To the Stoics, the Cosmos was organised around the incarnate rationality of Logos, following in the tradition of Heraclitus. The rationality of reality is inextricably entwined and expressed by Logos. That’s the cosmic logos and the same principle applies to individual rational beings, the individual logos. The personal and impersonal logoi all share the same principle.

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.

Virtue, First Classness, and Naturality

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).

Use and mention

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.