_ad hoc_ would not be able to apprehend; but the kind of intellect we
know of and possess is an expression of vital adjustments, and is
tethered to nature.

That a few eternal essences, then, with a few of their necessary
relations to one another, do actually appear to us, and do fascinate
our attention and excite our wonder, is nothing paradoxical. This is
merely what was bound to happen, if we became aware of anything at
all; for the essence embodied in anything is eternal and has necessary
relations to some other essences. The air of presumption which there
might seem to be in proclaiming that mathematics reveals what has to
be true always and everywhere, vanishes when we remember that
everything that is true of any essence is true of it always and
everywhere. The most trivial truths of logic are as necessary and
eternal as the most important; so that it is less of an achievement
than it sounds when we say we have grasped a truth that is eternal and
necessary.

This fact will be more clearly recognised, perhaps, if we remember
that the cogency of our ideal knowledge follows upon our intent in
fixing its object. It hangs on a virtual definition, and explicates
it. We cannot oblige anybody or anything to reproduce the idea which
we have chosen; but that idea will remain the idea it is whether
forgotten or remembered, exemplified or not exemplified in things. To
penetrate to the foundation of being is possible for us only because
the foundation of being is distinguishable quality; were there no set
of differing characteristics, one or more of which an existing thing
might appropriate, existence would be altogether impossible. The realm
of essence is merely the system or chaos of these fundamental
possibilities, the catalogue of all exemplifiable natures; so that any