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5. LECTURE V. PSYCHOLOGICAL AND PHYSICAL CAUSAL LAWS (continued)
* The theory of quanta suggests that the continuity is only apparent. If so, we shall be able theoretically to reach events which are not processes. But in what is directly observable there is still apparent continuity, which justifies the above remarks for the prevent.
Laws embodied in differential equations may possibly be exact, but cannot be known to be so. All that we can know empirically is approximate and liable to exceptions; the exact laws that are assumed in physics are known to be somewhere near the truth, but are not known to be true just as they stand. The laws that we actually know empirically have the form of the traditional causal laws, except that they are not to be regarded as universal or necessary. "Taking arsenic is followed by death" is a good empirical generalization; it may have exceptions, but they will be rare. As against the professedly exact laws of physics, such empirical generalizations have the advantage that they deal with observable phenomena. We cannot observe infinitesimals, whether in time or space; we do not even know whether time and space are infinitely divisible. Therefore rough empirical generalizations have a definite place in science, in spite of not being exact of universal. They are the data for more exact laws, and the grounds for believing that they are USUALLY true are stronger than the grounds for believing that the more exact laws are ALWAYS true.
Science starts, therefore, from generalizations of the form, "A is usually followed by B." This is the nearest approach that can be made to a causal law of the traditional sort. It may happen in any particular instance that A is ALWAYS followed by B, but we cannot know this, since we cannot foresee all the perfectly possible circumstances that might make the sequence fail, or know that none of them will actually occur. If, however, we know of a very large number of cases in which A is followed by B, and few or none in which the sequence fails, we shall in PRACTICE be justified in saying "A causes B," provided we do not attach to the notion of cause any of the metaphysical superstitions that have gathered about the word.
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