fy more, but still remains
apparently indivisible. I say, that if this happened, we should
believe in a minimum of extension; or if some _a priori_
metaphysical prejudice prevented us from believing it, we should at
least be enabled to conceive it."--(P. 84.)

The natural conclusion of most men under such circumstances would be,
that there was some fault in the microscope. But even if this conclusion
were rejected, we presume Mr. Mill would allow that, under the supposed
circumstances, the exact magnitude of the minimum of extension would be
calculable. We have only to measure the _minimum visibile_, and know what
is the magnifying power of our microscope, to determine the exact
dimensions. Suppose, then, that we assign to it some definite
magnitude--say the ten billionth part of an inch,--should we then
conclude that it is impossible to conceive the twenty billionth part of
an inch?--in other words, that we have arrived at a definite magnitude
which has no conceivable half? Surely this is a somewhat rash concession
to be made by a writer who has just told us that numbers may be conceived
up to infinity; and therefore, of course, down to infinitesimality.

Mr. Mill concludes this chapter with an assertion which, even by itself,
is sufficient to show how very little he has attended to or understood
the philosophy which he is attempting to criticise. "The law of Excluded
Middle," he says, "as well as that of Contradiction, is common to all
phenomena. But it is a doctrine of our author that these laws are true,
and cannot but be known to be true, of Noumena likewise. It is not merely
Space as cognisable by our senses, but Space as it is in itself, which he
affirms must be either of unlimited or of limited extent" (p. 86). At
this sentence we fairly stand aghast. "Space as it is in itself!" the
Noumenon Space! Has Mr. Mill been all this while "examining" Sir William
Hamilton's philosophy, in utter ignorance that the object of that
philosophy is the "Conditioned in Time and _Space_;" that he accepts
Kant's analysis of time and space as formal necessities of thought, but
pronounces no opinion whatever as to whether time and space can exist as
Noumena or not? It is the phenomenal space, "space as cognisable by our
senses," which Sir W. Hamilton says must be either limited or unlimited:
concerning the Noumenon Space, he does not hazard an opinion whether such
a thing exists or not. He says, indeed (and this is probably