CHAPTER II. ilI fed." For they separate the middle term both from the subject and predicate of the conclusion, and when two ideas disagree to a third, we cannot infer that they either agree or disagree with each other. Yet where the negation is a part of the middle term, the two premises may look like negatives according to the words but'one of them is affirmative in sense ; as, " What has no thought cannot reason ; but a worm has no thought ; there- fore a worm cannot reason." The minor proposition does really affirm the middle term concerning the subject, namely, a worm is what has no thought, and thus it is properly in this syllogism an affirmative proposition. VII. "From two particular premises nothing can be con- cluded." This rule depends chiefly on the first axiom. A more laborious and accurate proof of these rules, and the derivation of every part of them in all possible cases, from the fore -going axioms, require so much time, and are of so little importance to assist the right use of reason, that it is needless to insist longer upon them here. See all this done in- geniously in the Logic called the Art of Thinking, Part III. Chap., III, &c. SECT. III. Of the Moods and Figures of simple Syllogisms. SIMPLE syllogisms are adorned and surrounded in the common books of Logic with a variety of inventions about moods and figures, wherein by the artificial contexture of the letters A, E, I, and O, men have endeavoured to transform Logic, or the Art of Reasoning, into a sort of mechanism, and to teach boys to syllogise, or frame arguments and refute them, without any real inward knowledgeof the question. This is almost in the same manner as school-boys have been taught perhaps in their trifling years to compose Latin verses, that is, by certain tables and squares, with a variety of letters in them, wherein by counting every sixth, seventh, or eight letter, certain Latin words should be framed in the form of hexameters or pentame- ters ; and this may be done by those who know nothing of Latin or of verses. I confess some of these logical subtleties have much more use than those versifying tables, and there is much ingenuity discovered in determining the precise number of syllogisms that may be formed in every figure, and giving the reasons of them, yet the light of nature, a good judgment and due con- sideration of things, tend more to true reasoning than all the trappings of moods and figures. But lest this book be charged with two great defects and imperfections, it may be proper to give short hints of that which some logicians have spent so much time and paper upon. All the possible compositions of three of the letters, A, E, Ì, O to make three propositions amount to sixty -four ; but fifty - VoL. vtt. I-I it
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