Instances of Presence. Instances of Absence. A B C C H F _p q r_ _r x v_ A D E B D K _p s t_ _q y s_ A F G E G M _p u v_ _t f u_ Then A is probably the cause or a condition of _p_, or _p_ is dependent upon A: first, by the Canon of Agreement in Presence, as represented by the first set of instances; and, secondly, by Agreement in Absence in the second set of instances. For there we see that C, H, F, B, D, K, E, G, M occur without the phenomenon _p_, and therefore (by Prop. II. (a)) are not its cause, or not the whole cause, unless they have been counteracted (which is a point for further investigation). We also see that _r, v, q, s, t, u_ occur without A, and therefore are not the effects of A. And, further, if the negative instances represent all possible cases, we see that (according to Prop. I. (b)) A is the cause of _p_, because it cannot be omitted without the cessation of _p_. The inference that A and _p_ are cause and effect, suggested by their being present throughout the first set of instances, is therefore strengthened by their being both absent throughout the second set. So far as this Double Method, like the Single Method of Agreement, relies on observation, sequence may not be perceptible in the instances observed, and then, direct causation cannot be proved by it, but only the probability of causal connection; and, again, the real cause, though present, may be so obscure as to evade observation. It has, however, one peculiar advantage, namely, that if the second list of instances (in which the phenomenon and its supposed antecedent are both absent) can be made exhaustive, it precludes any hypothesis of a plurality of causes; since all possible antecedents will have been included in this list without producing the phenomenon. Thus, in the above symbolic example, taking the first set of instances, the supposition is left open that B, C, D, E, F, G may, at one time or another, have been a condition of _p_; but, in the second list, these antecedents all occur, here or there, without producing _p_, and therefore (unless counteracted somehow) cannot be a condition of _p_. A, then, stands out as the one thing that is present whenever _p_ is present, and absent whenever _p_ is absent.