One of the difficulties in writing a textbook like Introductory Logic is that, for most of the questions, there are often several possible correct answers. Rather than writing “Answers may vary” every time, I elected in the answer key to give a typical correct answer to each question that could have more than one possible answer.
But all the possible correct answers for Exercise 25 are worth a little more thought. In this exercise, I ask students to write schemas of syllogisms that have a given set of fallacies. If for each problem I only allow those fallacies and no others, there are a reasonably small number of identifiable answers for each problem. Here they are (for the sake of space, I gave the answers as mood & figure, rather than schema):
1. Illicit major, illicit minor.
Six possible correct answers: AOE-1; IOE-1, 2; OIE-2, 4; OAE-4
2. Two negative premises, undistributed middle.
Two possible correct answers: OOO-3; OOE-3
3. Two negative premises, negative premise and affirmative conclusion.
Twenty-six possible correct answers: EEA, EEI, EOA, EOI, OEA, OEI, OOA, OOI (all four figures of each, except EOA-1, 2 and OOA-1, 2, which also have an Illicit Minor, and OOA-3, OOI-3, which also have an Undistributed Middle).
4. Two affirmative premises and a negative conclusion, illicit major.
Seven possible correct answers: AAE-1; IAO-3, 4; AIO-1, 3; AAO-1, 3
5. Illicit major, illicit minor, undistributed middle, and two affirmative premises and a negative conclusion.
Four possible correct answers: IIE-1, 2, 3, 4
A few notes on the above:
- If you allow the syllogisms to make more fallacies than those given, then there are even more possible correct answers.
- It was a fun challenge to determine all these possibilities.
- Let me know if you catch me in an error, or if there are possible correct answers that I have missed.