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Back to the ancients to find the future of science

Stoic Physics, Gödel, and Quantum Mechanics

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.”

From Dirac Razor to Stoic Razor

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.” 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 “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. 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.

Gödel versus the Stoics

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 A which are valid but cannot be proven. Thus, Gödel’s incompleteness theorem effectively states that any consistent axiomatic mathematical system A can be cut down the middle into two sides with what I will call the Gödel Razor. On one side of the razor, the left side say, will be all of theorems provable from A. On the right side of razor is the murky side of the system made up of all the rest of the well-formed formulas of A some of which will be logically valid but unprovable from A. Gödel’s incompleteness theorem says that these valid but unprovable propositions must always exist no matter what. Many consider that Gödel’s incompleteness theorem to be the most important of the twentieth century.

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 contingently true, in this case contingent on the axioms A. The Stoics made a clear distinction between the contingently true and the truth. The contingently true was considered incorporeal. That is fair enough. There is nothing more abstract and incorporeal than being contingent on a set of abstract axioms A. For the Stoics, just as the true was incorporeal, the truth was corporeal. This might seem quite odd. How can a truth be corporeal? What is a good example of a corporeal truth?

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.

In Concluding

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 fromal 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…

Final Points

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.

Shariing
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