divided them into sects and schools, carrying on a vigorous warfare
against one another. And after more than two thousand years the same
discussions continue, philosophers are still ranged under the same
contending banners, and neither thinkers nor mankind at large seem
nearer to being unanimous on the subject, than when the youth Socrates
listened to the old Protagoras, and asserted (if Plato's dialogue be
grounded on a real conversation) the theory of utilitarianism against
the popular morality of the so-called sophist.

It is true that similar confusion and uncertainty, and in some cases
similar discordance, exist respecting the first principles of all the
sciences, not excepting that which is deemed the most certain of them,
mathematics; without much impairing, generally indeed without impairing
at all, the trustworthiness of the conclusions of those sciences. An
apparent anomaly, the explanation of which is, that the detailed
doctrines of a science are not usually deduced from, nor depend for
their evidence upon, what are called its first principles. Were it not
so, there would be no science more precarious, or whose conclusions were
more insufficiently made out, than algebra; which derives none of its
certainty from what are commonly taught to learners as its elements,
since these, as laid down by some of its most eminent teachers, are as
full of fictions as English law, and of mysteries as theology. The
truths which are ultimately accepted as the first principles of a
science, are really the last results of metaphysical analysis, practised
on the elementary notions with which the science is conversant; and
their relation to the science is not that of foundations to an edifice,
but of roots to a tree, which may perform their office equally well
though they be never dug down to and exposed to light. But though in
science the particular truths precede the general theory, the contrary
might be expected to be the case with a practical art, such as morals or