Which of the following is correct in the context of Syllogism? A. With two…
2024
Which of the following is correct in the context of Syllogism?
A. With two negative premises, affirmative conclusion can be drawn.
B. Predicate of the conclusion is the minor term.
C. Middle term must be distributed at least once in the premises.
D. With two universal premises, particular conclusion can be drawn.
E. The term distributed in the conclusion must be distributed in the premises.
Applying the standard (modern) rules of the categorical syllogism, choose the most appropriate answer from the options given below:
Answer: D. C and E Only — Concept — the rules that decide a categorical syllogism. Every categorical syllogism carries exactly three terms: the minor term, which is the subject of the…
- A.
B and C Only
- B.
A and C Only
- C.
D and E Only
- D.
C and E Only
Show answer & explanation
Correct answer: D
Concept — the rules that decide a categorical syllogism. Every categorical syllogism carries exactly three terms: the minor term, which is the subject of the conclusion; the major term, which is the predicate of the conclusion; and the middle term, which appears in both premises and never in the conclusion. Validity is settled by structure alone, through four standing rules:
Distribution of the middle term — the middle term must be distributed in at least one premise; otherwise the argument commits the fallacy of the undistributed middle.
Distribution in the conclusion — no term may be distributed in the conclusion unless it is already distributed in the premise in which it occurs; a breach is the illicit major or the illicit minor.
Quality — two negative premises yield no conclusion whatever, and if either premise is negative the conclusion must be negative.
Quantity — under the modern (Boolean) reading used by the standard rules, universal premises assert no existence, so they cannot license a particular conclusion; drawing one is the existential fallacy.
Application — each listed statement measured against those rules.
Statement | Rule it tests | What the rule gives |
|---|---|---|
A. Affirmative conclusion from two negative premises | Quality | Two negative premises license no conclusion at all, so certainly not an affirmative one — the statement does not hold. |
B. Predicate of the conclusion is the minor term | Roles of the three terms | The predicate of the conclusion is the major term, while the minor term is its subject — the statement does not hold. |
C. Middle term distributed at least once in the premises | Distribution of the middle term | This restates the rule itself; without it the undistributed-middle fallacy arises — the statement holds. |
D. Particular conclusion from two universal premises | Quantity | Universal premises assert no existence, so they cannot license a particular conclusion; where two universal premises do yield a valid conclusion at all, that conclusion is universal — the statement does not hold. |
E. Term distributed in the conclusion must be distributed in the premises | Distribution in the conclusion | This restates the rule itself; without it the illicit major or illicit minor arises — the statement holds. |
Cross-check.
Barbara — all M are P; all S are M; therefore all S are P. The middle term M is the subject of a universal affirmative in the first premise and is therefore distributed, and S, the one term distributed in the conclusion, is already distributed as the subject of the second premise, so both accepted rules are met.
Contrast — all cats are mammals; all dogs are mammals; therefore all dogs are cats. Here the middle term “mammals” is the predicate of two universal affirmatives and is never distributed, which is precisely why that inference collapses.
Result. The statements that hold are C and E.
Note on statement D. Traditional Aristotelian logic assumes existential import and permits subalternation, on which a universal conclusion also yields the corresponding particular one; on that older reading statement D would hold as well. The set of true statements would then be C, D and E, and no combination on offer would be exactly true. That is precisely why the question is anchored to the standard modern rules, on which universal premises carry no existential import — and on which exactly C and E hold.