Aristotle - The Organon ANALYTICA POSTERIORA Book 1 Part 15

Atomic connexions and disconnexions

1. Just as an attribute A may (as we saw) be atomically connected with a subject B, so its disconnexion may be atomic. I call 'atomic' connexions or disconnexions which involve no intermediate term; since in that case the connexion or disconnexion will not be mediated by something other than the terms themselves. It follows that if either A or B, or both A and B, have a genus, their disconnexion cannot be primary. Thus: let C be the genus of A. Then, if C is not the genus of B - for A may well have a genus which is not the genus of B - there will be a syllogism proving A's disconnexion from B thus: \

2. all A is C,

3. no B is C,

4. therefore no B is A. \

5. Or if it is B which has a genus D, we have \

6. all B is D,

7. no D is A,

8. therefore no B is A, by syllogism; \

9. and the proof will be similar if both A and B have a genus. That the genus of A need not be the genus of B and vice versa, is shown by the existence of mutually exclusive coordinate series of predication. If no term in the series ACD... is predicable of any term in the series BEF..., and if G - a term in the former series - is the genus of A, clearly G will not be the genus of B; since, if it were, the series would not be mutually exclusive. So also if B has a genus, it will not be the genus of A. If, on the other hand, neither A nor B has a genus and A does not inhere in B, this disconnexion must be atomic. If there be a middle term, one or other of them is bound to have a genus, for the syllogism will be either in the first or the second figure. If it is in the first, B will have a genus - for the premiss containing it must be affirmative: if in the second, either A or B indifferently, since syllogism is possible if either is contained in a negative premiss, but not if both premisses are negative.

10. Hence it is clear that one thing may be atomically disconnected from another, and we have stated when and how this is possible.

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