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Aristotle - The Organon - index for ANALYTICA PRIORIA Book 1 Part 6

The third figure

  
Paragraph 1 But if one term belongs to all, and another to none, of a third, or if both belong to all, or to none, of it, I call such a figure the third;
Paragraph 2 If they are universal, whenever both P and R belong to S, it follows that P will necessarily belong to some R.
Paragraph 3 If R belongs to all S, and P to no S, there will be a syllogism to prove that P will necessarily not belong to some R.
Paragraph 4 Nor can there be a syllogism when both terms are asserted of no S.
Paragraph 5 It is clear then in this figure also when a syllogism will be possible and when not, if the terms are related universally.
Paragraph 6 Again if R belongs to some S, and P to all S, P must belong to some R.
Paragraph 7 But whenever the major is affirmative, no syllogism will be possible, e.g. if P belongs to all S and R does not belong to some S.
Paragraph 8 But if the negative term is universal, whenever the major is negative and the minor affirmative there will be a syllogism.
Paragraph 9 But when the minor is negative, there will be no syllogism.
Paragraph 10 Nor is a syllogism possible when both are stated in the negative, but one is universal, the other particular.
Paragraph 11 Nor is a syllogism possible anyhow, if each of the extremes belongs to some of the middle or does not belong, or one belongs and the other does not to some of the middle, or one belongs to some of the middle, the other not to all, or if the premisses are indefinite.
Paragraph 12 It is clear then in this figure also when a syllogism will be possible, and when not;


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