“Oh?” said I. “Explain?”
“Well, I don’t know—it’s one of those things that are just kind of hard to explain,” said my brother.
“Oh?” said I again. “Then you must not really know it. The test of knowing something is being able to explain it.”
Until last week, I held to that dictum—that if you really know something, you ought to be able to explain it. If you can’t explain it, then you really don’t know it.
Until last week, that was.
Last week, I tried to explain shorter truth tables. Yes, huh?
In reality, the shorter truth table is a simple, easy concept to learn after working longer truth tables—it’s the difference between long division and short division with a small amount of guesswork thrown in gratis for entertainment.
I really do understand shorter truth tables. As I said, they are relatively simple—assume the proposition in question is invalid, set up the ‘equation’ so that it produces an invalid result and check for contradictions. If you find none, you assumed correctly, and the proposition is, in fact, invalid. If, however, you find a contradiction, your assumption was false and the proposition is actually valid.
As I said, it’s simple, especially on paper. I can work shorter truth tables in the dark in Hebrew if I want (well, almost: ת = ק ● פ or is it ט?)
If you set me in front of a white board, I can solve the problems. Unfortunately, I can’t explain in clear, coherent language how I’m solving the problems.
“And then, well, umm, you write this next to ‘P’ and work backwards until, uhh—”
“Oh, wait, I meant to write true, not false.”
By now, I could probably write a 20 page treatise explaining how to explain Logic principles:
- Make sure you come up with sample propositions to use in the exercises.
- Make sure you come up with sample proposition before you try to come up with sample propositions in class.
- Make sure the sample propositions are NOT real life examples—especially not theological statements. Otherwise students will worry about whether or not the statements are true or false, instead of examining the effect that their trueness or falseness has on the problem being solved.
- Make sure the sample propositions are SHORT! In other words, do not use statements such as “Martians drive limousines.” If you try to teach the biconditional with a statement such as this, you will end up with nonsense such as “It is true that Martians drive limousines if and only if it is false that Martians do not drive limousines.” Now say that twenty times fast with five students watching you.
Yes, I know Logic, particularly the part about shorter truth tables.
No, I can’t explain it coherently, but I could show you with a whiteboard. It’s just one of those things.
Therefore, I no longer believe that being able to explain something should be considered the ultimate test for knowing it. (Now, if you define ‘explaining’ as writing lengthy treatises which explain how to explain, perhaps I could still debate the theory?) It’s back to the Logic board for me.
Anyway—I take that back, mon frère.