pting 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
legislation. All action is for the sake of some end, and rules of
action, it seems natural to suppose, must take their whole character
and colour from the end to which they are subservient. When we engage in
a pursuit, a clear and precise conception of what we are pursuing would
seem to be the first thing we need, instead of the last we are to look
forward to. A test of right and wrong must be the means, one would
think, of ascertaining what is right or wrong, and not a consequence of
having already ascertained it.

The difficulty is not avoided by having recourse to the popular theory
of a natural faculty, a sense or instinct, informing us of right and
wrong. For--besides that the existence of such a moral instinct is
itself one of the matters in dispute--those believers in it who have any
pretensions to philosophy, have been obliged to abandon the idea that it
discerns what is right or wrong in the particular case in hand, as our
other senses discern the sight or sound actually present. Our moral
faculty, according to all those of its interpreters who are entitled to
the name of thinkers, supplies us only with the general principles of