A System of Logic, Ratiocinative and Inductive · John Stuart Mill
FIRST CANON.
_If two or more instances of the phenomenon under investigation have only one circumstance in common, the circumstance in which alone all the instances agree, is the cause (or effect) of the given phenomenon._ Quitting for the present the Method of Agreement, to which we shall almost immediately return, we proceed to a still more potent instrument of the investigation of nature, the Method of Difference. § 2. In the Method of Agreement, we endeavored to obtain instances which agreed in the given circumstance but differed in every other: in the present method we require, on the contrary, two instances resembling one another in every other respect, but differing in the presence or absence of the phenomenon we wish to study. If our object be to discover the effects of an agent A, we must procure A in some set of ascertained circumstances, as A B C, and having noted the effects produced, compare them with the effect of the remaining circumstances B C, when A is absent. If the effect of A B C is _a b c_, and the effect of B C _b c_, it is evident that the effect of A is _a_. So again, if we begin at the other end, and desire to investigate the cause of an effect _a_, we must select an instance, as _a b c_, in which the effect occurs, and in which the antecedents were A B C, and we must look out for another instance in which the remaining circumstances, _b c_, occur without _a_. If the antecedents, in that instance, are B C, we know that the cause of _a_ must be A: either A alone, or A in conjunction with some of the other circumstances present.
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