done at once ; and, in order to proceed regularly with the
demonstration, we must premise :-
1. The true definition of a thing neither involves nor
expresses anything beyond the nature of the thing defined. From
this it follows that-
2. No definition implies or expresses a certain number of
individuals, inasmuch as it expresses nothing beyond the nature
of the thing defined. For instance, the definition of a triangle
expresses nothing beyond the actual nature of a triangle : it
does not imply any fixed number of triangles.
3. There is necessarily for each individual existent thing a
cause why it should exist.
4. This cause of existence must either be contained in the
nature and definition of the thing defined, or must be postulated
apart from such definition.
It therefore follows that, if a given number of individual
things exist in nature, there must be some cause for the
existence of exactly that number, neither more nor less. For
example, if twenty men exist in the universe (for simplicity's
sake, I will suppose them existing simultaneously, and to have
had no predecessors), and we want to account for the existence of
these twenty men, it will not be enough to show the cause of
human existence in general ; we must also show why there are
exactly twenty men, neither more nor less : for a cause must be
assigned for the existence of each individual. Now this cause
cannot be contained in the actual nature of man, for the true
definition of man does not involve any consideration of the
number twenty. Consequently, the cause for the existence of
these twenty men, and, consequently, of each of them, must
necessarily be sought externally to each individual. Hence we may