ll 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 sy