we expect to find repeated beyond the occasions on
which we have observed them, and others that we do not expect to find
repeated. If it is a sound basis of inference that we are in search
of, it is evidently to these first, the coincidences that we are
assured of finding again, that we must direct our study. Let us see
whether they can be specified.

(1) If there is no causal connexion between A and B, using these
as symbols for the members of a coincidence--the objects that are
presented together--we do not expect the coincidence to be repeated.
If A and B are connected as cause and effect, we expect the effect
to recur in company with the cause. We expect that when the cause
reappears in similar circumstances, the effect also will reappear.

You are hit, _e.g._, by a snowball, and the blow is followed by a
feeling of pain. The sun, we shall say, was shining at the moment of
the impact of the snowball on your body. The sunshine preceded your
feeling of pain as well as the blow. But you do not expect the pain
to recur next time that the sun shines. You do expect it to recur next
time you are hit by a snowball.

The taking of food and a certain feeling of strength are causally
connected. If we go without food, we are not surprised when faintness
or weariness supervenes.

Suppose that when our village matron administered her remedy to her
own child, a dog stood by the bedside and barked. The barking in that
case would precede the cure. Now, if the matron were what we should
call a superstitious person, and believed that this concomitant had
a certain efficacy, that the dog's barking and the cure were causally
connected, she would take the dog with her when she went to cure her
neighbour's child. Otherwise she would not. She would say that the
barking was an accidental, casual, fortuitous coincidence, and would
build no expectation upon it.

These illustrations may serve to remind us of the familiar fact that
the causal nexus is at least one of the things that we depend on in
our inferences to the unobserved. To a simple sequence we attach
no importance, but a causal sequence or consequence that has been
observed is a mainstay of inference.

Whether the causal sequence holds or not as a matter of fact, we
depend upon it if we believe in it as a matter of fact. But unless
it does hold as a matter of fact, it is valueless as a guide to the
unknown, and our belief is irrational. Clearly, therefore, if rational
belief