the man's death, through merely knowing that he has died as the result
of arsenic poisoning. Thus, if we are to take the cause as one event and
the effect as another, both must be shortened indefinitely. The result
is that we merely have, as the embodiment of our causal law, a certain
direction of change at each moment. Hence we are brought to differential
equations as embodying causal laws. A physical law does not say "A will
be followed by B," but tells us what acceleration a particle will have
under given circumstances, i.e. it tells us how the particle's motion is
changing at each moment, not where the particle will be at some future
moment.
* 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.
Public-domain text, read in full here on John Shaqi.
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