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Aristotle - The Organon - index for ANALYTICA PRIORIA Book 1 Part 5

The second figure

  
Paragraph 1 Whenever the same thing belongs to all of one subject, and to none of another, or to all of each subject or to none of either, I call such a figure the second;
Paragraph 2 If then the terms are related universally a syllogism will be possible, whenever the middle belongs to all of one subject and to none of another (it does not matter which has the negative relation), but in no other way.
Paragraph 3 It is possible to prove these results also by reductio ad impossibile.
Paragraph 4 It is clear then that a syllogism is formed when the terms are so related, but not a perfect syllogism;
Paragraph 5 But if M is predicated of every N and O, there cannot be a syllogism.
Paragraph 6 Nor is a syllogism possible when M is predicated neither of any N nor of any O.
Paragraph 7 It is clear then that if a syllogism is formed when the terms are universally related, the terms must be related as we stated at the outset:
Paragraph 8 If the middle term is related universally to one of the extremes, a particular negative syllogism must result whenever the middle term is related universally to the major whether positively or negatively, and particularly to the minor and in a manner opposite to that of the universal statement:
Paragraph 9 If then the universal statement is opposed to the particular, we have stated when a syllogism will be possible and when not:
Paragraph 10 Again let the premisses be affirmative, and let the major premiss as before be universal, e.g. let M belong to all N and to some O.
Paragraph 11 It is clear then from what has been said that if the terms are related to one another in the way stated, a syllogism results of necessity;


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