Aristotle - The Organon - index for ANALYTICA PRIORIA Book 2 Part 15

Drawing a conclusion from opposed premisses

Paragraph 1 In what figure it is possible to draw a conclusion from premisses which are opposed, and in what figure this is not possible, will be made clear in this way.
Paragraph 2 In the first figure no syllogism whether affirmative or negative can be made out of opposed premisses:
Paragraph 3 In the middle figure a syllogism can be made both oLcontradictories and of contraries.
Paragraph 4 In the third figure an affirmative syllogism can never be made out of opposite premisses, for the reason given in reference to the first figure;
Paragraph 5 We must recognize that it is possible to take opposites in the way we said, viz. 'all science is good' and 'no science is good' or 'some science is not good'.
Paragraph 6 It is clear too that from false premisses it is possible to draw a true conclusion, as has been said before, but it is not possible if the premisses are opposed.

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