Incompleteness

The Asifoscope

Reality always has more properties than are derivable from any of our theories about it.

Take a plate, for example, and drop it. The way it breaks could not have been known before. The description (as a plate) only covers a part of its properties. Those of the properties that are not covered by it, I call the residuum (of that object with respect to that description). When you drop the plate, it is destroyed as a plate, but the process of breaking into shards is a normal process for the underlying system. This underlying system emulates the object (the plate in our example).

Any “system” that can be destroyed, i.e. leave the scope of a particluar description of it, is incompletely described by that description.

Is it possible to describe anything completely or is there always a residuum, so you can destroy the system?

(Picture from http://commons.wikimedia.org/wiki/File:Scherben_(Polterabend).jpg)

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