Posted by n_alex
on November 6, 2005 at 10:56 PM PST
This will be my last blog entry in this space. Reexamining assumptions made in first entry, jotting down some closing thoughts, and laying some clues as to what follows.
In my first blog entry at Java.net, I wrote on August 09, 2003 that "Logic is the foundation of philosophy." I now know that this is most untrue.
This is as untrue as anything I've ever said or written, moreso because it undergirded two years of feverish research. Logic is a formal, mechanically limited contraction of reason. Mechanics and logic exist in what the geometer Bernhardt Riemann would call a limited, finite "manifold" of possible action.
I've been reading a good amount of Kurt GÃ¶del, particularly his essay in the Schilpp anthology for Einstein, his contributions to Robinson's "Non-Standard Analysis", and his earlier works on incompleteness theorem.
GÃ¶del successfully showed in his youth that no logical system could ever prove all of its own axioms, and thus all were incomplete if consistent. This incompleteness is especially true and evident in the discrete mechanical devices with which we compute. It becomes specifically poignant in the context of rule engine design.
Reason, by contrast, is based on a geometry of a higher order. Put succinctly, if reason were a sphere, logic would be the shadow of that sphere on your desk. Rather than logic, reason brought to bear on the exploration of ignorance is the foundation of all philosophy. Logic is a fossil by comparison, as the water in my breath is a fossil.
This research has set my feet in the last six months onto an unexpected course in mathematics and philosophy, after a brief (and fascinating) foray into rule engine design. Bearing in mind the inscription above the entrance of Plato's academy, "No one should enter who knows not geometry", I've thrown myself at the task of learning how to think in terms of actions taking place on n-dimensional surfaces. Anyone who wishes to understand what I mean by "mechanically limited contraction of reason" should read GÃ¶del and probably Riemann as well. Of course there are others worthy of attention who lived and worked in this vein, all prior to 1900, but they're in the margins.
These two should get you started. Don't ever rely on books about GÃ¶del and Riemann, or web sites about them. To hell with contemporary analysis, stick to primary source materials. Just read them, and read what they read.
As for me, I'm stepping back from logic and mechanics for a while, in order to work on something infinitely more important. I've reenrolled in a University, and have a new curriculum before me. Java was fun and I'll cross its path again eventually, but next time it'll be as a man to a chisel, not as a child to a sword. My rule engine work is concluded as well for the forseeable future.
And so I sign off, and leave the following question for you to consider. Which generates more energy when destroyed? An atom, or an axiom?