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Aristotle - The Organon - index for ANALYTICA PRIORIA Book 2 Part 3

... in the second figure

  
Paragraph 1 In the middle figure it is possible in every way to reach a true conclusion through false premisses, whether the syllogisms are universal or particular, viz. when both premisses are wholly false;
Paragraph 2 (1) if A belongs to no B and to all C, e.g. animal to no stone and to every horse, then if the premisses are stated contrariwise and it is assumed that A belongs to all B and to no C, though the premisses are wholly false they will yield a true conclusion.
Paragraph 3 (2) Again if one premiss is wholly false, the other wholly true:
Paragraph 4 (3) Also if one premiss is partially false, the other wholly true.
Paragraph 5 (4) And if both the premisses are partially false, the conclusion may be true.
Paragraph 6 It is clear also that our thesis holds in particular syllogisms.
Paragraph 7 (5) nothing prevents A belonging to all B and to some C, though B does not belong to some C, e.g. animal to every man and to some white things, though man will not belong to some white things.
Paragraph 8 (6) It is clear too that though both premisses are false they may yield a true conclusion, since it is possible that A should belong both to B and to C as wholes, though B does not follow some C.


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