I remember one technique you employed in logic class to teach enthymemes was the citation of examples of these in scripture. Have you ever used John 18:30? “They answered and said unto him, ‘If he were not a malefactor, we would not have delivered him up unto thee.’ ” Does that combine an enthymeme and a hypothetical syllogism?
Strictly speaking, John 18:30 is just a conditional proposition, and so neither an enthymeme nor a hypothetical syllogism, which are both arguments. But conditional propositions are very much like self-contained arguments, and I think we can analyze this one as such without doing too much violence to the original.
In this case, we would first simplify the proposition using the Rule of Transposition, making it, “If we have delivered him up to thee, then he is a malefactor.” This could then be interpreted as this enthymeme: “Jesus is a person we have delivered up to thee, therefore Jesus is a malefactor.” Put into categorical form, with the missing premise in parentheses, and we get this complete syllogism:
(All persons we deliver up to thee are malefactors.)
All Jesus is a person we have delivered up to thee.
∴ All Jesus is a malefactor.
Their reasoning was valid, but the conclusion is false. Thus we know that one of the premises is false. Which one, do you think?