But in the division of their own subject they follow Aristotle, and so lose their way.
It is plain that an act of reasoning is a mental thing in the first place, and only when uttered, and thus in a secondary sense, is it a material object. The classification of arguments should therefore follow mental characteristics. Logicians make it follow the material characteristics of the terms in which the arguments are uttered. Their moods of the syllogism are mere varieties of expression, not varieties of reason.
The number of these moods is accidental, depending on flexibility of language and ingenuity in inventing varieties of syntax. Mere transposition of premises constitutes a difference of mood. Logicians however pretend to base their numeration on a more general necessity. They calculate from the distinctive parts of the three propositions forming a syllogism, varied by negation, &c., that there ought to be sixty-four moods. Experience proves that in spite of their free and easy method of multiplying syllogistic varieties they cannot produce anything like that number. One logician has thirty-six moods, another thirty-two, a third eleven; the more orthodox fix the number at nineteen. But they all admit that every argument can be reduced to one of four fundamental types—the moods of the First Figure. Why then have more classes than these four? Because, says Whately, it would be 'occasionally tedious' to reduce every argument to the first figure.
If the 11, 19, 32, or 36 classes were natural arguments taken down untouched from men's lips, and it was found to be useless and troublesome to reduce them to four artificial forms, the plea might be admitted. But the so-called valid syllogisms are themselves artificial, and just as tedious to make as the moods of the first figure. Not only so, but an elaborate system of mnemonic rules is provided for reducing the valid moods to the fundamental moods, thus admitting that the former are only intermediate halting places between the natural speech and the fundamental moods. It is expected that the intermediates should be reduced to the first figure.
Is there anything analogous to this sort of division in any science or branch of practical thought? Would logicians themselves sanction such a classification in a natural science? If a zoologist, for example, were to determine beforehand how many classes of animals there ought to be, would they not say he was acting improperly? If, after discovering that he had five times as many classes as he could find animals to put into them, he still retained his classification and required his pupils to write out the names or symbols of all the useless classes—would not logicians be apt to call him a pedant? Yet in a modern work on logic such a task is prescribed for students:—
'Write out the sixty-four moods of the syllogism, and strike out the fifty-three invalid ones.'
We might have excused the existence of a merely verbal classification in logic, if it were accompanied by and subordinated to a classification of theorems considered as mental facts. But in syllogistic the verbal is the dominant classification, and we have seen from the procedure of Sir William Hamilton—in dropping his categorical judgments—that when the two principles of division conflict, it is the mental which has to give way. The Letter is allowed to kill the Spirit.
All the Moods reducible to One. Syllogists appear not to know their own schematism very well. They say there are four ultimate moods, which it is impossible to reduce to any lower number. But since each of the four is, mentally, a double classification, it must be possible to reflect this common property in the mode of expression. The difference between them can only be verbal. Let us adopt another than the ordinary symbolism.
Cut a card into three triangular pieces of unequal size, and call them by the letters A, B, C, beginning with the largest. These are the terms of the syllogism.