Beta, EIEs, oratory and logic
Many of the people who are typed as EIEs are known for their oratory skills, especially if they're involved in politics. But if you listen to speeches from these presumed EIEs, they're basically all about logic. It may not be very complex logic, like some sort of mathematical theorem, but still the idea is to mention some logical reason, based on various facts and logical constructions, to believe this or that, and then make people feel something about it.
The only difference between logic in EIE oratory and that in, say, LIE or LII types, seems to be that it is aimed to inflame people in a certain direction. Various reasons and syllogisms are given with the intended effect that people will react very strongly to some injustice or other issue. Actually, this seems to be the goal of all oratory, but it's most closely associated with EIE.
Yet this is very different from the way people commonly think of Fe; there's this association that somehow base-Fe types are all about being expressive and leading with their enthusiasm, which may be true in certain situations, but it doesn't seem to be the whole story.
Maybe one way of looking at it is that all rational functions, including Fe and Fi, are really about logic, but just a different "side" or "different use" of it.