“ever learning, and never able
to come to the knowledge of the truth.”
(2 Timothy 3:7)

Allegedly, all answers eventually lie…in science. Science is empirical and theoretical. Reason is the dictate of science and the scientific method is its embodiment. The scientific method is the essence of objectivity and every step is to be traceable and repeatable. Mathematics is the language and foundation of science. It may be arguably stated that the foundations of mathematics are Logic, Arithmetic, Geometry, and Metamathematics. Metamathematics may be used as an umbrella term to encompass Set Theory, Proof Theory, Model Theory, and possibly more.

‘Meta’ is a combining form forming words that refer to a change of position or condition. It may also be behind, after, beyond or something of a higher kind. ‘Meta’ is the outside talking about the inside. Metamathematics is mathematics talking about mathematics through a finite system that analyzes the foundational truths of mathematics.

An analogy of the ‘meta’ concept would be learning a foreign language. Metalanguage is language talking about language or teaching another language. Assume that a teacher and pupil share the native tongue of English. The foreign language that the pupil desires to learn is French. The native tongue of English would be the metalanguage. The foreign tongue of French would be the object language because that is the subject of their conversation. The metalanguage talks about the object language as the native tongue speaks of the foreign tongue. It takes English to teach French to English speaking pupils.

The metalanguage defines a matter’s scope through framing the object and bridging it to our understanding. It is a method that conveys meaning through the translation of words, its definitions, and rules of grammar from the object language.


Before metamathematics, mathematics was simply accepted as the foundation of science. Some may argue that it would have been best to leave well enough alone. Things can get messy if the philosophical gets involved because it asks so many questions. Meta-mathematics is necessary to mathematics because it probes for certainty. Certainty comes through proof and rigor. Proof lends itself to the scientific method. Every step in analysis must be held accountable. Accountability is logical and thus one can trace,check, and repeat those steps within the procedure. It determines legitimacy in order to forward those truths to others. Metamathematics may also be defined as logic, philosophy, mathematics, and life compressed down to a symbolic system. Metamathematics may also be thought of as a mathematical approach to philosophy. Like most things of a philosophical nature, one may be haunted by its downside.

Mathematics essentially deals with quantity, shape, order, and procedure. The scientific method is nothing more than science applying proof to itself. Proof is what derives the traceable steps and the check for error. Things are considered true if one can repeat those steps at any given time. In theory, the purpose of science is to gain understanding and to turn everything into a formula. On the surface, things were deemed to be solid.

The only people interested in matters of foundational proof are mathematicians and philosophers. The reputation of mathematics was bedrock solid, able, and stable. The formal entrance of doubt arrived in the late nineteenth century when George Boole’s intent was passed off to David Hilbert. Shoring up foundations required bracing mathematics with the axiomatic. Everything was to be symbolically reduced to a formula and this would also magically eliminate the notion of paradox. Tragically, the magic did not happen because everything had to be strictly defined and proven. Things usually get messy when people take a closer look.


Their premise was to rewrite mathematics into an axiomatic manner. Everything would be linked, clean, and theoretically invincible. It never got past its own foundations of logic and arithmetic. The mantle had been passed to Hilbert and all of his time and effort had suddenly come to naught. Mathematics was like everything else in life and it was reluctant to accept that normalcy. The dream of a total form of axiomatic mathematics was a beautiful failure. The argument could easily be made that if Hilbert would have succeeded in this endeavor, then that success would equate to be less than its failure. It would be like winning the war but losing every battle that formed the war. It makes no sense, but irony seems to keep stupidity as an irrepressible step-child that is so much fun to unleash at a party. Hilbert’s failure did not open the door for Godel’s success. Godel bypassed Hilbert and all of those doors. It was as if he could walk through walls. Spirits pay little heed to matters of the tangible and the surfaces beneath their purpose.

Language resides in an epic scope because words may not only be defined by generalities, they may also carry multiple definitions. The language of logic carries a stricter sense of honed details. Language has too much room to move while logic remains statuesque, frozen in its place. Paradox still breathed between those two polarities. It is a madding affair because it seems contradictory to eliminate contradiction. What if contradiction could hold a more natural place than its absence?

Language, grammar, semantics, and all such tools were now added to the process of seeking completion. In time, the philosophical would have to admit its involvement as well. A greater arsenal was required to hone things down to the fundamental. Another contradiction rises through the increasing complexity of the process of getting back to the basics. In seeking completeness, we discover our lack. That infuriating beauty inhabits metamathematics. Philosophy has held this discourse for years. It had become accustomed to the blemishes. Mathematicians were new to this feeling. That nervy stance was then passed off to science as it sought its own resolution. This became the problem with science. Something was whispered and that doubt could not be shaken. It was as if an unwritten rule had been broken. The rule of one field resolving a matter before passing it off to other fields. The mathematicians did not abide by this notion. Their nervy stance became a contagion. If there is mere trembling at the foundation, then what of the frenzied shaking of matters that reside upon their surface?

The overlooked must be stated within this melee. Logic was once a branch of literature and language. Somewhere through this process of ages, mathematics pilfered logic and it fit like a glove. It was as if it had always been its own. Arithmetic and geometry were the original cornerstones of mathematics. They are now joined by logic, set theory, and metamathematics. Those foundations had been expanded with too great of an ease. It is as


if no one noticed and even fewer cared. Should not language and philosophy also be included within this mix? Does metamathematics become the umbrella to hold this and anything else that may be added at some future date?

We leave with these things frayed and swaying within the wind. In seeking the complete, we see how incomplete we have been. The meta was supposed to clarify, but a greater mess remains in its wake. If omens were to loom, the world never trembled. Trepidation passes through oblivious glances. These frays expand beyond their original breach. The world never knows and indifference seems comfortable with the unknown.




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