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 these two divisions of abstract thought to

the same formal types. His labors have not yet borne fruit in proportion

to their value, and they are, I believe, comparatively little known.

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