necessity be either true or false. From true propositions then we cannot infer a falsity, but from false premises we may infer the truth, except that not the why, but the mere that (is inferred), since there is not a syllogism of the why from false premises, and for what reason shall be told hereafter.
First then, that we cannot infer the false from true premises, appears from this: if when A is, it is necessary that B should be, when B is not it is necessary that A is not, if therefore A is true, B is necessarily true, or the same thing (A) would at one and the same time be and not be, which is impossible. Neither must it be thought, because one term, A, is taken, that from one certain thing existing, it will happen that something will result from necessity, since this is not possible, for what results from necessity is the conclusion, and the fewest things through which this arises are three terms, but two intervals and propositions. If then it is true that with whatever B is A also is, and that with whatever C is B is, it is necessary that with whatever C is A also is, and this cannot be false, for else the same thing would exist and not exist at the same time. Wherefore A is laid down as one thing, the two propositions being co-assumed. It is the same also in negatives, for we cannot show the false from what are true; but from false propositions we may collect the truth, either when both premises are false, or one only, and this not indifferently, but the minor, if it comprehend the whole false, but if the whole is not assumed to be false, the true may be collected from either. Now let A be with the whole of C, but with no B, nor B with C,