Given below are two premises. Four conclusions are drawn from those two…

Concept. A categorical syllogism contains exactly three terms. The middle term is the one that occurs in both premises, and it must be absent from the conclusion. The major term becomes the predicate of the conclusion, and the minor term becomes its subject. A conclusion is validly drawn only if it links the minor term to the major term, and it can never be stronger than the premises that support it: when one premise is particular (a "some" statement), the conclusion must also be particular.

Application. Identify the three terms in the given premises:

• Middle term: saints — the only term that occurs in both premises.

• Major term: religious — the predicate of the major premise, "All saints are religious."

• Minor term: honest persons — the subject of the minor premise, "Some honest persons are saints."

Now combine the premises step by step:

1. "Some honest persons are saints" guarantees that at least one individual belongs to both the class of honest persons and the class of saints.

2. "All saints are religious" applies to that individual, because the individual is a saint; therefore that individual is religious.

3. The same individual is thus both honest and religious, so at least one honest person is religious.

4. Expressed as a categorical proposition: Some honest persons are religious. The pattern is a universal affirmative major premise together with a particular affirmative minor premise, the middle term standing as subject of the major and predicate of the minor — mood AII, traditionally named Darii — which is a valid form.

Cross-check. Compare the other three statements against the same rules:

• "Some saints are honest" keeps the middle term "saints" inside the statement and says nothing about religious persons. Because the two premises are expressly labelled major and minor, what is asked for is the syllogistic conclusion, which must drop the middle term and join the minor term to the major term; this statement is only the conversion of the minor premise — a valid immediate inference from that one premise alone, not a conclusion drawn from the two premises taken together.

• "All saints are honest" is a universal claim, but the only information relating honest persons to saints comes from a particular premise, and a particular premise can never support a universal conclusion.

• "All religious persons are honest" makes "religious" the distributed subject of a universal claim, whereas "religious" is undistributed in the premise that introduces it, where it is only the predicate of an A-proposition. A term may not be distributed in the conclusion unless it is already distributed in its premise, and since "All saints are religious" is the designated major premise, "religious" is the major term — so this is the fallacy of illicit major.

Result. The conclusion that follows validly from both premises together is "Some honest persons are religious."