“The aggregate is an effect of its individual members.”

He may be answered as follows:

Either there is no aggregate here distinct from the individual members—just as ten has no aggregate distinct from its ten individual units—or the aggregate is distinct from its members, as with a triangular shape: the union of the three sides is distinct from their existing separately. The same applies to ten units arranged in a row: their arrangement is distinct from ten considered without qualification. If the former is the case, then the aggregate consists of the successive individual members, all of which are contingent; hence the entire aggregate is contingent.

If the latter is the case, then “aggregate” may mean the configuration formed by their union, excluding the individual members themselves; or the individual members, excluding their union; or both together. The first is what he intended in his question.

We have, however, mentioned everything that might be said. Thus, if he says:

“Their union is contingent, and its existence is determined by the successive individual members,”

he may be answered as follows:

Their union would therefore be an effect of the individual members, necessitated and entailed by them. The individual members are contingent, and the effect of something contingent must, a fortiori, itself be contingent. Thus, each individual member would be contingent, and the aggregate itself would also be contingent. Yet this contingent aggregate is an effect of those contingent members. It is already known that what is contingent does not exist by itself. Therefore, none of those individual members would exist by itself, nor would the aggregate exist by itself. Thus there would be no