Un Petit Combination…
is a little gimmick in a game of chess that secures a tiny but significant advantage without the flash and noise of some complicated strategem. Such elegance finesses characterized the style of the former world champion, J.R. Capablanca. They are impressive because everybody can understand them, but very few can find them during a game. I ran across something like a petit combination in an early chapter of Probability Theory: The Logic of Science, the posthumous masterpiece of E.T. Jaynes, a book which has finally been published after a long and almost legendary career in manuscript. Jaynes manages to duplicate in a couple of paragraphs the famous Kurt Godel finding that no mathematical system can prove its own consistency. Since, fraud that I am, page 45 of this tome is probably as far into the work as I’m going to get with any detectable level of understanding, I take this opportunity to boil the argument down still further for the benefit of anybody whose aptitude for higher math is even more fraudulent than mine:
It is a well known that any conclusion whatsoever can be validly drawn from contradictory premises. In particular, the conclusion, “This system is consistent” can easily be derived from inconsistent premises.
Worked out example:
If Ernie is a drunken sot and Ernie is not a drunken sot, then Ernie is a drunken sot. But if it’s true that Ernie is a drunken sot, it’s also true that either Ernie is a drunken sot or these premises are consistent. But if Ernie is a drunken sot and Ernie is not a drunken sot, then Ernie is not a drunken sot. And if Ernie is not a drunken sot and it’s true that either Ernie is a drunken sot or these premises are consistent, these premises are consistent. QED. Repeat until you are a drunken sot.