Abstract

According to Aristotle’s demarcation, there are two kinds of science. There are the special sciences characterised by their determined study object. This embraces all traditional sciences including classical physics and axiomatic mathematics. Secondly, the science nowadays called metaphysics, is characterised by its study object having an undetermined genus. In this paper, I identify the quantum object as an instance of the fundamental study object of metaphysics.

Every science, to be tractable, requires first principles. For the special sciences, the first principles Ψ play the role as the foundational *indemonstrables* of the system, assumed true. The special sciences hence are based on rule-based ethics to apply deductive inference from the indemonstrables Ψ on the left to infer the consequents Θ on the right, as illustrated by the syllogism schematic F:

In the case of metaphysics, the reasoning is reversed. Starting from the right with the study-object Θ’ itself, the inference arrives at the indemonstrables Ψ’. This can be understood as what I call a *co-syllogism* G, illustrated by the schematic:

I refer to deductive inference #1 as expressing *left-side rationality* and non-deductive inference #2 as expressing *right-side rationality*.

In mathematics, naturality is colloquially regarded as avoiding *ad hoc* arbitrary constructs. Set theory is inadequate as a basis for formalising naturality. One must turn from the world of symbols to the “dyads” of Category Theory and the notion of *natural transformations*. A tractable starting point is to define naturality in terms of demanding *First Classness* (FC) defined as

In a world of undistinguished entities, one starts with entity X. This violates FC as X becomes a distinguished entity. Thus, FC theory must be *starting point invariant*. We are already on our way with our “logic of discovery,” and understanding the nature of the quantum object.

A key player in the solution is the role of category theoretic *adjointness*. Even #2 may be considered as the right adjoint of #1.

This approach involves reverse-engineering the Stoic synthesis of ethics, logic, and physics. Real physics results will be demonstrated using this physics-without-number methodology.

Keywords: Logic of discovery, ampliative reasoning, emergence, Stoicism, Category Theory

(to appear)

]]>**Naturality as Universal Normative Authority in Stoic Logic**

D.J.H. Moore

Logic Colloquium European Summer Meeting of the Association for Symbolic Logic

Presented 23^{rd} July 2021 (paper to follow)

To be tractable, every science requires first principles. Each special science embarks from a foundation of axioms, empirical laws, etc., thus employing a rule-based ethic to rationally arrive at consequent knowledge β. The construct can be represented schematically as

α → β #1

At the other limit we find *metaphysics*, the only science lacking determined genus and thus devoid of *a priori* knowledge. This leads to a *right-side *rationality schematic:

*Α* ← *Β* #2

Here, rationality flows in the opposite direction with *a priori* knowledge *Β* on the right and the consequent *Α* on the left. This schematic no longer illustrates a syllogism but its converse, a *cosyllogism *(not to be confused with Peirce’s abductions*. *For that the cosyllogism be* tractable*, *a priori* knowledge *Β* must be formalised in some way. We resort to the only viable normative authority available – naturality.

In mathematics, naturality is colloquially regarded as involving constructs that are free of *ad hoc* subjective choices. Traditional set theory mathematics is ill-equipped to formalise the ethics of naturality. The alternative is Category Theory originally developed “to study functors and natural transformations”. Natural transformations can be formalised in the form of naturality squares that commute where two sides are left and right adjoints making up “natural” symmetries – arguably the most ubiquitous and fundamental generic structure underlying mathematics.

In this paper, category theory itself will be shown to participate in its own natural symmetry with its own “right adjoint” complementary opposite providing a natural way of formalising the cosyllogistic reasoning in #2.

The paper then goes on to show that the resulting cosyllogistic “right-side” rationality provides a means of reverse engineering the natural rationality underlying the five indemonstrables of ancient Stoic logic.

**Keywords**: cosyllogism, metaphysics, naturality, adjunctions, Stoic indemonstrables

**References:**

Bobzien, Suzanne, **Stoic Syllogistic**, Oxford Studies in Ancient Philosophy, Vol. 14, pp.133-92.1996

If one is interested in developing the Foundations of Science there is no better place to start than to reach an understanding of the Logos. What is its architecture ad what are its fundamental constituents? That is indeed the objective of my project. I do not pretend that my account will coincide perfectly with historical Stoicism. Rather than claim what the Stoics may have said, much of an unknown anyway, my approach is always to state what they *should* or *would* have said according to the basic Stoic paradigm as I understand it. Even in today’s rich scientific environment, I believe the Stoic paradigm needs little modification. It was modern 2500 years ago, and still is. What can benefit from modification is the well recognized, rickety foundations of modern science. Stoic natural philosophy can come to the rescue here.

My approach is also quite different to the scholars as they concentrate on forensic historical and textual analysis. Hence, my approach may not always gain their approval.

Concerning the global architecture of the Logos, It appears that for the Stoics there is not one Logos but two (Kamesar 2004):

Puisqu’il y a, selon les Stoïciens, deux sortes de discours, l’un intérieur et l’autre proféré, et encore l’un qui est parfait et l’autre qui est déficient, il convient de bien préciser lequel de ces deux discours ils refusent aux animaux.(Fortis 1996)

Developing a theme originally proposed by Plato, the Stoics maintained that the logos was in fact double consisting of the logos *prophorikos* and logos *endiathetos*. The logos *prophorikos* was expressed in “uttered language” and was considered deficient. The logos *endiathetos* corresponded to internal language and was considered perfect. Invoking the bilateral brain architecture metaphor, the *prophorikos* logos would merit being called the *left-side* logos, whilst the *endiathetos* logos would correspond to the *right-side* logos. The left-side logos is capable of speech whilst the right-side logos is mute, in line with biological brain architecture. Although mute, the right-side is not without linguistic capability but not for communicating to the outside world but being more concerned with internal communication. Plato thought that the mute right-side logos was based on an internal language where the soul communicated with itself.

Summarising, the main point I am illustrating here is that of the two-paradigm-paradigm and noting that it is nicely wrapped up in the Stoic notion of the two logoi. The Stoics claim that one of the logoi is deficient. This is the “left-side” logos, the one associated with modern day conventional “first order abstract” reasoning. One can formally illustrate the deficiency in the form of Gödel’s famous Incompleteness Theorems. The Stoics got there first!

Only by going over to second order abstraction, as used by the Stoics, can the deficiencies of the first order left-side logos be overcome.

But what is second order abstraction?. I explain that elsewhere, but a key aspect is the treatment of properties. First order abstraction says (according to me) that the property of an object is not an object. All modern Western science and mathematics uses this principle. The Stoics radically differ from present day scientists on this question (and differ from Epicureans, Plato, Aristotle…). Without a shadow of doubt, the Stoics always maintained that the property of an object ** is an object in its own right**. This might seem a minor point but it is not. It is massive. The Stoics reject second class entities. By considering that the property of an entity is an entity in its own right, the Stoics enter into the domain of second order abstraction.

All objects must be first class entities. In Computer Science this is the same principle underlying Object-Oriented programming; perhaps the most important paradigm in the subject. The Stoics integrated it into their physics and their ethics. There is no fundamental ontological hierarchy between the gods and man. “We are all gods” one Stoic once said. Biological life is driven by the same kind of life principle as the universe. The principle was applied to promote the rights of women, and also the rights of slaves. Slaves were human beings like free men and should be treated fairly, despite their less favourable lot. The Stoics were the first to talk about the rights of children.

In the times I was a practicing software engineer and academic it took me a long time to deeply understand first classness even restricted to my field of expertise. It is the nearest thing to Virtue that I can think of – at least in a technical sense. This is where Computer Science differs from classical physics and mathematics. Physics and traditional mathematics are devoid of ethics in their epistemology, They both claim to be amoral. In Computer Science developing software systems one is confronted with the stark reality of the Virtue of First Classness on one side and vice on the other. Real sinning becomes possible. What is vice in software development? Violating First Classness. Everyone does it at some time or another by taking naïve short cuts and paying dearly for it. The retribution can be terrible leading to extreme unhappiness as one drowns in one’s own “spaghetti code.”

To emulate nature one should respect First Classness.

I am attempting a bit of humour here in trying to demystify Virtue. Virtue is more sophisticated than First Classness though. There is also another related construct in mathematics called *naturalness*. In mathematics, being natural means to avoid making arbitrary choices. Choices must be fundamental, not that of a pastrycook. Everything must have its own “Sufficient Reason,” as Leibniz called it. The choices must be “natural.” Natural mathematics is the beautiful, and fundamental mathematics. Birkhoff and MacLane invented the very important field of Category Theory in order to explore “natural transformations.” This is an example of mathematical Virtue, if you like.

Category Theory, for me, has become a tool for exploring Virtue. But we need a Stoic version of Category Theory — that is what I’m working on at the moment.

Nature lives according to First Classness and naturalness.

First classness and naturalness require second order abstraction and things really become beautiful. I can give precise formulations of second order abstraction, first classness and naturalness, but that will have to wait for another time.

I like the twin logoi idea as it helps to order one’s knowledge. Take the ancient subject of rhetoric for example. Rhetoric was part of Stoic logic and involves rationality expressed as a linear monolog. It clearly belongs to the left-side logos. On the other side is dialectics. Rhetoric is opposed to dialectics where the latter expresses rationality in terms of natural oppositions. That is a right-side discipline. In fact it can be dialectical rationality in terms of opposites is what the right side logos is all about. The dialectic principle seems so important that it must find an opposite to itself. Hence the need for rhetoric and the left-side hemisphere of the bilateral logos.

One should realise that violating First classness and naturality is not like breaking the ten commandments of Moses. There is no rule book for pure First Classness and naturality. It’s more like violating the “rules of grace” that some theologians saw in Christ. I quite like this theological construct of literal restrictive laws versus the much less tangible but real “laws of grace.” Think about it, using your right-side logos of course. Leibniz did (Leibniz 1989).

Logos is a notoriously slippery entity to discuss. When I discuss it, the reader might get confused or rather think that I am getting confused. I will seem to be committing the cardinal rhetorical sin of analytic philosophy. My analytic philosopher will severely mark me down saying that I am consistently confusing “use and mention,” a major crime for the analytical thinker. But I am in good company as they keep saying that about Leibniz. And some critics of the Stoics were keen to make that sort of criticism there too. After all, they were said to be “More extravagant than the poets!”

So, one minute I am talking about the logos as if it is mind. Then I talk about the two hemispheres of the brain as logos. Then I talk about the cosmic logos. Is that a cosmic mind? Or the way that Nature is organised? Is the logos mind trying to understand nature or is logos the rational principle by which nature is organised and understood? One minute I am talking hard science and mathematics and then slipping into theology and the gods.

This is not necessarily messy thinking, even though obviously loose. It is a consequence of what Aristotle discovered back in antiquity. There are two kinds of science, there are the ordinary sciences where their object of study falls under a determined genus. There is another kind of science where the object of study has no determined genus. The later kind of science became known as metaphysics. I call it simply *generic or universal science*. Aristotle saw it as the science of Being – pure ontology. The former is left-side, the latter kind of science right side rationality. When you study this science-without-determined-genus thing then you fall foul of Use and Mention barriers so dear to the tunnel visioned, left -side thinking, analytic philosopher. But in the universal rationality of the dialectical logos there are no such barriers only easily traversable modalities.

Chiesa, C. (1992). “Le problème du langage intérieur dans la philosophie antique de Platon à Porphyre.” __Histoire Épistémologie Langage__: 15-30.

Fortis, J.-M. (1996). “La notion de langage mental : problèmes récurrents de quelques théories anciennes et contemporaines.” __Histoire Épistémologie Langage__: 75-101.

Kamesar, A. (2004). “The Logos Endiathetos and the Logos Prophorikos in Allegorical Interpretation: Philo and the D-Scholia to the Iliad.” __Greek, Roman, and Byzantine Studies__ **44**(2): 163–181.

Leibniz, G. W. (1989). The Principles of Nature and of Grace, Based on Reason. __Philosophical Papers and Letters__. L. E. Loemker. Dordrecht, Springer Netherlands**: **636-642.

[1] « Puisqu’il y a, selon les Stoïciens, deux sortes de discours, l’un intérieur et l’autre proféré, et encore l’un qui est parfait et l’autre qui est déficient, il convient de bien préciser lequel de ces deux discours ils refusent aux animaux» (DA III, 2, I) cited in Chiesa, C. (1992). “Le problème du langage intérieur dans la philosophie antique de Platon à Porphyre.” __Histoire Épistémologie Langage__: 15-30.

If this perspective is accepted, then the four-letter alphabet that encodes biological life should also map to the subatomic particles of matter. The result should be a “periodic table” for subatomic particles.

I am writing this all up. This post is an excerpt. A sneak preview of such a periodic table can be explored in my online database.

The problem introduced in this section was admirably described in the short lead in to a conference entitled *Metaphysical Principles* soon to be held at the College de France in Paris. The problematic is simply rolled out as:

Metaphysics has traditionally been conceived, if no longer as the “science”, at least as the study of “first principles”.

A terse enumeration of what is often meant by “first principles” followed. The role of the Principle of Non-Contradiction gets a mention and Leibniz’s favourite term “Sufficient Reason” is slipped in. Also listed is the circular problem of establishing the grounding of metaphysics as well as handling the metaphysics of the grounding. Then there is the relationship between metaphysics and the axiomatic: metaphysical axioms anyone? In brief, if metaphysics is to advance, what kind of principles are involved? Are the principles formal or just intuitive?

This project claims to provide answers to these questions in the only definitive way possible; viz., by reverting back to the age-old original project of developing metaphysics as a full-blown science in its own right. Given the nature of the endeavour, this is an all-or-nothing project. There can be no half measures.

It was Leibniz that clearly laid out the task ahead when he declared his dream of a simple universal unifying science. The new approach with its accompanying algebra based on “only a few letters” and a radically simplifying geometry would greatly ease the cognitive burden of fundamentally explaining how and why Nature actually work. In his words:

If it were completed in the way in which I think of it, one could carry out the description of a machine, no matter how complicated, in characters which would be merely the letters of the alphabet, and so provide the mind with a method of knowing the machine and all its parts, their motion and use, distinctly and easily without the use of any figures or models and without the need of imagination. Yet the figure would inevitably be present to the mind whenever one wishes to interpret the characters. One could also give exact descriptions of natural things by means of it, such, for example, as the structure of plants and animals. (Leibniz)

Like many of his time, and previous times for that matter, Leibniz believed that not only were the existence of plants and animals explicable in terms of some kind of life-principle. The universe itself was also a living organism based on the very same principle. Newton was of similar mind. He even imagined that the “veins” he saw in the rockface of mines he visited were the veins of planet earth as a living and breathing biosphere. The philosopher Spinoza added a theological twist to the living universe version: the universe was a pantheist living god. For Leibniz, biological lifeforms and the cosmic lifeform were based on the same life principle.

The science envisaged by Leibniz not only would involve a universal and simplifying algebra, he famously claimed that its semantics would be explained in the form of an equally universal and simplifying geometry *without number* that he called *analysis situs.*

Leibniz’s *analysis situs* dream geometry was to rest in limbo until Leibniz’s bicentennial celebration. A mathematical competition was organised with a prize to whoever could solve Leibnitz’s problem of a geometry without number. At first there were no entrants. Mobius eventually enticed Herman Grassmann to enter. Grassmann obliged as even though he had not developed a geometry without number he had developed a geometry without coordinates. He was subsequently awarded the prize. A key aspect of his geometry was his notion of a geometric outer product construct which lead to an algebra. Hamilton and Cayley extended the approach to a universal geometric product. In modern times, David Hestenes refined the system and called the result Geometric Algebra (GA) which is how it is known today.

Also inspired by Grassmann. Heaviside and Gibbs independently developed a simple vector and matrix approach to geometry which became linear algebra. In its most generalised abstract form it becomes *Algebraic Geometry *( AG).

We thus have two distinctly different geometries, GA and AG, If you are a stalwart of FORTRAN programming you are more than likely an AG, linear algebra fan. On the other hand. If you are into Object Oriented programming and like simplicity, power, and elegance in your geometry then you will be an advocate of GA. I personally like to refer to these two geometric takes on the world as using left or right side rationality. GA is right side, AG is left side. These are the two takes on the geometry of reality, one synthetic, the other analytic.

Most advanced computer graphics in virtual reality and advanced games, employ GA. Most physicists tend to find that AG, linear algebra is sufficient as they are mainly interested in sheer number crunching.

Is Geometric Algebra the answer to Leibniz’s dream? When used as Conformal Geometric Algebra (CGA) David Hestenes thinks so. So does Hongbo Li who specialises in developing incredibly hyper-simple proofs for geometric theorems only made possible through CGA.

However, what is ignored in these claims is the even bigger picture painted by Leibniz. This mathematical geometry is to provide the algebra of all the natural forms of Nature. In other words, the project should explain the inner workings of the genetic code and unravel its semantics. Genetic engineering should be more than cut and splice. That works but one should know why before messing around with Nature. And one should also be able to explain the inner workings of matter in the quantum mechanics domain, perhaps with the same four-letter code!

Such a big picture enterprise is the one undertaken in this project.

What Leibniz’s dream adds to the equation is a glimpse of how this “life principle” might look like once rendered into a formal tractable form. He imagined that it was expressible in a geometric algebra of only a few letters. We now know that all Biological lifeforms are organised around the same code, the genetic code, and certainly based on “only a few letters,” namely four. We know that the algebra is expressed at the molecular level through the DNA genetic material. The genetic material is separate from the functional material making up the body of the organism. Because the genetic and functional matter are separate in biological organisms, I will refer to them as bi-orgs.

A common misunderstanding is that the genetic code was the subject of evolution. Like everything biological, it just evolved. But there is absolutely no evidence that the genetic code evolved. All evidence is to the contrary as it seems certain that the genetic code has remained unchanged over billions of years. Some explain it as a great “historic accident” appearing fully formed at the same time as the emergence of biological life.

However, if the universe hosting these bi-org lifeforms is based on the same life principle, then it too should be based on the same code. Like all living creatures the universe should “have its own DNA,” so to speak. If so, where is it? Where is our universe’s genetic code? The fact is that no one has found the universe’s DNA. No matter how hard the physicists look, they only see the same old molecules and particles. The evidence is pretty compelling. This suggests two possibilities. The first hypothesis is that Leibniz was wrong. Putting aside biological matter, the universe is simple a great conglomerate of inanimate stuff. It’s all just dead Cartesian matter. The second hypothesis is that the matter is self-managed Leibniz style matter subject to some kind of life principle . In this case the genetic matter and the managed matter are “mixed” and in superposition in some way. The genetic and the managed matter will all appear as being the same stuff. Our universe, as such an organism would not be a bi-org, but a mono-org where the genetic and the managed appear to be one.

Thus, does our universe consist of dead Cartesian stuff or living, self-managed Leibnizian stuff? I argue for the latter explanation. To me, the universe is a living mono-org organism. In which case the form of elementary particles for the mono-org should be expressible in perhaps exactly the same four-letter code as for bi-orgs. Bi-orgs express divergence of the genetic and managed, mono-orgs express a more primitive pre-divergence form. Such an hypothesis raises the challenge of matching the genetic code common for all bi-orgs to the subatomic particles making up biological matter.

After considerable time and effort, I have come up with what I believe to be such a match. The result is my version of a “periodic table” for the sub-atomic particles of physics. The table includes all the known together with the as yet to be discovered, unknowns. Many and perhaps all of the latter may not be directly detectable, but their existence can be imputed by my non-empiricist methodology.

The methodology is based on pure reason dedicated to the age-old ontological question of “What *is*?” Resolving this question in a tractable and coherent way naturally leads to an ontology formalised algebraically by what I call the generic code. The genetic code is one such instance of its application applicable to biorgs. The methodology is easier to understand in its application to mono-orgs as we can intuitively discern the function of the entities emerging from of our enumerative ontology.

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I presented a paper in the session on “Physics and Logic.” organised by Bob Coecke.

Keywords**:** Periodic table of subatomic particles, Geometric Algebra, Stoic Logic, operational calculus, sub-quarks.

*Abstract*

The problem tackled in this work is to develop from purely rational considerations the foundations and ontology of forms universally applicable to any self-managed autonomous system. The physics universe is a special case of such a system. The approach is fundamentally a priorist and so free of empirical or axiomatically determined structures. Key aspects of the approach are developed from a reconstruction of Stoic natural philosophy and logic.

Leibniz famously introduced a new dimension into this ancient problematic, notably that of developing a theory of the forms of nature in terms of a “geometry without number”. Nowadays we see that there are two modern geometric traditions, one analytic (Analytic Geometry [AG] generalized from linear analysis) and the other synthetic (Geometric Algebra [GA]). GA arises from the exterior and geometric products of Grassmann developed further by Cayley and Hamilton and in modern times by David Hestenes. Hestenes and others claim that GA is the fulfillment of Leibniz’s dream. GA certainly provides the great simplifications that Leibniz demanded and is free of coordinates. But it is not free of number, nor does it provide an algebra based on “a few letters” that would describe the forms of nature both in the biological and non-biological worlds.

This work is presented as a true fulfillment of Leibniz’s dream by developing a more fundamental version of GA which is truly a “geometry without number” and integrating it into a radical reconstruction of Stoic logic and physics.

Since the universe we live in can be considered as a totally autonomous self-managed system, the resulting theory should be applicable to developing the foundations of physics from a fundamental quantum perspective. This turns out to be possible and, unlike String Theory, leads to practical results. One result is the development of a sort of “Periodic Table” of subatomic particles that extends beyond the already known constituents. The theory predicts a lower “sub-quark” level as the primary substratum and. Unlike the Standard Model” does not require quarks with fractional charge. Everything is presented in terms of geometric semantics including such allusive notions as “colour charge.”

The end result can best be understood as “doing a Heaviside” by presenting quantum mechanics in a time independent “non-diachronic” form. This approach is considered as the complementary opposite of the present day standard approach. The tools of Laplace formalize Heaviside’s approach and works well for DEs but not for partial DEs. To universally handle the latter, a more powerful formalism is required. The elements of that approach can be found in Stoic logic once properly reconstructed and explained.

Full paper and book in preperation

**Database
**The prototype database for “the periodic table of subatomic particles” can be found here. on this website here..

**Power Point Presentation **

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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.

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).

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