it beautiful or good.  The case is not such as if we were dealing with existence.  Existence is arbitrary; it is a questionable thing needing justification; and we, at least, cannot justify it otherwise than by taking note of some affinity which it may show to human aspirations.  Therefore our private endearments, when we call some existing thing good or beautiful, are not impertinent; they assign to this chance thing its only assignable excuse for being, namely, the service it may chance to render to the spirit.  But ideal necessity or, what is the same thing, essential possibility has its excuse for being in itself, since it is not contingent or questionable at all.  The affinity which the human mind may develop to certain provinces of essence is adventitious to those essences, and hardly to be mentioned in their presence.  It is something the mind has acquired, and may lose.  It is an incident in the life of reason, and no inherent characteristic of eternal necessity.

The realm of essence contains the infinite multitude of Leibnitz’s possible worlds, many of these worlds being very small and simple, and consisting merely of what might be presented in some isolated moment of feeling.  If any such feeling, however, or its object, never in fact occurs, the essence that it would have presented if it had occurred remains possible merely; so that nothing can ever exist in nature or for consciousness which has not a prior and independent locus in the realm of essence.  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.  That particular part of the realm of essence which