f individuality, or mathematical
unity, has been, as I shall show hereafter, a fruitful source of error
in both religious and metaphysical theories. Pure logic deals with
quality only, not with quantity.

The second law is that of Limitation. As the first is sometimes called
that of Affirmation, so this is called that of Negation. It prescribes
that a thing is not that which it is not. Its formula is, "A is not
not-A." If this seems trivial, it is because it is so familiar.

These two laws are two aspects of the same law. The old maxim is, _omnis
determinatio est negatio_; a quality can rise into cognition only by
being limited by that which it is not. It is not a comparison of two
thoughts, however, nor does it limit the quality itself. For the
negative is not a thought, and the quality is not _in suo genere
finita_, to use an expression of the old logicians; it is limited not by
itself but by that which it is not. These are not idle distinctions, as
will soon appear.

The third law comes into play when two thoughts are associated and
compared. There is qualitative identity, or there is not. A is either B
or not B. An animal is either a man or not a man. There is no middle
class between the two to which it can be assigned. Superficial truism as
this appears, we have now come upon the very battle ground of the
philosophies. This is the famous "Law of the contradictories and
excluded middle," on the construction of which the whole fabric of
religious dogma, and I may add of the higher metaphysics, must depend.
"One of the principal retarding causes of philosophy," remarks Professor
Ferrier, "has been the want of a clear and developed doctrine of the
contradictory."[28-1] The want is as old as the days of Heraclitus of
Ephesus, and lent to his subtle paradoxes that obscurity which has not
yet been wholly removed.

Founding his arguments on one construction of this law, expressed in the
maxim, "The conceivable lies between two contradictory extremes," Sir
William Hamilton defended with his wide learning those theories of the
Conditioned and the Unconditioned, the Knowable and Unknowable, which
banish religion from the realm of reason and knowledge to that of faith,
and cleave an impassable chasm between the human and the divine
intelligence. From this unfavorable ground his orthodox followers,
Mansel and Mozley, defended with ability but poor success their
Christianity against Herbert Spencer and his disciples, who als