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.
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...
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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...
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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...
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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...
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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.
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