Page:O. F. Owen's Organon of Aristotle Vol. 1 (1853).djvu/300

 because it is impossible that C should be with B, with nothing of which A is present; for otherwise the proposition A C will be no longer true, at the same time, if both are true, the conclusion also will be true. But it is also possible that C B may be true, when the other proposition is false, as if B is in C and in A, for one if must necessarily be under the other, so that if A should be assumed present with no C, the proposition will be false. It is clear then, that when one proposition is false, and also when both are, the syllogism will be false.

In the middle figure, however, it is not possible that both propositions should be wholly false, for when A is present with every B, it will be impossible to assume any thing, which is present with every individual of the one, but with no individual of the other; but we must so assume the propositions that the (middle) may be present with one (extreme), and not be present with the other, if indeed there is to be a syllogism. If then, when they are thus assumed, they are false, it is clear that, when taken contrarily, they will subsist vice versâ, but this is impossible. Still there is nothing to prevent each being partly false, as if C is with A, and with a certain B; for if it should be assumed present with every A, but with no B, both propositions indeed would be false, yet not wholly, but partially. The same will occur when the negative is placed vice versâ. But it is possible that one proposition, and either of them, may be false, for what is present with every A, will be also with B, if then C is assumed present with the whole of A, but not present with the whole of B, C A will be true, but the proposition C B false. Again, what is present with no B, will not be present with every A; for if with A, it would also be with B, but it was not present; if then C should be assumed present with the whole of A, but with no B, the proposition C