Richard Taylor gives an argument in his book Action andPurpose to show that the cause of an event B is the set of conditions, from among all those conditions that occurred, "each of which was necessary, and the totality of which was sufficient, for the occurrence of B. 'u This argument relies on the principle that necessarily, all the conditions necessary for the occurrence of an event are together sufficient for the occurrence of that event. This principle, I shall argue, is mistaken, and hence Taylor's argument is unsound. This principle is true just in case the following inference is valid.
The set of conditions A includes every condition necessary for the occurrence of B. Therefore, the conditions in A are together sufficient for the occurrence of B.
So, if I am right, this inference is invalid. I think it is worthwhile to point out that Taylor's principle is mistaken and that the above inference is invalid because philosophers thinking about causation are apt to accept both.
Taylor's argument goes as follows:
... the cause, A, of an event, B, is that totality of conditions, from among all those, but only those, that occurred, each of which was necessary for the occurrence of B. Now if this set of conditions, A, is thus understood, as it should be, to include every condition, out of that totality that occurred, that was necessary for the occurrence of B, then we can say that the set of conditions, A, is also sufficient for B, since no other condition was necessary. We can, accordingly, understand the relationship between any set of conditions A, and any set B, expressed in the statement that A was the cause of B, to be simply described in this fashion: That A was the set, from among all those conditions that occurred, each of which was necessary, and the totality of which was sufficient, for the occurrence of B. (p. 27)
The conclusion of this argument is a definition of the statement that A was the cause of B, where A and B are understood to be sets &conditions.