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By Root 3488 0

be changed without any change in the ideas. Of the first kind are resemblance, contrariety, degrees in quality, and proportions in quantity or number. But spatio-temporal and causal relations are of the second kind. Only relations of the first kind give certain knowledge; our knowledge concerning the others is only probable. Algebra and arithmetic are the only sciences in which we can carry on a long chain of reasoning without losing certainty. 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. (Spatio-temporal 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 subject 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 the statements of logic. As he puts it: 'There is no object, which implies the existence of any other if we consider these objects in themselves, and never look beyond the ideas which we form of them.' Hume argues from this that it must be experience that gives knowledge of cause and effect, but that it cannot be merely the experience of the two events A and B which are in a causal relation to each other. It must be experience, because the connection is not logical; and it cannot be merely the experience of the particular events A and B, since we can discover nothing in A by itself which should lead to produce B. The experience required, he says, is that of the constant conjunction of events of the kind A with events of the kind B. He points out that when, in experience, two objects are constantly conjoined, we do in fact infer one from the other. (When he says 'infer', he means that perceiving the one makes us expect the other; he does not mean a formal or explicit inference.) 'Perhaps, the necessary connection depends on the inference,' not vice versa. That is to say, the sight of A causes the expectation of B, and so leads us to believe that