Take the simplest conceivable case, which hardly amounts to Inference, that of producing a given straight line. How is it that this is possible? Because the direction of the straight line is universal and self-identical as against possible directions in space, and it acts as a rule which carries you beyond the given portion of it. This might fairly be called an “immediate inference.” So I presume that any curve can be constructed out of a sufficient portion of the curve, although, except with a circle, this is more than repeating the same line over again. The content has a nature which {140} is capable of prescribing its own continuation. A curve is not a direction; a truth which is a puzzle to the non-mathematician--it is a law of continuous change of direction. _System the ultimate condition of Inference_ 3. _Ultimately_ the condition of inference is always a system. And it will help us in getting a vital notion of inference if we think, to begin with, of the interdependence of relations in space--in geometrical figures, or, to take a commonplace example, in the adjustment of a Chinese puzzle or a dissected map. Or any of the propositions about the properties of triangles are a good example. How can one property or attribute determine another, so that you can say, “Given this, there must be that”? This can only be answered by pointing to the nature of a whole with parts, or a system, which just means this, a group of relations or properties or things so held together by a common nature that you can judge from some of them what the others must be. Not all systems admit of precise calculation and demonstration, but wherever there is inference at all there is at least an identity of content which may be more or less developed into a precise relation between parts. For example, we cannot construct geometrically the life and character of an individual man; we can argue from his character to some extent, but the connection of facts in his personal identity is all that we can infer for certain; and even this involves a certain context of facts, as in circumstantial evidence. Yet this simplest linking together of occurrences by personal identity is enough to give very startling inferences. Thackeray’s story of the priest is a good instance of inference from mere identity. “An old abbé, talking among a party of intimate friends, happened {141} to say, ‘A priest has strange experiences; why, ladies, my first penitent was a murderer.’ Upon this, the principal nobleman of the neighbourhood enters the room. ‘Ah, Abbé, here you are; do you know, ladies, I was the Abbé’s first penitent, and I promise you my confession astonished him!’” Here the inference depends solely on individual identity, which is, as we saw, a kind of universal.