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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*In this article I briefly present the case that Stoic natural philosophy provides the missing meta-language to finally make sense of quantum mechanics. Modern Stoic writers such as Lawrence C Becker dismiss Stoic physics as an embarrassment. Becker tries to cobble together a hybrid of Stoic ethics with what is essentially a modern version of Epicurean physics. The result is an Epicurean Stoicism, an oxymoron if ever there was one. To Chrysippus, the very core of ethics arises from the fundamental physical principles of matter. If Stoic physics is as Becker describes it merely a “flippant speculation about physical processes,” it is hard to see that Stoic ethics could possibly escape the same epitaph*.

In Hellenistic times, the two dominant philosophical schools of thought were the Epicureans and the Stoics. Of course, there were also the Sceptics who sat on the fence advocating suspension of judgment as Sceptics do. Leaving aside the fence sitters, my interest is in the two opposing camps with the Epicureans on one side of the fence and the Stoics on the other. Of the two camps, the easiest to understand is the Epicurean philosophy. The reason is that, in so many ways, the Epicurean worldview corresponds pretty much to that of present day, modern science. Epicurean doctrine differs from modern science in that, like practically all natural philosophy in antiquity, it was non-empirical. Add empirical methodology, the associated quantification, and one ends up grosso modo with scientific methodology resembling modern physics. Charles Sanders Peirce picked up on this when he wrote that the philosophy of John Stuart Mills corresponded almost exactly with that of the Epicureans.

Epicureanism is materialist, determinist, and above all, fundamentally atomist. Epicureanism studies the reality “out there,” a reality that is assumed mind independent and behaving in a completely deterministic way – well *almost* in a completely deterministic way. Unbridled determinism leaves no place for free will and that poses a problem. To leave some slack for free will, Epicure added a fresh ingredient, He added an escape clause to his atomist, deterministic equation. Certainly, reality could be, in the limit, totally explained by the deterministic motion of the atoms making up the material universe. However, this motion was not *totally* deterministic. Apparently, every now and then an atom exhibits an imperceptible random “swerve.” If this were not the case, the universe would never have evolved beyond its point of departure. Instead, as a gross accumulation of random Epicurean Swerves, the universe nano-swerved into the state that we see it in today. And there you have it. With a bit of creative elaboration, this worldview could also even embrace Darwin’s theory of evolution. After matter nano-swerves to a certain state of affairs, matter starts micro mutating in such a way as to produce organic compounds, elementary life forms, amoeba, monkeys, and eventually us. We are all the end result of trillions of Epicurean swerves.

Classical nineteenth century physics has no need for the Epicurean Swerve as it saw a completely deterministic form of atomism, much like that of Leucippus and Democritus who preceded Epicure. But modern physics is not classical it is quantum. Unlike classical physics, quantum mechanics has been developed in order to explain its own version of the non-deterministic Epicurean Swerve. According to quantum mechanics, reality “out here” is not deterministic but permeated with its own versions of the Epicurean Swerve, The observed non-deterministic behaviours of nature at the quantum level are sometimes referred to as the “quantum mysteries” or even as examples of quantum “weirdness.” Specifically, this includes the questions of entanglement, Heisenberg’s uncertainty principle, the collapse of the wave function, the mysteries of the two-slot experiment, and Einstein’s comment regarding “spooky action at a distance.”

With the advent of quantum mechanics, the chief casualty of classical physics is the concept of the mind independent reality. The isolation of the objective world of objects from the subjective world of the subject is unachievable in practice. Somehow, the lot of object and subject are intimately entwined and interdependent on each other. The most frank admission of the new reality comes from the Copenhagen interpretation of Quantum Mechanics. Expressed by Dirac, often referred to as the Dirac Razor. The Razor sates that the new physics was basically a formal scheme limited to the prediction of experimental results. Anything to say about ontological or other philosophical questions was strictly outside the realm of physics.

In other words, one should avoid sounding silly by claiming that something exists in “the world out there.” Instead, the only objective knowledge about what exists is that which exists concurrent with the instant of measurement. This can be thought of as moment when object and subject are both present. Both share the same “now”, so to speak. It is in this idealised instant that we start to glimpse the need for a change of paradigm. Dirac’s Razor declares that the new physics requires a dramatic paradigm shift from classical physics. However, the new physics does not explain the new paradigm. The new physics simply cries out, as Richard Feynman put it,”Shut up and calculate!” Instead of the new physics leading to a clearer and more insightful insight into the nature of reality, it provides the opposite – a mindless, numbing mania of number, measurement, and obscure abstraction. The curious public demand more, they demand an explanation.

The missing paradigm can be found by breaking away from the Epicurean style realism and changing philosophical camp to that of the Stoics. The Stoics can be said to have their own version of Dirac’s Razor and the primacy of the moment. The Stoic version states:

Entities in the past or the future do not objectively exist. The only entities that exist are those immediately present with the subject.

The Stoics exploited this principle in their ethics, teaching not to fear anything in the past or the future as such things do not objectively exist and so cannot exercise any powers on the present. You need not fear or worry yourself about things in the past or the future as such things do not objectively exists. The Stoics thus become heroes of the present, mastering the integrity of ** now**.

The same principle underpinned their physics. To the Stoics, entities had to be material and corporeal ,capable of acting and being acted upon by other material corporeal entities. Of course, all such acting and acting upon only occurs in the present. Implicitly or explicitly present in the present must be the subject. Thus, the nowness involved in the Stoic Razor is that of the subject, the subject in question. This means that the principle must apply to the universe we live in, the universe as subject bathing in its nowness. Moreover, the same principle must also apply to any other subject such as living organisms and of course to human beings, be they slaves or freemen, man, woman, or child. Whether animate or inanimate, all creatures become heroes of their own present, an individual presence that is distinct but harmonious with that of Nature.

I interpret and express the underlying, universal principle of Stoicism in this form, as the Stoic Razor. The Razor is synonymous with the principle of life. The physics and logic of life must be based on this universal principle. It is important to note that present day computer controlled robotic systems violate this principle. The “present” or “nowness” owned by a robot is dominated by pre-programmed instructions. Instead of being a hero of the present and making its own way in the world, the robot is a slave to its past.

The Stoic Razor principle dictates all entities that objectively exist. The principle applies to all organisms, be they animates such as biological life forms, or inanimates like the universe we live in. All such organisms are dictated by this draconian condition. But here is the catch. Here is the rub. The condition is so draconian that it must apply to itself. The principle demands that an organism obey the principle at all costs then, in the same breath, it demands that the same organism must refuse to be dictated by any principle whatsoever outside its immediate presence. What this means is that the principle is non-programmable.

We see here the flip side to what could be called the Gödel Razor. The formalisation of the pre-programmed robot or Turing Machine is in the form of an axiomatic mathematical system. To be non-trivial, the axioms must include those of elementary arithmetic. For any such non-trivial axiomatic system ** A**, Gödel’s first Incompleteness Theorem applies. The incompleteness theorem comes up with its own version of a principle G applied negatively to itself. Expressed as the proposition G:

G: The proposition G cannot be proved.

Now if G can be proven from the axioms ** A**, the mathematical system must be inconsistent as G says that G cannot be proven. On the other hand, if we assume that the system is consistent then there must exist propositions in

Mathematics is interested in all of the propositions on the left side of the Gödel Razor These are all the provable theorems of the axiomatic system ** A**. In principle, it is possible to program a Turing Machine to mechanically enumerate all of the theorems on the left side of the Gödel Razor. However, on the right side there are also some propositions that are valid. These are valid theorems of the system but are unprovable. Mathematicians may be interested in these unprovable theorems but Gödel has proven them to be out of bounds to the traditional paradigm of mathematics.

This is the point where the ancient Stoics can step in. We, as Stoics, can take a fresh look at proposition G above. We say that a proposition is true if it can be proven from the axioms ** A**. The Stoics refer to this as the

The best example I can come up with is none other than Gödel’s central proposition G where we add the proviso that G *must be a corporeal truth*! Following the Stoics, to be a corporeal truth G must involve material corporeal bodies acting on and being acted upon and all of this taking place in the present. Here we have left the world of abstract mathematics and have entered the world of an organism pushing and shoving, toing and froing, in such a way as to maintain the veracity and hence truth of a fundamental proposition, notably the proposition G. Somehow it seem that for this organism, assuring the truth of G is so important that its life depended upon it. The bodies immediately associated with or owned by the organism must act and be acted upon in such a way that the proposition G is valid. Imagine that this organism is fighting for life. The organism’s prime purpose in life is to assure that the proposition G corresponds to the truth. The organism will do anything within its physical powers for this to be the case. These are desperate times. Moreover, there seems to be no let up. It seems that this preoccupation will endure throughout its life right up to the day it dies. From cradle to the grave, for this organism G is and must be maintained as a fundamental truth. This is a self-justifying truth and hopefully for the organism, it’s going to work.

Now it is time to read the fine print. What does this organism-backed proposition G actually say? G states that G cannot be proven. Now G might conceivably contain some more fine print. This is of no concern to us but might be of some concern to the organism fighting for its particular mode of life. Extra specificity in the proposition G is permissible as long as it is free from any entanglement with nefarious activity outside the organism’s precious nowness.

I hope that I have written graphically enough to convey the central message. The epistemological foundation of present day science and its realist mind independent view of the world is Epicurean in Nature. Quantum Mechanics with its associated quantum mysteries and weirdness throws a spanner in the works. Stoic natural philosophy based on its logic, physics and even its ethics provides a way out of the conundrum. I sketch out how the Stoic paradigm is diametrically opposed to that of axiomatic mathematics. Everything provable in an axiomatic mathematical system can be enumerated by a Turing machine type computer. But Gödel showed that certain truths are out of bounds of formal mathematics. However, I claim that they are not out of bounds to another kind of formalism — that implicit in Stoic natural philosophy. Truths on the out of bounds side of Gödel’s Razor become accessible from within my interpretation of the Stoic paradigm.

The simple message I am trying to convey in this article is that the principle of Stoicism involves a universal life principle that underlies the organisation of all animate life as well as inanimate life like our universe as an organism in its own right. The organisational principle is the opposite to formal axiomatic mathematics. Deterministic systems like mathematics aspire to establish a chain of relations from the a priori to the a posteriori, from the axiom to the theorem, from cause to effect. This is the reason of the robot. The reason of life involves an organism hell bent on proving its own self-reliance by NOT being dependant on the a priori. The robot is driven by the a priori; The life form is driven from what it now is not by what it ever was.

However badly I may have explained it, just go back to the Gödel proposition G and see how Gödel handled it for mathematics. Then, take the opposite to that, and you have the Stoic paradigm in a nutshell…

Objection:

Robots are pre-programmed and life forms are not. But every biological life form is programmed by its genome is it not? Are not life forms just robots pre-programmed in their DNA?

Response:

I explain elsewhere that the genetic code is not a programming language. Mathematical language and all computer-programming languages encode diachronic structures. The most elementary diachronic structure is the Peano successor function that both Russel et al and Gödel used to generate the natural numbers. I claim that the genetic code is a calculus of physics and logic that is without number and so free of any successor function. No diachronic structure is allowed. It only codes the present. You have to read my book and other work to get a fuller grasp of that though. The genetic code is a non-diachronic coding technology, not a language in the usual sense.

Objection:

Biological life forms are coded in the genetic code. How can the universe be seen as a life form when there is no sign of a genetic code?

Response:

I rename the genetic code the *generic **code*. Biological life forms I classify as animates. In animates the generic code is expressed as genetic material (DNA or RNA) separate from the functioning material. Organisms like our universe I call inanimates. In inanimates, there is no distinction between genetic material and functional material. It is all the one stuff. The four letter of the generic code, combined in triads correspond to the elementary particles in physics. On my web site, I have constructed an interactive database that shows this correspondence. Paper 4 is a draft of how that all works. (more is in the pipeline) In other words, the Standard Model of particle physics and much more, can be worked out from first principles by a reinvigorated Stoic natural philosophy as a kind of metaphysics.

Objection:

Stoic physics is based on the ancient four-element theory of Empedocles. This theory has long been debunked and replaced by modern physics.

Response:

Quantum physics has come to the same kind of conclusion as Empedocles and, in particular, Heraclitus. There are four kinds of tension, four kinds of fundamental force in particle physics and quantum mechanics as is well accepted. Foursomes occur regularly throughout physics and even in mathematics. In Category Theory, there are four kinds of morphism, epi, mono, bi and iso. Aristotle’s syllogistic logic was the first to provide a logical basis for a four-element aspect to logic. One can explore that in the four terms of syllogistic logic in my Aristotle Engine on my website. However, the Stoic five indemonstrables provide a direct statement of the logic behind the four-element theory of matter. The third syllogism actually corresponds to the fifth Stoic element *pneuma* and can be used to construct the other four classic elements.

The Scholastics used the letter AEIO to label the four terms of the syllogism. Nature uses the letters ATGC in the genetic cum generic code to code the basic building blocks of life. In my writings I show how this relates to Stoic logic and the ancient four element theory of matter as well as the modern four force theory of physics.

See also “**Stoics and the Double Logos**.“

Like Odin, the ancient Norse god of thought and logic, present day physics achieves rational clarity by a simple astuce, that of being one eyed. According to present day orthodoxy, there is only one scientific paradigm. Science is mono-lateral, not bilateral. The paradigm must be fundamentally left side and thus realist. The apparent weirdness thrown up by quantum theory demands a quest for further refinement of existing orthodoxy, not another radically different paradigm switch. There is no right side science. This is not the position taken in this paper. One can still remain true to the one eyed Western tradition illustrated by the monocular Odin, god of reason. All one has to do is to use the other eye but not at the same time of course.

I argue that science must be bilateral. There must be two separate, fundamentally opposed but complementary paradigms.

The idea is far from novel. Bohm argued his own form of bilateralism with his notions of the Explicate and Implicate orders. Dirac saw the two paradigms of physics as one fundamentally temporal and the other as fundamentally spatial. The philosophers see it as an opposition between physics and metaphysics.

The general characteristics of the left side paradigm correspond to what is called the Scientific Method. As well as being fundamentally realist, the methodology is reductionist, atomist, and dualist. If there is going to be a symmetry between the two paradigms, the right side methodology one would expect the right side paradigm to be non-realist, non-atomist, and non-dualist, whatever these terms might eventually mean once formalised.

Underlying these dichotomies between realism and non-realism, dualism and monism and so on, there must be a fundamental dichotomy from which all others arise.

An intuitive, informal idea of the fundamental dichotomy is that between object and subject. Both the left side and right side paradigms embrace this same dichotomy right at the very core of their respective formalisms. However, they treat the subject object dichotomy in quite opposite ways. These two ways to treat the subject object dichotomy establishes a further dichotomy between the left and right paradigms. The difference between the left and right paradigm treatments of the object subject dichotomy is as follows. The left side paradigm articulates the epistemological configuration of the traditional classical sciences.

The left side paradigm starts with the subject-object dualism taken at the macro level that demands a pure realism where the object of study is objectified by eliminating all reference to the subject, which remains forever invisibly off stage. In empirical science, the object of the science is embraced in an environment called the controlled experiment, a subject free laboratory. The subject, in this context, becomes impersonal and has sometimes been referred to operate as the God’s eye view and even the view from nowhere, empirical scientists would probably prefer the interpretation of the view of the objective, dispassionate observer. Traditional mathematics objectifies its each of its problem domains by a controlled rational environment defined by a set of axioms. The subject is nowhere to be seen in axiomatic mathematics, as all mathematical entities are objects. Like in the empirical sciences, the implicit macro level impersonal is invisible in the formalism. Given an axiomatic system A, the only macro dualism in mathematics is the notion of the mathematically dual system A`. However, the allusive subject is nowhere to be seen in A` as, just like system A, the mathematical entities of A’ are all objects. Axiomatic mathematics is a two-headed coin.

The strength of Western culture is to be like Odin, one eyed. But which eye? Right eyed is to be left-brained. That is the way of present day science. The secret towards an integrated scientific view of reality may be to be one eyed but to change from one eye to the other, depending on circumstance or lack thereof. Only to be one eyed at the one time. Present day science is fixed right eyed, hence left brained. The alternative perspective is ignored. What is needed is a bilateral approach to science. Present day science is mono-lateral. Odin was much wiser than that, surely.

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