Experiment and induction

Sir Karl Popper has argued that a scientific idea can never be proven true, because no matter how many observations seem to agree with it, it may still be wrong.

On the other hand, a single contrary experiment can prove a theory forever false.

For a brief formulation of the problem of induction we can turn to Born, who writes: '. . . no observation or experiment, however extended, can give more than a finite number of repetitions'; therefore, 'the statement of a law - B depends on A - always transcends experience. Yet this kind of statement is made everywhere and all the time, and sometimes from scanty material. '

In other words, the logical problem of induction arises from (1) Hume's discovery (so well expressed by Born) that it is impossible to justify a law by observation or experiment, since it 'transcends experience'; (2) the fact that science proposes and uses laws 'everywhere and all the time'. (Like Hume, Born is struck by the 'scanty material', i.e. the few observed instances upon which the law may be based.) To this we have to add (3) the principle of empiricism which asserts that in science only observation and experiment may decide upon the acceptance or rejection of scientific statements, including laws and theories.

These three principles, (1), (2), and (3), appear at first sight to clash; and this apparent clash constitutes the logical problem of induction.

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