A while ago Jeff Rients beat me to posting my favorite Captain Kirk pic, but this one is a close second. This is only indirectly related to Incompleteness, but I like it, so there it is.
Anyway, I'm reading Star Trek and Philosophy, The wrath of Kant, edited by Jason T Eberl and Kevin S Decker.
Heh, heh, Decker, Star Trek, wink wink, nudge nudge.
My brother gave it to me. He's Chief I.T. guy at a local bank, and was tasked to put together a clip show of Star Trek images for a presentation to bank personnel. The speaker was Jason Eberl.
Why, or who it was that thought that a speaker who's subject was the philosophy revealed by Star Trek should give a presentation to a small town bank staff is unknown to me. My brother says that he enjoyed the blank looks and confused stares as much as the speech itself.
After the talk, Eberl gave me little brudder a copy of his book, since he liked the clip show so much. Little brudder gave me the book to digest and condense for him since he says he only got 17 pages into it before grinding to a halt.
I'm about halfway through it now, and I can't blame him. Eberl obviously knows and loves both Trek and philosophy, but his writing is like chewing dry oatmeal.
Fortunately, several other philosophers contribute chapters to the book, so it's not all tough going.
The part of this that applies to Old School gaming is a paragraph in a chapter called, Death and rebirth of a Vulcan mind by Walter Robinson, writing as Ritoku, Professor of Vulcan Philosophy, Starfleet Academy.
"Quantum physics is full of examples such as the principle of uncertainty, the wave-particle paradox, the problem of non-locality in particle interaction, and so forth. Even at the level of pure logic there is inherent uncertainty as entailed by the "Principle of Incompleteness," known on Earth as Godel's Theorem, which states that given any formal system of logic sufficiently complicated to be descriptive of experience, if it explicitly states all functional axioms, theorems, and postulates, it will contain contradictions. The Principle of Incompleteness demonstrates that in order to maintain non-contradiction in formal reasoning, it is necessary to have open-endedness."
I thought to myself when I read that, "I'd game with that Dude."
It looks to me to toe-nail into the Old School philosophy quiet nicely. A lot of the difference between Old and New is the fact that Old is incomplete by the lights of the New. OD&D, and AD&D don't have a "core mechanic", at least not as I would consider one. They're really many disparate subsystems held together by the direction of the DM. Old School is like a suit of armor, it's composed of many parts which don't always fit together and must be worn and directed to achieve it's full effect.
New school often seems to want mechanical perfection and seamless functioning. It seems to lean toward ever more complicated systems that attempt to cover all possibilities. It wants a system that can stand on it's own without a guiding intellect.
I was once of a similar mind. When I was young, I was a ruthless Min/Maxer, and I always sought to come up with the Total System. That clockwork set of rules that could account for every possible action in the game. That's a perpetual motion machine, however, it's not going to happen. I learned eventually that the tighter you close your fist, the more star systems will slip through your fingers. Heh...
Old School's incompleteness is completeness. A perfect simulation of an in-game fantasy reality can't be achieved with formal set of rules, but it can be approached if the rules are seen as guidelines, or sign posts to direct the flow of the game in the direction that is most congenial to your gaming spirit.
The fact that Old Guard games are open-ended, system wise, is what allows them to expand to cover all extingentcies. Games that exhaustively define all skills, and abilities, block off unlisted possibilities in the minds of players. They look at the rules as a menu of choices, as the only choices available to them. This shrinks the scope of the game and makes it less than it can be.
That is the contradiction in modern gaming. The Game is supposed to be a vehicle for the imagination. A certain amount of structure is necessary for the game to hang together, but too great a degree of definition in the rules begins to blinker the players more than it enhances the game. So, in order to maintain non-contradiction in the game, only a certain level of sophistication in the rules needs to be allowed.
The degree of that sophistication and its level of definition is for each of you to determine for your own game. Hell, you might even let the players have some input. Not me though.
The rampant expansion of the Old School Renaissance is driving me mad, mad I tell you! For nearly twenty years, I thought I was just about the last guy on earth who gave a crap about AD&D, or OD&D. I was pretty isolated, I guess. I just didn't run into anyone else who still played. 
