Aristotle - The Organon - index for ANALYTICA PRIORIA Book 1 Part 15

Possibility, impossibility

Paragraph 1 If one premiss is a simple proposition, the other a problematic, whenever the major premiss indicates possibility all the syllogisms will be perfect and establish possibility in the sense defined;
Paragraph 2 It is clear that perfect syllogisms result if the minor premiss states simple belonging:
Paragraph 3 Since this is proved it is evident that if a false and not impossible assumption is made, the consequence of the assumption will also be false and not impossible:
Paragraph 4 Since we have defined these points, let A belong to all B, and B be possible for all C:
Paragraph 5 We must understand 'that which belongs to all' with no limitation in respect of time, e.g. to the present or to a particular period, but simply without qualification.
Paragraph 6 Again let the premiss AB be universal and negative, and assume that A belongs to no B, but B possibly belongs to all C.
Paragraph 7 If the minor premiss is negative and indicates possibility, from the actual premisses taken there can be no syllogism, but if the problematic premiss is converted, a syllogism will be possible, as before.
Paragraph 8 Clearly then if the terms are universal, and one of the premisses is assertoric, the other problematic, whenever the minor premiss is problematic a syllogism always results, only sometimes it results from the premisses that are taken, sometimes it requires the conversion of one premiss.

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