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Aristotle - The Organon - index for ANALYTICA PRIORIA Book 2 Part 4

... in the third figure

  
Paragraph 1 In the last figure a true conclusion may come through what is false, alike when both premisses are wholly false, when each is partly false, when one premiss is wholly true, the other false, when one premiss is partly false, the other wholly true, and vice versa, and in every other way in which it is possible to alter the premisses.
Paragraph 2 For (1) nothing prevents neither A nor B from belonging to any C, while A belongs to some B, e.g. neither man nor footed follows anything lifeless, though man belongs to some footed things.
Paragraph 3 (2) Also if each premiss is partly false, the conclusion may be true.
Paragraph 4 (3) Similarly if one of the premisses assumed is wholly false, the other wholly true.
Paragraph 5 (4) Again if one premiss is wholly true, the other partly false, the conclusion may be true.
Paragraph 6 (5) It is clear also in the case of particular syllogisms that a true conclusion may come through what is false, in every possible way.
Paragraph 7 It is clear then that if the conclusion is false, the premisses of the argument must be false, either all or some of them;


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