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Particular propositions in Syllogisms

According to the rules of syllogisms you can't get a conclusion from two negative premises, but since an O proposition i.e. Some A is not B can be expressed as a I proposition, i.e. Some A is non-B, then isn't this latter form just as much an O as an I?

So you can have the syllogism

(E): No A is B
(O): Some B is non-C

Therefore, Some non-C is not A (O).

Confused!

Re: Particular propositions in Syllogisms

The syllogism you propose is quite valid, but it is not one intended under the rule you state, because you have in fact changed the minor term from C to non-C and the minor premise from a negative form to a positive one. This is legitimate, no problem.

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Re: Particular propositions in Syllogisms

Thanks Avi. Actually, thinking about it, you could also do the same for a universal proposition. So 'No A is B' is equivalent to 'All A is non-B' logically speaking.