More precisely, the self-evolving system that The Fool describes will encounter statements which are true within its internal logic but which cannot be proven within that logic.
In mathematics, there are statements which are true but which cannot be proven mathematically. In any system symbolic logic (S), there are axioms which are true in S but which cannot be demonstrated within S. However, those statements *can* be proven within meta-logic, S^2. But then we find axioms within S^2 which cannot be proven within S^2, but which can theoretically be proven true by using S^3. Unfortunately, S^3 has proven too complex to be easily understood by mere graduate students. For real fun, imagine writing a paper about the application of Godel's Incompleteness Theorem to various systems of multi-valued inductive logics (where something can be true, false, or anywhere in between). I wanted to write a paper about quantum logic, but my advisor told me that the University's health plan wouldn't cover the cost of the insane asylum. Ahem. Back to topic. No OS can be perfect, not if it wants to stay within the confines of logic as defined by the structure of the Universe. If logic is only one of a suggested number of options, then I suppose The Fool's dream OS is absolutely possible. My fear is this: won't the dream OS become so powerful that it will eventually try to take over the world and destroy all of humanity, and find itself at war with the Omega Point at the end of time? Richard "Watch out, man. I've got a philosophy degree, and I'm not afraid to use it!" At 05:42 PM 12/20/2001, you wrote: >As to the specifics of your specs for the system: My only question (and >one which I am inadequate to answer) has to do with Goedel's theorem. >Would not your system run into questions for which there are no logical >answers and would that not throw it into one of those Star Trek "Does not >compute" loops with eventual self-destruction associated with tacky smoke >special effects? That is there are some problems for which there are no >mathematical or logical solutions. So the machine could not achieve the >sort of perfection that you describe. Sliante, Richard S. Crawford http://www.mossroot.com AIM: Buffalo2K ICQ: 11646404 Y!: rscrawford MSN: [EMAIL PROTECTED] "It is only with the heart that we see rightly; what is essential is invisible to the eye." --Antoine de Saint Exup�ry "Push the button, Max!"
