of science” and certainly not “true,” but “within the scope of scientific interest.” One might say that mathematical claims are those that, whether true or false, fall within the domain of mathematics in that they are decidable by its procedures; then one is using the word “mathematical” in a sense analogous to that in which “scientific” is used above.)

Popper’s criterion of demarcation, he admits, rests, if not securely then at least squarely, on a convention. He distinguishes science from nonscience, he tells us, not on the basis of some discernible intrinsic difference between scientific and nonscientific propositions, but on the basis, in effect, of a decision that the science/nonscience distinction be made along the line of demarcation. This decision, he admits, is not beyond rational dispute; however, he adds that any such dispute can be only among those who share his purposes, and whether one does that or not, he holds, is beyond rational dispute. Thus if Popper succeeds in marking off what is of scientific interest from what is not, he feels he will have been triumphant. The logical positivists, he contends, shared his purpose but, by appealing to the verification principle (which, roughly, asserts that a sentence has truth value only if it is either a tautology or is empirically confirmable or disconfirmable) as their principle of demarcation, failed to provide a basis for distinguishing science from metaphysics. The core of their failure, Popper suggests, is found in their acceptance of induction as a confirmation method. By contrast, and without claiming anything about whether metaphysical propositions have truth value, Popper holds that his own criterion does mark out the desired distinction. If one has some other end in mind, there is neither reason nor need to suppose his criterion will serve that end.

Popper, then, views science as an empirical theoretical system—a system of synthetic or nontautological statements that represents not only a possible but also the actual world of experience. That a system does represent the world is guaranteed only by its having been exposed to unsuccessful falsification attempts. This, Popper notes, falls short of the ideal of philosophers who require that meaningful statements be conclusively verifiable or in principle determined as true. It replaces this ideal by another: that a scientific statement be capable of being refuted by experience. Lest this seem to trivialize natural laws, Popper points out that the more ways there are of refuting a proposition, or the more ways there are of its going wrong, then the more information the proposition contains. Information content waxes proportionate to falsifiability potential.

Falsification Criterion

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The falsification strategy, Popper notes, is made possible by an asymmetry between verification and falsification; that a proposition cannot be verified or established does not entail that it cannot be falsified or refuted, and that a proposition can be falsified does not entail that it can be verified. Further, although even if one limits oneself to propositions with empirical content, no set of singular statements will entail a universal statement, but a universal statement will entail singular statements. The failure of the verification principle, Popper asserts, is no reason to expect the falsification criterion to suffer a similar fate.

A complication, if not a problem, arises, however, from the fact that rarely if ever does a theory all by itself entail any predictions; it does so only together with auxiliary hypotheses. Schematically, one has not that T (theory) entails P (prediction), but that T and H (auxiliary hypothesis) entails P. If, then, one deduces P from T and H, and discovers that under the relevant controlled experimental conditions, P turns out to be false, various alternatives remain open. One could reject the rule of inference by which P was derived, claim that the experiment was not properly conducted, or deny that one’s perception of the result was correct, although these alternatives may often seem radical. Or one could reject T, or else H. If one rejects H, one can retain T without recourse to any of the other alternatives noted. If one always rejects the auxiliary hypothesis, no theories will ever be falsified. To put it mildly, this would be inconvenient for Popper’s perspective.

Popper is fully aware of the problem. To meet it, he specifies that when a member of a scientific community proffers a theory, the person must specify the conditions under which the theory itself (and not some other proposition, be it auxiliary hypothesis or whatever) is to be abandoned. In such fashion, as it were, those who play the game of science must be prepared to say when they will admit defeat.

Popper maintains that his view provides for the objectivity of scientific theories, which, he contends, lies in their being intersubjectively testable. If science is to have an empirical basis, he states, the propositions composing this basis must themselves be objective and hence intersubjectively testable. Therefore, they must entail predictions and so on ad infinitum so that science can contain no ultimate statements. The infinite regress thus produced, he argues, is not vicious. True, every claim can be tested, and testing must stop somewhere so that some claim is accepted that is not tested—some claims will be accepted as correct observational reports without their having run a falsification gauntlet. However, this, Popper reminds us, violates no tenet of his philosophy of science, and in principle, one can test any proposition one wishes.

The net effect of this is that scientific knowledge is possible without its being required to rest on allegedly indubitable propositions. Popper explicitly rejects the view that science is made up of propositions about which scientists are rightly epistemically certain—about which it is logically impossible to be wrong—and his methodology in philosophy of science rules out science’s having, or needing, indubitable foundations. In this important respect, as in others, he differs from classical empiricism.


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Additional Reading

Burke, T. E. The Philosophy of Popper. Manchester, England: Manchester University Press, 1983. Argues that, despite Popper’s disclaimer, intellectual and moral relativism are inherent in his philosophy of science.

Levinson, Paul, ed. In Pursuit of Truth: Essays on the Philosophy of Karl Popper on the Occasion of His Eightieth Birthday. Atlantic Highlands, N.J.: Humanities Press, 1982. Laudatory articles that provide a good introduction to Popper’s ideas and their impact on the philosophy of science. The last four essays focus on Popper himself.

Magee, Bryan. Philosophy and the Real World: An Introduction to Karl Popper. La Salle, Ill.: Open Court, 1985. First published as Popper in 1973, this brief but comprehensive exposition of Popper’s ideas remains the best introduction to Popper’s thought for the general reader.

O’Hear, Anthony. Karl Popper. London: Routledge and Kegan Paul, 1980. A negative evaluation of Popper’s philosophy of science, arguing against his rejection of certainty and denying Popper’s contention that the principle of falsification is an adequate criterion for distinguishing what is true science from nonscience.

O’Hear, Anthony, ed. Karl Popper: Philosophy and Problems. Royal Institute of Philosophy series. Cambridge, England: Cambridge University Press, 1995. This collection of essays examines Popper’s philosophy. Includes bibliography and index.

Raphael, Frederic. Popper. New York: Routledge, 1999. An excellent biographical introduction to the thoughts of the philosopher, clearly presented and requiring no special background. Bibliography.

Schilpp, Paul Arthur, ed. The Philosophy of Karl Popper. 2 vols. La Salle, Ill: Open Court, 1974. Contains thirty-three critical essays, mostly by noted philosophers; Popper’s extensive “Replies to My Critics”; his intellectual autobiography (revised and separately published as Unended Quest in 1976); and a substantial bibliography.

Shearmur, Jeremy. The Political Thought of Karl Popper. London: Routledge, 1996. This book examines Popper’s contributions to political science. Includes bibliography and index.

Stokes, Geoff. Popper: Philosophy, Politics, and Scientific Method. Key Contemporary Thinkers series. New York: Blackwell, 1998. This volume, one in a series on contemporary philosophers, focuses on Popper’s contributions to social science methodology. Includes bibliography and index.

Williams, Douglas. Truth, Hope, and Power: The Thought of Karl Popper. Toronto: University of Toronto Press, 1989. Interprets Popper’s social and political thought as a powerful defense of individualism and liberal democracy against the best known justifications of collectivism and utopianism in the Western philosophical tradition.

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