iliarly known
as Logic. This science was long looked upon as a completed one, and at
the commencement of this century we find such a thinker as Coleridge
expressing an opinion that further development in it was not to be
expected. Since then it has, however, taken a fresh start, and by its
growth has laid the foundation for a system of metaphysics which will be
free from the vagaries and unrealities which have thrown general
discredit on the name of philosophy.

In one direction, as applied logic and the logic of induction, the
natural associations of ideas have been thoroughly studied, and the
methods by which they can be controlled and reduced have been taught
with eminent success. In this branch, Bentham, Mill, Bain, and others
have been prominent workers.

Dealing mainly with the subjects and materials of reasoning, with
thoughts rather than with thinking, these writers, with the tendency of
specialists, have not appreciated the labors of another school of
logicians, who have made the investigation of the process of thinking
itself their especial province. This is abstract logic, or pure logic,
sometimes called, inasmuch as it deals with forms only, "formal logic,"
or because it deals with names and not things, "the logic of names." It
dates its rise as an independent science from the discovery of what is
known as "the quantification of the predicate," claimed by Sir William
Hamilton. Of writers upon it may be mentioned Professor De Morgan, W.
Stanley Jevons, and especially Professor George Boole of Belfast. The
latter, one of the subtlest thinkers of this age, and eminent as a
mathematician, succeeded in making an ultimate analysis of the laws of
thinking, and in giving them a symbolic notation, by which not only the
truth of a simple proposition but the relative degree of truth in
complex propositions may be accurately estimated.[24-1]

This he did by showing that the laws of correct thinking can be
expressed in algebraic notation, and, thus expressed, will be subject to
all the mathematical laws of an algebra whose symbols bear the uniform
value of unity or nought (1 or 0)--a limitation required by the fact
that pure logic deals in notions of quality only, not of quantity.

This mathematical form of logic was foreseen by Kant when he declared
that all mathematical reasoning derives its validity from the logical
laws; but no one before Professor Boole had succeeded in reaching the
notation which subordinated t