Two Hostel-Fee Syllogisms at a Debate Trial
At a debate-team selection trial in a government college, two students propose arguments about the hostel fee waiver. The coach writes the first on the board: 'All hostellers are mess-fee payers; some scholarship holders are not mess-fee payers; therefore some scholarship holders are not hostellers.' A team member objects that the middle term is undistributed in both premises, so the argument must be invalid. The coach then writes a second argument: 'All hostellers are mess-fee payers; some day scholars are not hostellers; therefore some day scholars are not mess-fee payers.' The team has 15 minutes to decide which argument can be used in the final round and to prepare a rule-by-rule justification. The final round permits only valid categorical syllogisms with three terms. They must state figure and mood, identify any illicit process, and propose a one-premise correction that would make the second argument valid without changing its conclusion's quality.
1. Analyse the first argument. State its figure and mood, identify the distribution of each term, and decide whether the team member's objection about the middle term is correct.
Read the worked answer
Let S = scholarship holders, H = hostellers, M = mess-fee payers.
- Major premise: All H are M - an A proposition.
- Minor premise: Some S are not M - an O proposition.
- Conclusion: Some S are not H - an O proposition.
The middle term is M, and it is the predicate in both premises, so this is Figure 2. The mood is AOO-2, traditionally Baroco.
Distribution:
- In the major A, H is distributed, M is not distributed.
- In the minor O, M is distributed, S is not distributed.
- In the conclusion O, H is distributed, S is not distributed.
The middle term M is undistributed in the major premise but distributed in the minor premise, so it is distributed at least once. The team member's objection is therefore false. The major term H is distributed in both the major premise and the conclusion; the minor term S is undistributed in both. No rule is violated. The argument is valid.
2. Analyse the second argument. If it is invalid, name the rule violated and the fallacy.
Read the worked answer
Let D = day scholars, M = mess-fee payers, H = hostellers.
- Major premise: All H are M - A.
- Minor premise: Some D are not H - O.
- Conclusion: Some D are not M - O.
The middle term H is the subject of the major premise and the predicate of the minor premise, so this is Figure 1, mood AOO-1.
Distribution check:
- Major A: H distributed, M undistributed.
- Minor O: D undistributed, H distributed.
- Conclusion O: D undistributed, M distributed.
The middle term H is distributed in both premises, so that rule is satisfied. But the major term M is undistributed in the major premise and distributed in the conclusion. That violates the rule that a term distributed in the conclusion must be distributed in its premise. The fallacy is illicit process of the major term. The argument is invalid.
3. Propose a one-premise correction that keeps the same conclusion and makes the second argument valid. State the new mood and figure.
Read the worked answer
Change the major premise from 'All hostellers are mess-fee payers' to 'All mess-fee payers are hostellers' - that is, All M are H.
The corrected argument is:
- Major: All M are H - A.
- Minor: Some D are not H - O.
- Conclusion: Some D are not M - O.
Now the major term M is distributed as the subject of the major A, and it is also distributed in the conclusion O. The middle term H is undistributed in the major premise but distributed in the minor premise, so it is distributed once. The minor term D remains undistributed in both the minor premise and the conclusion. One premise is negative and the conclusion is negative, so the negative-premise rule is respected.
The middle term H is the predicate in both premises, so the corrected form is Figure 2, mood AOO-2 - Baroco. The conclusion's quality is unchanged: it remains a particular negative. The corrected syllogism is valid.