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

by George Hastings McNair

(A)  All (S)
A is (M)
B

(I) ∴ Some (S)
A is (G)
C

We note at once that the middle term is undistributed, hence the mood I
A
I is invalid in the first figure; reference to the valid moods in figure one “checks” this conclusion. Since no premise, other than the first, can be particular, then all save the first must be universal.

The truth of the first rule has been demonstrated, and now we may follow a similar plan to prove the truth of the second rule.

Problem: To prove that the last premise may be negative.[11]

Data: Given the last completed syllogism:

All A is D
All D is E
∴ All A is E

Let us make the last premise negative (E) and test the result. (As all but the first must be universal we cannot use an O.)

All A is D