CHAPTER VIII.

ADAPTATION OP PROCESS OF THOUGHT TO ALGEBRAICFORMULAS.

(97). Syllogism. —(98). Algebraic Formulae.

(97). The laws regulating the natural processof thought, can not only be exemplified by mecha-nical contrivances, but can also be adapted toalgebraic forxnula3. In logical works the notationwhich is used is remarkable for its extraordinaryvagueness of character. Thus logicians set outthe syllogism-

all men die .

all men belong to the class ofrational beings .

every Y is Xevery Y is Z

therefore some rational beings) therefore some Z’sdie .I are X ’s.

Upon this plan logicians exemplify what they calllogical deductions, but the most casual examina-tion will sufficiently explain why no man of senseever employs logical ambiguities, for how possiblyaccording to the ordinary use of symbols andwords can every Y be both X and Z, and yet onlysome Z’s be X ’s, for the word is or be denotes