The 'indissoluble' or 'inseparable' association, which became the grand arcanum of the school, while intended to answer some of these difficulties, raises others. Mill seems to insist upon splitting a unit into parts in order that it may be again brought together by association. So J. S. Mill, in an admiring note, confirms his father's explanation ('one of the most important thought in the whole treatise') of the infinity of space.[554] We think space infinite because we always 'associate' position with extension. Surely space is extension; and to think of one without the other implies a contradiction. We think space infinite, because we think of a space as only limited by other space, and therefore indefinitely extensible. There is no 'association,' simply repetition. Elsewhere we have the problem, How does one association exclude another? Only, as J. S. Mill replies, when one idea includes the idea of the absence of the others.[555] We cannot combine the ideas of a plane and a convex surface. Why? Because we have never had both sets of sensations together. The 'commencement' of one set has always been 'simultaneous with the cessation of another set,' as, for instance, when we bend a flat sheet of paper. The difficulty seems to be that one fact cannot be contradictory of another, since contradiction only applies to assertions. When I say that A is above B, however, I surely assert that B is below A; and I cannot make both assertions about A and B at the same time without a contradiction. To explain this by an association of simultaneous and successive sensations seems to be a curiously roundabout way of 'explaining.' Every assertion is also a denial; and, if I am entitled to say anything, I am enabled without any help from association to deny its contradictory. On Mill's showing, the assertion and the denial of its contradiction, instead of being identical, are taken to be two beliefs accidentally associated. Finally, I need only make one remark upon the fundamental difficulty. It is hard to conceive of mere loose 'ideas' going about in the universe at large and sticking accidentally to others. After all, the human being is in true sense also an organised whole, and his constitution must be taken into account in discovering the laws of 'ideation.' This is the point of view to which Mill, in his anxiety to get rid of everything that had a savour of _a priori_ knowledge about it, remains comparatively blind. It implies a remarkable omission. Mill's great teacher, Hartley, had appealed to physiology in a necessarily crude fashion. He had therefore an organism: a brain or a nervous system which could react upon the external world and modify and combine sensations. Mill's ideas would have more apparent connection if they could be made to correspond to 'vibratiuncles' or physical processes of some kind. But this part of Hartley's hypothesis had been dropped: and all reality is therefore reduced to the whirl of vagrant and accidentally cohering ideas in brains and clusters. His one main aim is to get rid of everything that can be called mystical and to trace all mental processes to 'experience,' as he understands experience--to show that we are never entitled to assert that two ideas may not be joined in any way whatever.