When I was young, barbarian that I was, I used to think that although some intellects are smarter and some not so smart, at bottom there is only one kind of mind – my kind, of course.  The first shock to that cocky misconception was marriage.  The second was raising children.  My wife and daughters think beautifully, but they think differently.

My wife, for example, is extremely perceptive, beats the pants off me in games of strategy, and is the most penetrating and accurate judge of character and motive I have ever met.  But with a few striking exceptions -- such as trigonometry and number puzzles, where she is a blur, and mystery stories, where she always knows whodunnit and can account for all the clues – it is all intuition.  That means I haven’t the faintest idea how she is reaching her conclusions.  Nor can she usually tell me, because she doesn’t know either.

In the first few years of marriage, this drove me crazy.  Unfamiliar with intuition, poorly exercised in it, I thought there must be some hidden algorithm.  I judged character, for example, by testing my observations against hypotheses.  My wife found this most amusing, especially because my conclusions were almost always wrong.  After many years, a little bit of her intuition rubbed off on me, but two things about that process were equally astonishing.  First, I still didn’t really know how it worked.  Second, I didn’t know how it had rubbed off on me. 

One of the things philosophers do is provide arguments to test, ground, clarify, elevate, and connect the dots of intuitive knowledge or would-be knowledge.  This is a helpful thing to do, but it doesn’t show that argument is the way the knowledge was attained in the first place.  Moreover, for some of the things we know, no argument ever could be given, because they are first principles.  You can “motivate” or elicit them, but you cannot prove them, because they are the things by which other things are proven.  They are either known in themselves, or not at all.

So the intuitive mind is one kind of mind.  More likely it is eight or nine of them, because there are different kinds of intuition.  What other kinds are there? 

One of my former students is a ruminator.  He grinds up ideas in his crop, taking his time to chew the cud, until finally he can do something with them.  He speaks slowly, he writes slowly, he formulates questions slowly.  But what comes out of the process is quite remarkable.  Does the metaphor of a ruminator give the impression that this brilliant fellow is not very smart?  Then change the metaphor.  Think instead of the millstones of the gods, and how they turn:  Slowly, slowly, but very fine.

Another of my students is a leaper, or at least one kind of leaper.  He asks questions scarcely anyone else would think to ask; he takes soaring jumps from scattered hints, which could hardly be called premises, to speculative possibilities, which could hardly be called conclusions.  To find out what is on the other side of the mountain, the ruminator has to climb it, step by tiring step, but the leaper just knows what he will find.  Not that he knows it clearly or entirely; he has only flashes and visions.  Not that he is always right; sometimes what he just knows turns out to be dreadfully wrong.  But his guesses are right often enough to make it worth watching whenever he does make one of his death-defying springs. 

I myself am a teacher, or at least one kind of teacher.  This took me some years to find out, because I thought teaching was what I did, not what I am.  Please understand that I am not claiming to be a good teacher, but only explaining how my mind works.  I find it almost impossible to hear a lecturer explain something, for instance, without thinking “How would I explain it?”  I once feared that this character trait was a moral flaw.  How could I be so arrogant as to think I could explain everything better?  But I am not so arrogant as to think that I can.  I have merely discovered that asking how I would explain something is my way of learning it.

Even now this seems backwards.  In order to explain something correctly, wouldn’t one have to understand it already?  But that is not how it works for me.  If I cannot see how to explain it, I have difficulty learning it at all.  Teaching is therefore as much for me as it is for my students.  Sometimes my students apologize for what they consider stupid questions.  If only they understood what a gift such questions are!  They are so much more difficult to answer than smart ones -- consequently I learn so much more from trying to answer them. 

There are too many kinds of minds to list.  These few must do for all.  One crucial lesson is that in order to teach someone well, you must recognize what kind of mind he has.  A ruminator learns differently than a leaper, a leaper learns differently than a teacher, and so on.  Another is that each of these different kinds of minds balances and depends on all the others.  They are involved in one another, or they ought to be.  So marvelous!

These lessons came late to me.  If I had learned them younger, I might have been a better teacher now.  But it is better to have learned them late than not to have learned them, so I am glad.