The Inconsistency

The loop that fails to close.

Formalist theories in mathematics are littered with large volumes devoted to consistency of the system in explaining itself. I intend to discuss here, the implications of such a delicately balanced formalist system gone all wrong. But before that, let's briefly understand what a formal system is. 

A formal system is a means of explaining any physical/non-physical system within the bounds of the universe. Perhaps even beyond that. The theory of physics can fall within the purview of a formalist interpretation, but so can the theory of post-modernist philosophy. It is the largest kind of generalization you can have, in view of defining a paradigm. 

Within such a system, you have the set of core fundamental truths, or axioms. These fundamental truths, or 'guiding lights', are explaniable and derivable only in a language or system that is one stratum higher -- a meta-language where even the guiding principles are merely derivable entities. Within the bounds of a formal system, however, for all practical purposes, the axioms are unchangable, cast in stone. It is like stating that 'matter exists', and, 'energy exists'. Both are uncontestable truths that cannot be questioned within the framework of the physical universe as we know it. (Possibly there might be an explanation in a meta-universe). A case in point here is, that you can have certain fundamental falsities, or anti-axioms too. 

Apart from this set of 'truths' is a set of Rules or Principles upon which you can derive more truths or 'guiding lights'. Such rules decide how more truths can be derived from the starting fundamental set of 'truths'. An example of such a Rule, (Call it Rule Number One) in light of the starting two 'truths' that we proposed about matter and energy, is as follows: 'One quantum of energy is convertible to a quantum of mass that is proportional to the quantum of energy undergoing the change.' (Essentially, stating that E = mass times speed-of-light squared). The rules give you an opportunity to come upon more 'truths' that are 'consistent' with the original set of truths from which they were 'derived'. 

Rules are very crucial, and must be crafted extremely carefully, if you intend to have the system remaining stable and functional under very stressed circumstances too. For example, imagine a rule, for the same formal system in consideration. The Rule Number Two says that 'The quantum of energy can half without the creation of any matter, if Buddha Smiles'. Now, assuming that no correlation Rule between the creation of mass and the smiling of Buddha is given, we can safely assume, that there will be an inconsistency if a quantum of energy either passes through the first rule, or through the second rule.

Essentially, bad Rules such as the ones we just discussed, can lead to arrival upon inconsistent truths in the system. And such truths can render your system unstable and essentially, you will need to get back to the drawing board to re-design your formal system. This is what happened when the constancy of mass and energy was questioned by Einstein, and a new Rule was created and added to the Formal System of Physics (assuming a hypothetical construct such as this exists) which stated that mass and energy are interconvertible by a New Rule (E = mass times speed-of-light squared). This stabilized the system.

Your life is a Formal System. So is mine. We are born, and fed with a set of core truths, and a set of guiding principles to use in order to build upon the set of core truths. More rules are added to your formal system once you interact with the Social Paradigm. But, your fundamental, core truths, the axioms, remain where they were. Gradually, using the Axioms and the Rules engine, you construct a large bank of Truths or Theorems for yourself. You know that eating healthy food helps you gain weight, and that drinking liqueur can harm your body. And it is all good. 

What do you do, if this system suddenly encounters a glitch? What do you do, if your set of core-truths or axioms suddenly gets challenged by a Truth that got constructed with the same set of carefully crafted Rules? If you assume the derived truth to be a falsehood, you will have to assume that your rules engine if flawed. And that it can lead to creation of several other falsehoods which apparently show up as truths. Or, you can trust the rules engine, and decide that one of your fundamental, starting truths, possibly, was misguided? Something was wrong with the core of your reactor, and not with the reactions?? Your system becomes unstable. You have no way to explain the inconsistency. You are a formal system now, that has no way to correct itself. 

This is a glitch, and as one with an elementary experience in numbers, I can say that glitches are dangerous. They can gradually go away, transit out of your system by a lovely convergence. OR, they can violently diverge, leading your system to an uncontrollable stage from where only a core-dump or a warm-reboot can bring it back. 

I stand here, looking at this inconsistency. I am scared, I have a glitch in my system. It can bring down my castle. It can cause untold damage. It is an unrectifiable mistake which has no solution. And I know not a meta-system where I can go back and ask for a re-check of my Formal system. God Help Me.