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For example, I had about six different Protestants respond to the following question with rants. But not one of them responded with a “yes” or a “no.”

Is the following a formally valid syllogism or a formally invalid syllogism?

Emily is the mother of Sam.
Sam is a fireman.
Emily is the mother of a fireman.

LOL! I seem to recall we dealt with this a while ago. Your syllogism is fine if you don't try to import complex ontologies into the terms. Sam being a firemen is one thing, and Jesus being God is quite another. The category of "fireman" does not describe a divine trinity of persons. The formal correctness of the syllogism assumes a proper analogy of terms. Put in colloquial terms, comparing apples to oranges is fruitless. :)

As for yes and no answers, they're fine, if and only if they are answerable that way. How about, when did you stop beating your wife? Not so easy to give a yes or no response, is it? That's called a loaded question. The question makes an assumption of facts not in evidence. If the responder simply says "yes" without qualification, they're admitting a fact that isn't true. Unhelpful, if truth is the objective.

I'm an attorney. In preparing a client for deposition or courtroom testimony, I tell them to watch out for false dilemmas, false "either/or" scenarios. If they need to qualify the answer, then they get to qualify the answer. If the other attorney tries to force them to admit something they really don't think is true, if I spot it first, I'll object, "the question assumes facts not in evidence." If the client spots the problem, they should ask for clarifications, or otherwise present an answer that best represents the truth, but should never allow themselves to be bullied into a false simplicity. Whatever works best for getting at the truth. Wouldn't you agree that is a worthy objective? A simple yes or no answer will do.

Peace,

SR