When a man lights upon a thought or is interested in
tracing a relation, he does not introduce those objects into the realm
of essence, but merely selects them from the plenitude of what lies
there eternally. The ground of this selection lies, of course, in his
human nature and circumstances; and the satisfaction he may find in
so exercising his mind will be a consequence of his mental disposition
and of the animal instincts beneath. Two and two would still make four
if I were incapable of counting, or if I found it extremely painful to
do so, or if I thought it naive and pre-Kantian of these numbers not
to combine in a more vital fashion, and make five. So also, if I
happen to enjoy counting, or to find the constancy of numbers sublime,
and the reversibility of the processes connecting them consoling, in
contrast to the irrevocable flux of living things, all this is due to
my idiosyncrasy. It is no part of the essence of numbers to be
congenial to me; but it has perhaps become a part of my genius to have
affinity to them.
And how, may I ask, has it become a part of my genius? Simply because
nature, of which I am a part, and to which all my ideas must refer if
they are to be relevant to my destiny, happens to have mathematical
form. Nature had to have some form or other, if it was to exist at
all; and whatever form it had happened to take would have had its
prior place in the realm of essence, and its essential and logical
relations there.
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