A Class Room Logic / Deductive and Inductive, with Special Application to the Science and Art of Teaching

by George Hastings McNair

Let us now make the first premise of the sorites particular and test.

Some A is B

All B is C

∴ Some A is C

Arranged logically:

(A)  All (M)
B is (G)
C

(I)  Some (S)
A is (M)
B

(I) ∴ Some (S)
A is (G)
C

Proof:

Since one premise is particular the conclusion must be particular. (Rule 7) As there are no negatives in the argument, only one conclusion is possible; namely, a particular affirmative (I). Thus, instead of the conclusion, “All A is C,” which is an (A), it must be, “Some A is C,” or an (I). Underscoring the distributed term, it is seen that the middle term is distributed in the major premise and that no term is distributed in the conclusion. Thus the mood is valid. This is “checked” when we recall that AII is always valid in the first figure. We have now shown that the first premise of a progressive sorites may be universal or particular. Let us furtherproceed to prove that all the other premises must be universal.