(I) THE CANON OF AGREEMENT.

If two or more instances of a phenomenon under investigation have only one other circumstance (antecedent or consequent) in common, that circumstance is probably the cause (or an indispensable condition) or the effect of the phenomenon, or is connected with it by causation.

This rule of proof (so far as it is used to establish direct causation) depends, first, upon observation of an invariable connection between the given phenomenon and one other circumstance; and, secondly, upon I. (a) and II. (b) among the propositions obtained from the unconditionality of causation at the close of the last chapter.

To prove that A is causally related to p, suppose two instances of the occurrence of A, an antecedent, and p, a consequent, with concomitant facts or events—­and let us represent them thus: 

Antecedents:      A B C          A D E
Consequents:     p q r        p s t;

and suppose further that, in this case, the immediate succession of events can be observed.  Then A is probably the cause, or an indispensable condition, of p.  For, as far as our instances go, A is the invariable antecedent of p; and p is the invariable consequent of A. But the two instances of A or p agree in no other circumstance.  Therefore A is (or completes) the unconditional antecedent of p.  For B and C are not indispensable conditions of p, being absent in the second instance (Rule II. (b)); nor are D and E, being absent in the first instance.  Moreover, q and r are not effects of A, being absent in the second instance (Rule II. (d)); nor are s and t, being absent in the first instance.

It should be observed that the cogency of the proof depends entirely upon its tending to show the unconditionality of the sequence A-p, or the indispensability of A as a condition of p.  That p follows A, even immediately, is nothing by itself:  if a man sits down to study and, on the instant, a hand-organ begins under his window, he must not infer malice in the musician:  thousands of things follow one another every moment without traceable connection; and this we call ‘accidental.’  Even invariable sequence is not enough to prove direct causation; for, in our experience does not night invariable follow day?  The proof requires that the instances be such as to show not merely what events are in invariable sequence, but also what are not.  From among the occasional antecedents of p (or consequents of A) we have to eliminate the accidental ones.  And this is done by finding or making ’negative instances’ in respect of each of them.  Thus the instance

     A D E
    p s t

is a negative instance of B and C considered as supposable causes of p (and of q and r as supposable effects of A); for it shows that they are absent when p (or A) is present.