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Aristotle - The Organon - index for ANALYTICA PRIORIA Book 1 Part 19

One necessary, other problematic, negative necessary

  
Paragraph 1 If one of the premisses is necessary, the other problematic, then if the negative is necessary a syllogistic conclusion can be drawn, not merely a negative problematic but also a negative assertoric conclusion;
Paragraph 2 For (1) it sometimes turns out that B necessarily does not belong to C.
Paragraph 3 (2) Nor again can we draw a necessary conclusion:
Paragraph 4 (3) Further it is possible also, when the terms are so arranged, that B should belong to C:
Paragraph 5 But if the premisses are similar in quality, when they are negative a syllogism can always be formed by converting the problematic premiss into its complementary affirmative as before.
Paragraph 6 Similar relations will obtain in particular syllogisms.
Paragraph 7 It is clear then from what has been said that if the universal and negative premiss is necessary, a syllogism is always possible, proving not merely a negative problematic, but also a negative assertoric proposition;


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