This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1850 Excerpt: ... second rule, which is a consequence of the first, is that the members of the division be opposed: as, even, uneven, rational, irrational. But what we have already said in the First Part, must be here noticed, viz., that it is not necessary for the differences, which constitute its opposed members, to be positive, but ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1850 Excerpt: ... second rule, which is a consequence of the first, is that the members of the division be opposed: as, even, uneven, rational, irrational. But what we have already said in the First Part, must be here noticed, viz., that it is not necessary for the differences, which constitute its opposed members, to be positive, but it is sufficient for one to be so, and for the other to be the genus alone with the negation of another difference. It is, indeed, in this very way that we make the members more certainly opposed. Thus, the difference between a beast and a man, is only the absence of reason, which is nothing positive; the unevenness of a number is only the negation of its divisibility into two equal parts. The first number has nothing which the compound number has not, unity being the measure of each, and that number which is called first, differs from the compound one only in this, that it has no other measure save unity. Nevertheless, it must be confessed that it is better to express the opposed differences by positive terms, when this can be done, inasmuch as this explains better the nature of the members of the division. This is why the division of substance into that which thinks, and that which is extended, is much better than the common one, into that which is material, and that which is immaterial, or equally into that which is corporeal, and that which is not corporeal, inasmuch as the words immaterial, or incorporeal, furnish us with an idea, only very imperfect and confused, of that which is understood much better by the expression, substance that thinks. The third rule, which is a consequent of the second, is that one of the members be not so contained in the other, that the other may be affirmed of it, although it may sometimes be contained in it ...
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