John: What do you think of the notion of Higher Education?
Sally: What do I think it means?
John: Yeah, as distinct from other kinds of education.
Sally: Well, in the first place, what is education?
John: I should think it's about having, giving or receiving knowledge.
Sally: And knowledge is about knowing true facts?
John: And there is no such thing as a false fact, right?
Sally: No, we should rightly call such a thing an inaccurate opinion.
John: Agreed - so knowledge has to do with facts - accurate opinions - corresponding to things as they actually are.
Sally: Yes, if you were to believe that lead is denser than water for example, that would be knowledge.
John: Because it's true.
Sally: And the statement 'lead is less dense than water' would be wrong.
John: And if I believed that, I would be wrong.
Sally: Well to be perfectly accurate John [smiles], a person can't be wrong. It
isn't as if there are two sorts of people walking about - wrong people and right
people.
John: No.
Sally: Rightness and wrongness are properties of statements or beliefs, to do with
their accuracy - how well they model the object or situation they relate to.
John: Quite. So a man is educated in proportion to how much truth he knows.
Sally: That is the way I would use the words truth, rightness, fact, knowledge and
education.
John: And the same would go for all the other species?
Sally: Yes. On this or any other planet anywhere in the universe.
John: So if a bird knew more about good nesting places than other birds, he would be
more educated than them in that respect.
Sally: Yes.
John: And if he had a greater knowledge of more things than others, we should say he
was more educated generally.
Sally: Yes.
John: The normal situation with humans is that different people have different
amounts of knowledge in different things.
Sally: I know.
John: Suppose one man had a great deal of knowledge about the life of St. Matthew and
another the same amount of knowledge about car mechanics, and they both had a similar
degree of knowledge about everything else. Who would you say was more educated?
Sally: I'd say they were equal. But I can see what you're getting at. The mechanic's
knowledge and the exercise of that knowledge would certainly appear to be more useful
to more people than that of the St. Matthew guy, but the latter would be held by many
to be the more educated.
John: Even though the mechanic's knowledge needs constantly to be updated and the
historian's consists essentially of the simple collation of already-existing
opinions.
Sally: Yes - if the car doesn't go we don't say the mechanic has a different slant on
things or has come up with new insights into the very nature of the motor car engine.
John: Or a fresh interpretation of the whole notion of vehicular perambulation.
Sally: No, it wouldn't do either for him to give a comprehensive and well-referenced
review of the various opinions people had about what was wrong with the car, no
matter how thoroughly he placed each view in its historical context. [Both laugh]
John: So can we return to the original question? What constitues 'higher' education?
Sally: Well I think we've kind of intimated one aspect of it - that of old-fashioned
elitism - let's not spend any more time on that.
John: Except to theorize that to some minds - the conservative old-school
ruling-class traditionalists perhaps - and later the emergent shopkeeper and merchant
middle class with their Eton and Harrow public schools - warmed to the pursuit of
already-existing knowledge - because it was easier - and because they feared change.
Sally: And liked to ape what they saw as their superiors.
John: Let's turn now to other, perhaps more cogent views on what constitues higher
education.
Sally: Yes - how can one piece of knowledge be justified as higher than another?
John: Let's look at it in terms of development - how one piece of knowledge builds on
and depends on a prior piece. In the early years of education, children learn about
whole numbers and counting. Then they learn to add them. The notion of length
follows. Next comes subtraction and following on from that the necessity for zero and
negative numbers. Then comes multiplication and the related ideas of area and volume,
rectangles, squares, cubes and cuboids. Next comes division, which necessitates the
notion of fractions and their representation as decimals. Then comes square roots.
When squares and circles are studied, the concept of irrational numbers becomes
necessary. All of this is motivated by the need to measure things in the world of
practical experience - traditionally the province of the lower classes incidentally.
Sally: Do keep to the point - ya bloody Marxist ya.
John: I could go on to show how the focus on rates of change - motivated largely by
the needs of machinery building in the Industrial Revolution - led to the development
of differential and subsequently integral calculus - which found uses in many other
areas of modern endeavour.
Sally: Let's see if I've got you right. Since each development in mathematics depends
and builds on previous mathematical knowledge, the latter concepts could be said to
be 'higher' than the former.
John: Yes, not necessarily more profound or more difficult. But since each concept is
a development of previous ones, that is the way it has to be taught, and as the pupil
'ascends' through his years in school, learning these concepts in sequence, it is
perhaps natural to think of calculus as 'higher' than arithmetic.
Sally: I'm glad you said 'not necessarily more profound or difficult'. I should think
that the difficulty comes only when the link to previous knowledge is not
established.
John: Hence the need for careful curriculum design.
Sally: And teachers with a broad knowledge of the subject up to the level they teach.
John: Of course learning - knowledge acquisition - is not necessarily linear - it's
often more tree-like in nature.
Sally: Yes, that accounts for specialization at the higher levels.
John: Yeah, it's interesting how that knowledge tree develops. When I was a pupil and
student, I didn't study set theory until I went to University. I was surprised when I
did study it how simple it was - no calculus, no rates of change, not even fractions.
It was built on concepts much further down the tree - elements, sets, cardinality,
and ideas borrowed from logic such as negation, conjunction, disjunction etc.Sally: That's what makes knowledge a tree and not a straight line.John: Yes. Of course set theory is now taught in primary school, because it depends
on so few prior concepts. No less profound for that - it's absolutely crucial in
computer science.
Sally: As is logic.
John: Yes - and these days computer scientists, mathematicians and electronics
engineers are far better logicians than the philosophers, who are still trying to
prove the existence of the non-existent with it.
Sally: Or the non-existence of the existent.
John: Talking of the non-existent, both glasses are empty.
Sally: Yeah both of mine are empty too. I think you will find it's your round dear
boy. Same again please.
[John gets the drinks in. Sally stares out the window, her mind on higher things.]
