I've spend the last two years doing a reasonable amount of teaching.
I suppose that every teacher wonders whether the students are really
"understanding" what we teach. This begs the question of what we mean by
One effect of doing a lot of teaching, has been that I have found that I
did not understand some things that I thought I did understand. A particular
example is Principal Components Analysis (PCA). I think I do understand it
now, but I did not before. I have taught something about PCA in the past, and
I think I was saying things that were true, but I didn't know why they were
What had happened was that I had heard other people that I trust say these
things about PCA. I heard the same thing a few times from a few different
people, and I added what they said to the store of things I "knew".
In my case, I think I was using what Perkins, Allen and
Hafner call "makes-sense epistemology" (). Someone
using makes-sense epistemology is not reasoning or criticizing what they have
heard. They are not asking "could that be wrong?". Their criterion for
accepting an argument is that the argument feels right or makes sense.
Naive reasoners might be said to have a "makes-sense epistemology." Of
course this does not mean that they have an explicit philosophy about what
grounds are necessary for belief. But it does mean something in terms of
the manifested behavior: such reasoners act as though the test of truth is
that a proposition makes intuitive sense, sounds right, rings true. They
see no need to criticize accounts that do make sense - the intuitive feel of
It seems to me that teachers are often in the situation where they cannot or
do not hope to teach the students why something is true, but only give them
a feeling for why something might be true. When we do this, we encourage
Does it matter that we often function on this intuitive makes-sense level?
Not if we think that most of what we are told is true. But, as Richard
Feynman put it: "Science is the belief in the ignorance of experts."