Mr Mill begins his work by analyzing and explaining the doctrine called the Relativity of Human Knowledge: 

’The doctrine (chap. ii. p. 5) which is thought to belong in the most especial manner to Sir W. Hamilton, and which was the ground of his opposition to the transcendentalism of the later French and German metaphysicians, is that which he and others have called the Relativity of Human Knowledge.  It is the subject of the most generally known and impressive of all his writings—­the one which first revealed to the English metaphysical reader that a new power had arisen in philosophy.  Together with its developments, it composes the Philosophy of the Conditioned, which he opposed to the French and German philosophies of the Absolute, and which is regarded by most of his admirers as the greatest of his titles to a permanent place in the history of metaphysical thought.  But, “the relativity of human knowledge,” like most other phrases into which the words relative or relation enter, is vague, and admits of a great variety of meanings,’ &c.

Mr Mill then proceeds to distinguish these various meanings, and to determine in which of them the phrase is understood by Sir W. Hamilton.

One meaning is, that we only know anything by knowing it as distinguished from something else—­that all consciousness is of difference.  It is not, however, in this sense that the expression is ordinarily or intentionally used by Sir W. Hamilton, though he fully recognizes the truth which, when thus used, it serves to express.  In general, when he says that all our knowledge is relative, the relation he has in view is not between the thing known and other objects compared with it, but between the thing known and the mind knowing—­(p. 6).

The doctrine in this last meaning is held by different philosophers in two different forms.  Some (e.g.  Berkeley, Hume, Ferrier, &c.), usually called Idealists, maintain not merely that all we can possibly know of anything is the manner in which it affects the human faculties, but that there is nothing else to be known; that affections of human or of other minds are all that we can know to exist—­that the difference between the ego and the non-ego is only a formal distinction between two aspects of the same reality.  Other philosophers (Brown, Mr Herbert Spencer, Auguste Comte, with many others) believe that the ego and the non-ego denote two realities, each self-existent, and neither dependent on the other; that the Noumenon, or ‘thing per se,’ is in itself a different thing from the Phenomenon, and equally or more real, but that, though we know its existence, we have no means of knowing what it is.  All that we can know is, relatively to ourselves, the modes in which it affects us, or the phenomena which it produces—­(pp. 9—­11).