Geometry is not so certain as algebra and arithmetic, because we cannot be sure of the truth of its
axioms. It is a mistake to suppose, as many philosophers do, that the ideas of mathematics "must
be comprehended by a pure and intellectual view, of which the superior faculties of the soul are
alone capable." The falsehood of this view is evident, says Hume, as soon as we remember that
"all our ideas are copied from our impressions."
The three relations that depend not only on ideas are identity, spatio-temporal relations, and
causation. In the first two, the mind does not go beyond what is immediately present to the senses.
(Spatiotemporal relations, Hume holds, can be perceived, and can form parts of impressions.)
Causation alone enables us to infer some thing or occurrence from some other thing or
occurrence: "'Tis only causation, which produces such a connexion, as to give us assurance from
the existence or action of one object, that 'twas followed or preceded by any other existence or
action."
A difficulty arises from Hume's contention that there is no such thing as an impression of a causal
relation. We can perceive, by mere observation of A and B, that A is above B, or to the right of B,
but not that A causes B. In the past, the relation of causation had been more or less assimilated to
that of ground and consequent in logic, but this, Hume rightly perceived, was a mistake.
In the Cartesian philosophy, as in that of the Scholastics, the connection of cause and effect was
supposed to be necessary, as logical connections are necessary. The first really serious challenge
to this view came from Hume, with whom the modern philosophy of causation begins. He, in
common with almost all philosophers down to and including Bergson, supposes the law to state
that there are propositions of the form "A causes B," where A and B are classes of events; the fact
that such laws do not occur in any well-developed science appears to be unknown to philosophers.
But much of what they have said can be translated so as to be applicable to causal laws such as do
occur; we may, therefore, ignore this point for the present.
Hume begins by observing that the power by which one object produces another is not
discoverable from the ideas of the two objects, and that we can therefore only know cause and
effect from experience, not from reasoning or reflection. The statement "what begins must have a
cause," he says, is not one that has intuitive certainty, like