### Reaching true conclusions from false premisses

 Paragraph 1 It is possible for the premisses of the syllogism to be true, or to be false, or to be the one true, the other false. Paragraph 2 First then that it is not possible to draw a false conclusion from true premisses, is made clear by this consideration. Paragraph 3 But from what is false a true conclusion may be drawn, whether both the premisses are false or only one, provided that this is not either of the premisses indifferently, if it is taken as wholly false: Paragraph 4 (1) Let A belong to the whole of C, but to none of the Bs, neither let B belong to C. Paragraph 5 (2) A similar proof may be given if each premiss is partially false. Paragraph 6 (3) But if one only of the premisses is false, when the first premiss is wholly false, e.g. AB, the conclusion will not be true, but if the premiss BC is wholly false, a true conclusion will be possible. Paragraph 7 (4) But if the premiss is not wholly false, a true conclusion is possible. Paragraph 8 (5) But if the premiss AB, which is assumed, is wholly true, and the premiss BC is wholly false, a true syllogism will be possible: Paragraph 9 (6) And if the premiss BC is not wholly false but in part only, even so the conclusion may be true. Paragraph 10 In particular syllogisms it is possible when the first premiss is wholly false, and the other true, that the conclusion should be true; Paragraph 11 (7) For nothing prevents A belonging to no B, but to some C, and B to some C, e.g. animal belongs to no snow, but to some white thing, and snow to some white thing. Paragraph 12 (9) Again if the premiss AB is true, and the premiss BC is false, the conclusion may be true. Paragraph 13 (10) Also if the premiss AB is partially false, and the premiss BC is false too, the conclusion may be true. Paragraph 14 (11) Also though both premisses are false the conclusion may be true.

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