Thinking about "illation" brought me to "intuition", and I discovered that contrary to what I had assumed, it is not cognate with "tuition". I had always thought "intuition"
was comprehension not acquired from teachers.

tuition [tju¢°'©¥ʃən]
noun
1 instruction, esp. that received in a small group or individually

2 the payment for instruction, esp. in colleges or universities
[ETYMOLOGY: 15th Century: from Old French tuicion, from Latin tuitio a guarding, from tueri to watch over]
tu'itional adjective


intuition [ˌ©¥ntjʊ'©¥ʃən]
noun
1 knowledge or belief obtained neither by reason nor by perception

2 instinctive knowledge or belief

3 a hunch or unjustified belief

4 (Philosophy) immediate knowledge of a proposition or object such as Kant's account of our knowledge of sensible objects

5 the supposed faculty or process by which we obtain any of these
[ETYMOLOGY: 15th Century: from Late Latin intuitio a contemplation, from Latin intueri to gaze upon, from tueri to look at]
"intu'itional adjective
"intu'itionally adverb(ial)

In reply to:

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from tueri to look at/from tueri to watch over

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I'd say that I have to 'watch over' my daughter's tuition, which is extremely high--and I also have to carefully 'look at' my intuition, which, although fairly good, can be as blasted wrong as my thought processing.

College tuitions have increased way out of proportion to inflation. Harvard tuition in the thirties was $400 per annum. I don't know what it is now, but I suspect it is forty times what it was then.