I’m familiar with syllogistic arguments, but hardly an expert. In a recent debate about logical fallacies, I made the following points.
So-called logical fallacies do not apply to inherently sound arguments (much as, for example, libel isn’t libel if the statement is true). Therefore, it is logically sound to "appeal" to numbers or to authorities IF the majority or the authority being cited: (1) has legitimate expertise on the topic (e.g., a doctor, not a mechanic on a medical matter); (2) is cited only in the area of its expertise (e.g., don't cite computer programmers on a biological question); and (3) the subject-matter experts generally agree on the statement (as, for instance, most oncologists agree that smoking is a cause of lung cancer). In other words, it is perfectly logical to accept as valid the consensus of lung-cancer researchers that smoking is a leading cause of lung cancer.
I may have phrased my case ineptly, but I wonder if my argument is correct, or at least on the right track.