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.
The Problem of Induction
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...
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