Must We Teach What Appeals to the Immature?

(This post is not in line with recent discussions of Aristotelian metaphysics.)

I've been worried recently about an issue in what might be deemed the 'sociology of education', which is this: To what extent are the things that we teach affected by the fact that our students are, in effect, adolescents, whose attention we can be guaranteed of having only for about 15 weeks? (This worry is similar to: many students read only in high school works of literature that they will not be capable of understanding, if at all, before they are middle-aged.)

Let me clarify. By 'adolescents' I do not mean to be disparaging. I allow that these students are as clever, strong of mind, and inquisitive, as you might want to insist. I say, only, that they are not mature. Their minds are not formed, and won't be so, on any reasonable standard, until they are in their mid-20s. (By 'formed' I do not mean 'settled', and I certainly do not mean 'dogmatic'. I mean, rather, that they lack the good judgment that comes of fuller experience.)

I pick the mid-20s as my mark from my own experience and that of friends. If you reject this, then we part as regards this subject.

By saying that we are guaranteed of their attention for 15 weeks, I mean that, even if we know that a student will take other philosophy courses, and we know which courses these are (say, the student is a philosophy major with some further, definite requirements to fulfill), still, we have to regard the lessons that we draw in our courses (and not to draw any lessons is itself to draw a lesson) as largely independent of what that student will study later.

Of course, instructors must also try to win the attention of students, for a variety of familiar reasons.

My worry is that, under these conditions, successful teaching means appealing to the 'adolescent mind', through unbalanced ideas--and that these ideas are never revisited or re-evaluated by students, when they've reached intellectual maturity, because they then lack sufficient time.

Here is an example of the sort of thing I mean (I could pick from dozens of others). It is common in introductory philosophy courses to introduce non-Euclidean geometries and draw a lesson from them in something like the following way (I compress, of course): "From antiquity it was common to regard axioms as self-evident truths. It was thought to be a 'fact' that a whole is greater than a part, or that things equal to the same thing are themselves equal. Likewise it was thought that the geometry of Euclid was true. But in the 19th c. it was discovered that there are non-Euclidean geometries that result from denying Euclid's fifth postulate-- Riemannian geometries, which deny that even one line can be drawn parallel to a line on through a point distinct from it, and Lobachevskian geometries which assert than many such lines can be drawn. What this shows is that axioms are neither true nor false, and that an axiomatic system is simply the study of the inferential relationship between some privileged propositions, the 'axioms', and derivative propositions, the 'theorems'."

I regard the thought, "There are non-Euclidean geometries; therefore no axiom systems are true", as an adolescent thought. Yet I am confident that there are several million attorneys, physicians, engineers, etc. who in a vague way accept the inference, because it was suggested to them when their minds were not well-formed, and who have no opportunity now to reconsider it.

That it is an adolescent thought: The appearance of non-Euclidean geometries shows merely that what was provisionally taken to be the unqualified formal study of space (only 'provisionally taken to be', because the status of the fifth postulate was disputed since antiquity), in fact is the formal study of space on a condition. Make that condition explicit: there are no different grounds now, than before, for counting it so qualified as true.

What sort of system of education could escape this difficulty? A fixed curriculum in a small college environment, such as one finds in St. John's (Annapolis, Santa Fe); or, a reasonably well-structured philosophy (or liberal arts) major, in which faculty actually confer and cooperate as regards the long-term intellectual progress of their students.