The Incompleteness Theorems: Godel

In my earlier discussion, I attempted to illustrate that the function of any form is a relative concept, essentially indeterminate, and that no indication of a form is sufficient to satisfy congruency, that the broader currency of the indication relies upon an interpretation within a language structure.

Kurt Godel, 1906-1978, put it another way in his Incompleteness Theorems:
http://www.exploratorium.edu/complexity/CompLexicon/godel.html
The following is copied from the above reference site.

"In 1931 the mathematician and logician Kurt Godel proved that within a formal system questions exist that are neither provable nor disprovable on the basis of the axioms that define the system. This is known as Godel's Undecidability Theorem. He also showed that in a sufficiently rich formal system in which decidability of all questions is required, there will be contradictory statements. This is known as his Incompleteness Theorem.
In establishing these theorems Godel showed that there are problems that cannot be solved by any set of rules or procedures; instead for these problems one must always extend the set of axioms. This disproved a common belief at the time that the different branches of mathematics could be integrated and placed on a single logical foundation."