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.

Thirty-two possible correct answers: EEA, EEI, EOA, EOI, OEA, OEI, OOA, OOI (all four figures of each)

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, especially numbers 1 and 4.
- Let me know if you catch me in an error, or if there are possible correct answers that I have missed.