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 what has misled Mr. Mill), that the laws of Identity, Contradiction, and Excluded Middle, are laws of things as well as laws of thought;[BC] but he says nothing about these laws as predicating infinite or finite extension. On the contrary, he expressly classifies Space under the law of Relativity, the violation of which indicates what may exist, but what we are unable to conceive as existing. Briefly, the law of Excluded Middle (to take this instance alone) is a law of things only in its abstract form, "Everything must be A or not A" (_extended_, if you please, or _not extended_); but in its subordinate form, "Everything extended must be extended infinitely or finitely," it is only applicable, and only intended by Hamilton to be applied, to those _phenomena_ which are already given as extended in some degree. [BC] _Discussions_, p. 603. We have now examined the first six chapters of Mr. Mill's book, containing his remarks on that portion of Sir W. Hamilton's philosophy which he justly regards as comprising the most important of the doctrines which specially belong to Hamilton himself. The next chapter is an episode, in which Mr. Mill turns aside from Sir W. Hamilton to criticise Mr. Mansel's _Bampton Lectures_. As our limits do not permit us to carry on the argument at present through the remainder of Mr. Mill's remarks on Hamilton himself, we shall conclude our notice with a few words on this chapter, as closing the properly metaphysical portion of Mr. Mill's book, and as affording ample proof that, in this department of philosophy at least, Mr. Mill's powers of misapprehension do not cease when Sir W. Hamilton is no longer their object.