The problem of induction is that we are never given sensory data from which the idea of a necessary connection could be derived; nor may we assert that such a connection exists even though it cannot be observed. Hume's first principle is “That there is nothing in any object, considered in itself, which can afford us a reason for drawing a conclusion beyond it.” To this he adds the principle “That even after the observation of the frequent or constant conjunction of objects, we have no reason to draw any inference concerning any object beyond those of which we have had experience.” From the sole premise that one billiard ball is rolling towards another it would never be possible “to infer motion in the second ball from the motion and impulse of the first.” No relations of force or power can be detected in the actual phenomena (the billiard balls). We need a bridge to carry us from a true belief in one matter of fact (the first ball will hit the second) to a true belief in another (the second ball will move). By ‘bridge' I mean a middle premise which would claim, quoting Hume, “that instances of which we have had no experience, must resemble those of which we have had experience, and that the course of nature continues always uniformly the same.” But this is impossible to prove. No matter how often we have seen a ball move when hit by another, this evidence provides no logical grounds for inferring that future collisions will necessarily have the same result. The logical gap can never be bridged.
Yet we cannot doubt that every event has a cause. Without a causal connection – Hume's ‘cement of the universe’ – there would be no empirical world of ordinary experience or scientific study. We happen to live in that world, so we're certain there is a causal connection. We also know that this indispensable feature of our world is neither observable nor logically deducible. So how...