verities, about which there can be no
shadow of doubt, no possibility of error.

The doctrine that water is composed of certain definite chemical
constituents in certain definite proportions, or the theory that the
nerves are the instruments of sensation and of motion, rests upon no
such foundation. Whenever water has been analyzed, it has yielded the
same separate elements in the same proportions; and whenever these
elements are put together in the same quantitative ratio they have
produced water; so that the conviction is proximately established in the
minds of all that water is invariably the product of these elements in
certain proportions. But this proof does not establish the
generalization as _inevitably true, nor show that it is impossible for
it to be otherwise_. It is _possible_, in the nature of things, for us
to conceive that the fluid which we call water may be produced from
other constituents than oxygen or hydrogen, or that such a fluid may
even now exist undiscovered, the product of elements altogether
unknown.

So in regard to the nerves. Observation and experiment have established
to the general satisfaction, that they are the instruments of sensation
and motion; but we are not _absolutely sure_ that this is the fact, nor
can we _know_ that a human being may not be born in whom no trace of
nerves can be detected, and who will nevertheless experience sensation
and exhibit motion. We may be as well satisfied, for all practical
purposes, of the nature of water and of the office of the nerves as of
the nature of a triangle; but the character of the evidence, on which
the convincement is based, is essentially different; being, in the one
case, incontrovertible and infallible; and, in the other, indecisive and
_possibly_ fallacious.

This repetition of that which has been substantially stated before,
brings us to the final consideration of the distinctive nature of
different departments of Thought, as indicated by the Methods of Proof
which respectively prevail in them; and hence as embodying either exact
and definite _Knowledge_, or only varying degrees of _Probability_. We
have already seen that in at least one sphere of intellectual activity
we are able to start from the most basic and fundamental conceptions,
from axiomatic truths so patent and universal that they cannot even be
conceived of as being otherwise than as they are, and to proceed from
them, by equally irresistible Inferences, to conclusi