(2) In the progressive sorites, if any premiss before the last were negative, we should have a negative conclusion in the syllogism in which it occurs. This would necessitate a negative minor in the next syllogism, which is inadmissible in the first figure, as involving illicit process of the major.
In the regressive sorites the proposition which stands first is the only one which appears as a major premiss in the expanded form. Each of the others is used in its turn as a minor. If any premiss, therefore, but the first were negative, we should have a negative minor in the first figure, which involves illicit process of the major.
§ 825. The rules above given do not apply to the irregular sorites, except so far as that only one premiss can be particular and only one negative, which follows from the general rules of syllogism. But there is nothing to prevent any one premiss from being particular or any one premiss from being negative, as the subjoined examples will show. Both the instances chosen belong to the progressive order of sorites.
(1) Barbara.
All B is A.
All C is B.
All C is A.
All B is A.
All C is B.
Some C is D.
All D is E
.'. Some A is E
[Illustration]
(2) Disamis.
Some C is D.
All C is A.
Some A is D.
(3) Darii.
All D is E
Some A is D.
Some A is E.
(1) Barbara.
All B is C.
All A is B.
All A is C.
All A is B.
All B is C.
No D is C.
All E is D.
.'. No A is E.