hich, although the resultant of its constitution, is not a property of
any of its elements. A whole number is thus a collection of 1s, but the
properties of the whole number are something quite different from that
of the elements through which it is constituted, just as an atom may be
composed of electrons and yet, in valency, possess a property that is
not the direct analogue of any property possessed by electrons not so
organized.

Natural science, however, considers such building up of its fundamental
entities into new entities as a process taking place in time rather than
as consequent upon change of form of the whole rendering new analytic
forms expedient. Hence it points to the occurrence of genuine novelties
in the realm of objective reality. Mathematics, on the other hand,
has generalized its concepts beyond the facts implied in spatial and
temporal observations, so that while significant in both fields by
virtue of the nature of its abstractions, its novelties are the
novelties of new conceptual formations, a distinguishing of previously
unnoted generalizations of relations existent in the realm of facts. But
the fact that time has thus passed beyond its empirical meaning in the
mathematical realm is no ground for giving mathematics an elevated
position as a science of eternal realities, of subsistent beings, or the
like. The generalization of concepts to cover both spatial and temporal
facts does not create new entities for which a home must be provided in
the partition of realities. Metaphysicians should not be the "needy
knife grinders" of M. Anatole France (cf. _Garden of Epicurus_, Ch. "The
Language of the Metaphysicians"). Nevertheless, the success of
abstraction for mathematical intelligence has been immense.

No significant thinking is wholly the work of an individual man. Ideas
are a product of social cooeperation in which some have wrested crude
concepts from nature, others have refined them through usage, and still
others have built them into an effective system. The first steps were
undoubtedly taken in an effort to communicate, and progress has been in
part the progress of language. The original nature of man may have as a
part those reactions which we call curiosity, but, as Auguste Comte long
ago pointed out (Levy-Bruhl, _A. Comte_, p. 67), these reactions are
among the feeblest of our nature and without the pressure of practical
affairs could hardly have advanced the race beyond barbarism. Scien