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19

and conclusion; that is, if it be true that if A is true
B is true, then should A occur as a premiss we have
a right to conclude B. The second relation is that expressed
by writing two graphs side by side AB,
that is to say, the relation of coexistence, and
the third is the relation of individual identity expressed
by the heavy line. Now whatever relation is analogous
to one of these three relations will be expressed by
graphs into which the corresponding
element of graphs enters and will therefore affect
reasoning and hence will be of logical importance.
Now the relation expressed by saying that one collection
is at least as great as another is precisely analogous
to the relation expressed by the scroll in graphs; and
that is why multitude which is the character of a collection
which constitutes it as great as what it is as great as is so very important
for logic.