urther about their relations.

The most obvious artifices of language are often the most deceptive and
bring on epidemic prejudices. What is this Mind, this machine existing
prior to existence? The mind that exists is only a particular department
or focus of existence; its principles cannot be its own source, much
less the source of anything in other beings. Mathematical principles in
particular are not imposed on existence or on nature _ab extra_, but are
found in and abstracted from the subject-matter and march of experience.
To exist things have to wear some form, and the form they happen to wear
is largely mathematical. This being the case, the mind in shaping its
barbarous prosody somewhat more closely to the nature of things, learns
to note and to abstract the form that so strikingly defines them. Once
abstracted and focussed in the mind, these forms, like all forms, reveal
their dialectic; but that things conform to that dialectic (when they
do) is not wonderful, seeing that it is the obvious form of things that
the mind has singled out, not without practical shrewdness, for more
intensive study.

[Sidenote: Forms are abstracted from existence by intent.]

The difference between ideal and material knowledge does not lie in the
ungenerated oracular character of one of them in opposition to the
other; in both the data are inexplicable and irrational, and in both
investigation is tentative, observant, and subject to control by the
subject-matter. The difference lies, rather, in the direction of
speculation. In physics, which is at bottom historical, we study what
happens; we make inventories and records of events, of phenomena, of
juxtapositions. In dialectic, which is wholly intensive, we study what
is; we strive to clarify and develop the essence of what we find,
bringing into focus the inner harmonies and implications of forms--forms
which our attention or purpose has defined initially. The intuitions
from which mathematical deduction starts are highly generic notions
drawn from observation. The lines and angles of geometers are ideals,
and their ideal context is entirely independent of what may be their
context in the world; but they are found in the world, and their ideals
are suggested by very common sensations. Had they been invented, by
some inexplicable parthenogenesis in thought, it would indeed have been
a marvel had they found application. Philosophy has enough notions of
this inapplicable sort--usuall