gism, as an
artificial form, is of little value in the perception of the agreements
between these intermediate and final terms, and of none whatever in the
discovery of the former. Analytical and identical propositions which merely
explicate the conception of the subject, but express nothing not already
known, are, in spite of their indefeasible certitude, valueless for the
extension of knowledge, and when taken for more than verbal explanations,
mere absurdities. Even those most general propositions, those "principles"
which are so much talked of in the schools, lack the utility which is so
commonly ascribed to them. Maxims are, it is true, fit instruments for the
communication of knowledge already acquired, and in learned disputations
may perform indispensable service in silencing opponents, or in bringing
the dispute to a conclusion; but they are of little or no use in the
discovery of new truth. It is a mistake to believe that special cases (as
5 = 2 + 3, or 5 = 1 + 4) are dependent on the truth of the abstract rule
(the whole is equal to the sum of its parts), that they are confirmed by
it and must be derived from it. The particular and concrete is not only
as clear and certain as the general maxim, but better known than this,
as well as earlier and more easily perceived. Nay, further, in cases
where ideas are confused and the meanings of words doubtful, the use of
axioms is dangerous, since they may easily lend the appearance of proved
truth to assertions which are really contradictory.

Between the clear daylight of certain knowledge and the dark night of
absolute ignorance comes the twilight of probability. We find ourselves
dependent on _opinion_ and presumption, or judgment based upon probability,
when experience and demonstration leave us in the lurch and we are,
nevertheless, challenged to a decision by vital needs which brook no delay.
The judge and the historian must convince themselves from the reports of
witnesses concerning events which they have not themselves observed; and
everyone is compelled by the interests of life, of duty, and of eternal
salvation to form conclusions concerning things which lie beyond the limits
of his own perception and reflective thought, nay, which transcend all
human experience and rigorous demonstration whatever. To delay decision and
action until absolute certainty had been attained, would scarcely allow
us to lift a single finger. In cases concerning events in the past, the