“The Lost Tools of Learning” is a wonderful lecture by one of my favorite authors, Dorothy L. Sayers. I particularly like this bit of clarification, one might say hairsplitting, as she addresses why logic and critical thought are important, even when applied to a purely theoretical question.
A glib speaker in the Brains Trust once entertained his audience (and reduced the late Charles Williams to helpless rage by asserting that in the Middle Ages it was a matter of faith to know how many archangels could dance on the point of a needle. I need not say, I hope, that it never was a “matter of faith”; it was simply a debating exercise, whose set subject was the nature of angelic substance: were angels material, and if so, did they occupy space? The answer usually adjudged correct is, I believe, that angels are pure intelligences; not material, but limited, so that they may have location in space but not extension. An analogy might be drawn from human thought, which is similarly non-material and similarly limited. Thus, if your thought is concentrated upon one thing–say, the point of a needle–it is located there in the sense that it is not elsewhere; but although it is “there,” it occupies no space there, and there is nothing to prevent an infinite number of different people’s thoughts being concentrated upon the same needle-point at the same time. The proper subject of the argument is thus seen to be the distinction between location and extension in space; the matter on which the argument is exercised happens to be the nature of angels (although, as we have seen, it might equally well have been something else; the practical lesson to be drawn from the argument is not to use words like “there” in a loose and unscientific way, without specifying whether you mean “located there” or “occupying space there.”
Source: The Lost Tools of Learning