(1) Comparison by mediation is untrustworthy, unless the qualities
compared be rigidly defined or restricted, as in geometry and the use
of standards (XXII). In geometry the only two qualities recognised
are figure and magnitude. The axiom of mediate comparison means that
things having the same magnitude as a third thing are to be considered
equal, though they may have different outlines. But the axiom is
liable to be untrue in things of three or more qualities. Add colour.
Then a white sphere may resemble a white cube on the one side, and a
black sphere on the other, but the white cube does not at all resemble
the black sphere. This axiom is therefore inadmissible or at
least extremely risky in logic, which treats of things having many
qualities.
(2) Comparison, however correctly performed, is never the end, but
only a means, of reasoning.