An Enquiry Concerning Human Understanding HTML version

VII. Of The Idea Of Necessary Connexion
48. The great advantage of the mathematical sciences above the moral consists in this,
that the ideas of the former, being sensible, are always clear and determinate, the smallest
distinction between them is immediately perceptible, and the same terms are still
expressive of the same ideas, without ambiguity or variation. An oval is never mistaken
for a circle, nor an hyperbola for an ellipsis. The isosceles and scalenum are distinguished
by boundaries more exact than vice and virtue, right and wrong. If any term be defined in
geometry, the mind readily, of itself, substitutes, on all occasions, the definition for the
term defined: Or even when no definition is employed, the object itself may be presented
to the senses, and by that means be steadily and clearly apprehended. But the finer
sentiments of the mind, the operations of the understanding, the various agitations of the
passions, though really in themselves distinct, easily escape us, when surveyed by
reflection; nor is it in our power to recal the original object, as often as we have occasion
to contemplate it. Ambiguity, by this means, is gradually introduced into our reasonings:
Similar objects are readily taken to be the same: And the conclusion becomes at last very
wide of the premises.
One may safely, however, affirm, that, if we consider these sciences in a proper light,
their advantages and disadvantages nearly compensate each other, and reduce both of
them to a state of equality. If the mind, with greater facility, retains the ideas of geometry
clear and determinate, it must carry on a much longer and more intricate chain of
reasoning, and compare ideas much wider of each other, in order to reach the abstruser
truths of that science. And if moral ideas are apt, without extreme care, to fall into
obscurity and confusion, the inferences are always much shorter in these disquisitions,
and the intermediate steps, which lead to the conclusion, much fewer than in the sciences
which treat of quantity and number. In reality, there is scarcely a proposition in Euclid so
simple, as not to consist of more parts, than are to be found in any moral reasoning which
runs not into chimera and conceit. Where we trace the principles of the human mind
through a few steps, we may be very well satisfied with our progress; considering how
soon nature throws a bar to all our enquiries concerning causes, and reduces us to an
acknowledgment of our ignorance. The chief obstacle, therefore, to our improvement in
the moral or metaphysical sciences is the obscurity of the ideas, and ambiguity of the
terms. The principal difficulty in the mathematics is the length of inferences and compass
of thought, requisite to the forming of any conclusion. And, perhaps, our progress in
natural philosophy is chiefly retarded by the want of proper experiments and
phaenomena, which are often discovered by chance, and cannot always be found, when
requisite, even by the most diligent and prudent enquiry. As moral philosophy seems
hitherto to have received less improvement than either geometry or physics, we may
conclude, that, if there be any difference in this respect among these sciences, the
difficulties, which obstruct the progress of the former, require superior care and capacity
to be surmounted.