Chemistry Lab ID Stickers: Illicit Major in a Syllogism
At a junior college, the laboratory committee is reviewing three statements before issuing ID stickers for the chemistry lab. P1: 'All students who completed the lab safety module are students permitted to use the chemistry lab.' P2: 'No students who missed the practical demonstration are students who completed the lab safety module.' A member proposes the conclusion C: 'No students who missed the practical demonstration are students permitted to use the chemistry lab.' Another member says the argument is valid because the conclusion simply combines the two premises. The committee has 18 students who missed the demonstration and 25 who completed the module; the records are complete. The chair asks for a standard-form analysis, a test of validity using the rules of syllogism or a Venn diagram, and a decision on whether any conclusion about missed-demonstration students and permitted users can be drawn. The committee must record the exact fallacy if the proposed conclusion does not follow, and must state what additional premise would make C valid.
1. Rewrite the argument in standard form. Identify the major, minor, and middle terms, and state the mood and figure.
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The conclusion is 'No S are P', where S = students who missed the practical demonstration and P = students permitted to use the chemistry lab. The middle term M = students who completed the lab safety module. Standard form places the major premise first: Major premise: All M are P ('All students who completed the lab safety module are students permitted to use the chemistry lab'). Minor premise: No S are M ('No students who missed the practical demonstration are students who completed the lab safety module'). Conclusion: No S are P. In figure 1 the major premise is M–P and the minor is S–M. The mood is AEE, so the form is AEE-1.
2. Test the argument. If it is invalid, name the fallacy and give a counterexample with actual categories.
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The argument is invalid. In the conclusion 'No S are P', the predicate P is distributed. In the major premise 'All M are P', P is undistributed. The syllogism therefore commits the fallacy of illicit major. A Venn test confirms this: the premises shade the intersection of S and M, and shade M outside P, but they do not force S outside P. Counterexample: suppose all students who completed the module are permitted to use the lab, and no student who missed the demonstration completed the module. It could still be that some students who missed the demonstration are permitted through a separate safety route. Then both premises are true and the conclusion is false. The conclusion does not follow.
3. What additional premise would make C valid? Explain briefly why it works.
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Add the premise 'All students permitted to use the chemistry lab are students who completed the lab safety module' (All P are M). With No S are M, the class S is excluded from M, and since all P is inside M, S is also excluded from P. The conclusion No S are P then follows validly. This additional premise is sufficient, though not the only possible repair. It blocks the counterexample in which a permitted user reaches the lab without completing the module. The committee should note that the original data alone do not justify C.