This brief phrase is the abstract of the whole system. Let us master it,
for it explains all Mill's theories. He has defined and restated
everything, from this starting-point. In all forms and all degrees of
knowledge, he has recognized only the knowledge of facts, and of their
relations.
Now we know that logic has two corner-stones: the Theories of Definition
and of Proof. From the days of Aristotle logicians have spent their time
in polishing them. They have only dared to touch them respectfully, as
if they were sacred. At most, from time to time, some innovator ventured
to turn them over cautiously, to put them in a better light. Mill
shapes, cuts, turns them over, and replaces them both in a similar
manner and by the same means.