On the Enumeration of the Exceptive Syllogisms [Which have a Separative Conditional Premiss]

Abstract

The exceptive syllogism which is compounded of conditional premisses that express a real separative proposition can either have two or more than two parts. Those which have two parts may have one affirmative and one negative parts, namely contradictory parts—as when we say ‘Either so or not-so’. If we except [i.e. assert] any one of them we produce the contradictory of the other. In this case the conclusion will be the same as the exceptive premiss. For if your exception is ‘but it is so’ you will produce ‘therefore it is not not-so’. This conclusion does not tell us anything more than what the conclusion, which we got when the exceptive premiss was identical with one of the parts in the conditional premiss, tells us. Also, if we except ‘But not not-so’ we produce ‘therefore it is so’. It is not unlikely that the exceptive premiss is not more known than the conclusion, and that it does not come to the mind before the conclusion. This kind of reasoning is useful when the syllogism is compounded of a connective and a separative proposition—as when they say ‘So is either so or not so, and if it is not so, then A is B; but A is not B; therefore it is so’. In this case the exceptive premiss is not the contradictory of one of the parts, but a statement implied by it. This syllogism will also be complete if its conditional premiss is a connective proposition. It is not unlikely that the separative will not be needed at all. Therefore, this kind of separative propositions are not very useful when used as premisses in an exceptive syllogism, for the parts (of the separative premiss) must not be opposed to each other in the above way. They should be opposed in this way: ‘If this is a number, then it is either even or odd’. When one of the parts is excepted, the contradictory of the other will be produced. If we except that it is even we produce that it is not odd. And this is the first mood.