certainty in the more northern kingdoms. Here then it seems evident,
that, when we transfer the past to the future, in order to determine
the effect, which will result from any cause, we transfer all the
different events, in the same proportion as they have appeared in
the past, and conceive one to have existed a hundred times, for
instance, another ten times, and another once. As a great number of
views do here concur in one event, they fortify and confirm it to
the imagination, beget that sentiment which we call belief, and give
its object the preference above the contrary event, which is not
supported by an equal number of experiments, and recurs not so
frequently to the thought in transferring the past to the future.
Let any one try to account for this operation of the mind upon any
of the received systems of philosophy, and he will be sensible of
the difficulty. For my part, I shall think it sufficient, if the
present hints excite the curiosity of philosophers, and make them
sensible how defective all common theories are in treating of such
curious and such sublime subjects.

               Sect. VII. Of the Idea of necessary Connexion

                             PART I.

  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.

  49. There are no ideas, which occur in metaphysics, more obscure and
uncertain, than those of power, force, energy or necessary
connexion, of which it is every moment necessary for us to treat in
all our disquisitions. We shall, therefore, endeavour, in this
section, to fix, if possible, the precise meaning of these terms,
and thereby remove some part of that obscurity, which is so much
complained of in this species of philosophy.

  It seems a proposition, which will not admit of much dispute, that
all our ideas are nothing but copies of our impressions, or, in
other words, that it is impossible for us to think of anything,
which we have not antecedently felt, either by our external or
internal senses. I have endeavoured* to explain and prove this
proposition, and have expressed my hopes, that, by a proper
application of it, men may reach a greater clearness and precision
in philosophical reasonings, than what they have hitherto been able to
attain. Complex ideas may, perhaps, be well known by definition, which
is nothing but an enumeration of those parts or simple ideas, that
compose them. But when we have pushed up definitions to the most
simple ideas, and find still some ambiguity and obscurity; what
resource are we then possessed of? By what invention can we throw
light upon these ideas, and render them altogether precise and
determinate to our intellectual view? Produce the impressions or
original sentiments, from which the ideas are copied. These
impressions are all strong and sensible. They admit not of