Medieval European philosophers were not after all simple-minded:
“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.'” — The Lost Tools of Learning, by Dorothy Sayers, originally seen here.
It reminds me of the recent astonishing discovery that ninety percent of our genetic material is not after all “junk DNA;” scientists just hadn’t figured out its purpose.
Sayers’ essay has a number of other observations on educating children:
“…even a rudimentary knowledge of Latin cuts down the labor and pains of learning almost any other subject by at least fifty percent.”
That’s certainly true. Latin is also very easy for a native speaker of English, so the payback is pretty high.
Elementary mathematics “…is neither more nor less than the rule of the syllogism in its particular application to number and measurement, and should be taught as such, instead of being, for some, a dark mystery, and, for others, a special revelation, neither illuminating nor illuminated by any other part of knowledge.”
I wish that were more widely appreciated.