What is the principle of life? The question is central to ethics. Ethics involves a purpose in life. An entity without ethical purpose has no life. An entity without life has no purpose. The life principle must be an ethical principle. I refer to biological life as animates, our universe as an inanimate. According to the Stoics, animates and inanimates are all organised along the same life principle. I concur. Thus all biological and non-biological beings must share the same generic ethical principle in order to be. The common generic ethical principle shared by Nature and its subjects is an ontological principle. What is this common ontological principle that enables life forms to be? This principle ethical, generic purpose must underlie the very fabric of all physical existence. The answer must be precise. It must be potentially formal and rigorous. The starting point will be found in the work of Kurt Gödel. Gödel worked in the domain of the only known formal system today, that of axiomatic mathematics.
A system based on axiomatic mathematics provides the formal example of what ethics, and life is absolutely not. If the system can be formalised in terms of axiomatic mathematics then it is, beyond all doubt, as dead as a dodo. Axiomatic mathematics is anathema to life.
Gödel Code versus Genetic Code
Nevertheless Kurt Gödel showed that formal mathematics could be described, in principle at least, by a universal code. The code is sometimes called the Gödel Code. The Gödel Code is not the Genetic Code because all it does is provide an arbitrary numbering system for uniquely numbering of all objects in the mathematical system. Every object has its distinctive Gödel Number. Any number will do the trick, as long as it is distinctive. It ends up that even mathematical proofs can, in principle, be known by a sequence of Gödel Numbers which in turn becomes a monolithic Gödel Number. Proofs become knowable by their distinctive Gödel Numbers. The whole idea is that the mathematical system could be talked about in terms of the Gödel Code. Since Gödel numbers were, after all arithmetic numbers, Gödel could talk about arithmetic mathematics in term of arithmetic mathematics.
Gödel used his Gödel Code to prove his famous Incompleteness Theorems, judged by many as the most important of the twentieth century. In essence, the first incompleteness theorem defines what I call the Gödel Razor. The theorem effectively places on the left side (say) of the Razor, all the theorems of the mathematical system which are provable. These provable theorems will all have Gödel Numbers and hence be nice. If you, as a theorem, have a Gödel Number proof then you are good for the mathematical system because you are provable. If you don’t, you will be on the right side of the razor as unprovable and so “bad” for mathematics. There is nothing that the mathematicians hate more than unprovable propositions. Here we have mathematical ethics at work. Provable propositions are good and this is how mathematicians make a living. These propositions can be called theorems and can be published in journals. These theorems are so good that they might even lead to academic promotion.
Now, as Gödel showed in his incompleteness theorem, the problem with mathematical ethics is that it is incomplete. Formal mathematics can discern provable and hence good theorems by the Gödel Numbers of their proofs. However, what about mathematical propositions which are valid but have no associated Gödel Number and hence are unprovable? Surely should not these unprovable theorems be considered “good” too? The sad fact is that mathematics can only deal with the contingently true and not truth. The contingently true lies on the left side of the Gödel Razor, the truth and its murky partners lie on the right side and out of reach of mathematics.
Note that the Stoics were well aware of this distinction between the true and truth. (The true was considered by the Stoics as incorporeal, the truth corporeal, but I won’t delve too deeply into that). So Gödel showed that formal mathematics can only access the true and never the truth. The key is that he provided a formal proof of this fact. Thus one must say to the mathematicians, “Eat your heart out, mathematics cannot handle universal truths but only the contingently true.” Gödel says so, trust me.
Mathematics is restricted to the left side of the razor where statements have associated Gödel numbers and are hence provable. On the right side of the razor there are mathematically coherent statements that are valid but have no associated Gödel Numbering. How can we, as mathematicians, ever prove these perfectly “good” statements? Calling a spade a spade, we simply cannot. Gödel says so. Thus, if we cannot prove the validity of statement S, who can? God perhaps, but we don’t have to go to such extremes. This valid statement S is unknowable in terms of the Gödel Code. Is there some other code that could do the job? I claim that there is such a code. I call it the Generic Code, but it is the same as the Genetic Code. S must be stated in the Generic Code and is associated with a corporeal entity that behaves in such a way that S is always valid. S will have no associated Gödel Number but it will have an associated Genetic Sentence made up from a string of letters from the four-letter Genetic Code. No third party mathematician is needed. What is needed is that the corporeal, non-abstract organism embracing the Genetic Sentence as its own “DNA”, so to speak. Simply in order to coherently exist, the organism has a heavy duty placed on its proverbial shoulders. It must obey as best it can, the essence of S. The generic essence of S can be quite precisely stated. The organism must keep S on the right side of the Gödel Razor. At all costs S must not risk having a Gödel Numbering. In short, S must not be deducible from any a priori structure. As the Stoics say, do not fear the past as the things in the past don’t exist. Only things in the present exist. Things in the present have no Gödel Numbering tying them back to rigid beginnings. Do not be prisoner of the past, is the message.
The Gödel Code is hard to explain. The Generic Code is even harder to express in words. Just think of dead mathematical objects being knowable as Gödel Numbers. Living entities are knowable by their Genetic Sentences. The generic sentences are expressed in the Genetic Code which is the calculus of the present, freed from deterministic shackles. There is only one such calculus, and the ancient Stoic logic provides the beginnings. No living thing inherits memories from before its birth. Even the universe reveals no forensic evidence that it was the product of some past cataclysmic collision or whatever, as would be the case for a non-living organism. The latter has a Gödel Numbering, the living universe can be known as a mass of Generic Sentences.
In animates the simple Genetic Sentence AUG codes the start codon and also transcribes to the amino acid Methionine. For an inanimate like our universe, there is no transcription. According to me, the Generic sentence AUG codes photons, AAG an up quark, AGG a down quark etc. (see my online Physics Engine).