(2a) Paying no regard to “figure,” derive as many conclusions as possible from the following sets of premises: E
I A
E.
Answer: E
I. The major premise of this mood, being negative, necessitates a negative conclusion, according to rule 6, and the minor premise, being particular, compels a particular conclusion, according to rule 8. Since the conclusion must be negative and particular, then O is the only one which can be drawn. The completed mood is E
I
O.
A
E. This mood must have a negative conclusion, because the minor premise is negative; this would necessitate either E or O;but O as a conclusion would be, in this case, a weakened one; since E distributing both terms would necessarily distribute the minor; which fact would permit the minor to be distributed in the conclusion. Thus the conclusion could just as well be universal as particular. The completed mood is A
E
E.
(2b) From the following sets of premises derive as many conclusions as possible paying no attention to figure: E
A A
A O
A.
(3a) Making use of all the general rules of the syllogism, test the validity of the following mood in all the figures: A
A
I.
Answer:
| 1 | 2 | 3 | 4 | ||||
| A | M — G | G — M | M — G | G — M | |||
| A | S — M | S — M | M — S | M — S | |||
| I | S — G | S — G | S — G | S — G |
An underscored symbol indicates a distributed term. Since A distributes its subject, the subjects of both premises are underscored in all the figures. No term is underscored in the conclusions; since I distributes neither term. In the first figure the middle term is distributed in the major premise, and no term is distributed in the conclusion. Since both premises are affirmative, the rules for negatives are not applicable; and as a particular may be drawn from two universals, if there is no violation of the rules for distribution, this mood seems to be valid in the first figure. It is, however, a weakened conclusion; since an A could just as well be drawn. The mood is invalid in the second figure because of undistributed middle, but valid in both the third and fourth; since in both cases the middle term is distributed at least once.
(3b) Determine the validity of the attending moods in all the figures giving reasons: I
A
I A
O
O E
A
O.