How well have computers been taught to jump out of the system? ... In a computer chess tournament ... one program, the weakest of all the competing ones, had the unusual feature of quitting long before the game was over. It was not a very good chess player, but it at least had the redeeming quality of being able to spot a hopeless position, and to resign then and there, instead of waiting for the other program to go through the ritual of checkmating ... Thus, if you define "the system" as "making moves in a chess game", it is clear that the program had a sophisticated, preprogrammed ability to exit from the system. On the other hand, if you think of "the system" as being "whatever the computer had been programmed to do", then ... the computer had no ability whatsoever to exit the system.Thus, it's all in how you define "the system". How PoMo.
The discussion of formal systems started to get me thinking about both the field of Physics and again my religious quest. Certainly the search for the grand unifying theory of physics is the search for the ultimate formal system. But my hunt for some kind of religio-spiritual truth was also a quest for the ultimate formal system. And, having just finished an election cycle, the search for, or adherence to a particular political ideology involves a formal system too.
If we ever find a grand unifying theory, two problems seem to arise (maybe three). The first is that it would seem that this unification would be subject to Godel's first incompleteness theorem: complete or consistent, not both. The second issue is that such a unification would be an example of a formal system that we (mankind) could not step out of and consider. Third, there's the fine tuning problem.
Here's something that struck me while reading that multiverse article. Certainly in Christianity (or Judeo-Christianity) we have the concept that Man is created in God's image. From a secular, socio-psychological perspective (or as Nietzsche might say), it's not hard to understand why the Man in God's image meme exists. And on the surface that meme seems incompatible with the concept of the multiverse. But it might just be right on. Going back GEB, if a defining characteristic of human intelligence is that it can, at will, step out of a formal system to make judgements or enter into a different formal system, and if human intelligence is created in the image of God, then God must be able to enter and exit formal systems at will too. But what sort of formal systems would a God deal with? Why not entire universes?
If God created the multiverse (i.e. an infinite set of universes), then ours is just one of an infinite number of permutations. Which helps assuage the fine tuning problem (we, then, aren't really fine tuned so much as just a probability). It also clears up the Man in God's Image meme. God can jump from one formal system (one universe) to the next just as we jump from Minesweeper to Solitaire. We inherit it from Him. And it sort of even answers the Godel Incompleteness problem in that whatever unification we came up with obviously wouldn 't be complete for all the other universes.
Yes, cramming the infinite and the unknowable into our puny linguistic constructs and conceptions is whack and narcissistic.