“The limits of my language mean the limits of my world.” – Ludwig Wittgenstein, Tractatus Logico-Philosophicus, 5.6.
There is a gap in our language and I want to try to close it by suggesting a new philosophical term. What I am looking for is a term for an entity that exists but cannot be described completely by any single formal theory (or algorithm), something for which a complete and at the same time exact description is impossible in principle or at least for all practical purposes, e.g. for reasons of complexity.
It seems to me that human beings as well as their societies and cultures are such entities, but I think many physical systems are such entities as well. Actually, the word “system” does not really fit here because it has a connotation of something systematic, i.e. something that can be captured completely and exactly by some theory. Scientists use the term “system” as a very general term for practically everything and just assume that everything is a “system”. There seems to be a tacit (and I suppose: wrong) assumption in science that everything is formalizable, and this assumption seems to be hidden right inside the term “system”.
It is, however, not the aim of this article to investigate the question if such entities really exist in physical reality (they definitely do within mathematics, so at least there is no contradiction in the concept). What I want to do in this post is just to propose a word so that it becomes a little bit easier to think and talk about such things, a word that can then be used in discussions about what things are (or are not) such entities, why they are (or are not) or such things even exist.
Instead of using a circuitous circumlocution like “something for which every formal theory of it is incomplete” and instead of using a negative term derived from another word by means of “non-“, “in-“, “un-“ or “a-“, like “non-formalizable”, “informal” etc., we should have a simple positive term.
Antique mythology has often provided the material for new words and terms in science and philosophy, so looking for a fitting new philosophical term, I came upon Proteus. My previous post on this blog was an attempt to play with this figure a little bit and attach a few philosophical thoughts to it in order to see if it fits the bill.
Proteus, an ancient god of the seas, has the ability of changing shape. He does not even have any primary, “real”, definite shape. The idea of such a good might have emerged from the experience of sailors with the unpredictability of the weather and the seas. Modern science has made some progress in the area of weather forecasts, but there is reason to believe that an exact long term forecast of the weather will always remain impossible, so here we have a prime example from science.
In an article about Proteus, Wikipedia tells us:
“He can foretell the future, but […] will change his shape to avoid having to.[…] From this feature of Proteus comes the adjective protean, with the general meaning of “versatile”, “mutable”, “capable of assuming many forms”. “Protean” has positive connotations of flexibility, versatility and adaptability.”.
The German counterpart of that article informs us that stoic philosophy and its allegorical interpretation of myths used the Proteus figure and its ability to transform itself to illustrate the creative changes of the elements in the cosmos.
So I want to suggest deriving the term we are looking for from the name “Proteus”. I suggest the word “proteon” to mean something (an object or a process) that cannot be described by any single formal theory. This means that each formal (i.e. exact) description of a proteon it is incomplete, although the possibility to extend or improve any given description of it might exist. There might be different reasons why something cannot be described completely but I would like to keep the meaning of the term a little bit vague here, so there might be several different types of proteons that have this property for different reasons. The term may also be used for cases where a complete formal description might be possible theoretically (“in principle”) but where it is practically impossible, e.g. for reasons of complexity. A proteon is not a system. Within the terminology proposed here, the term “system” may be viewed as the opposite of the term “proteon”. Moreover, in the context of this terminology, I would use the (already existing) adjective “protean” to refer to something that is a proteon. I suggest using the plural “proteons” but I would not mind if somebody prefers to speak of “protea”.
I don’t know if this proposal is going to catch on. Language is a part of culture and I suppose both culture and language are proteons, so I cannot predict with certainty what is going to happen. When it comes to proteons, seeing and noticing is more important than deriving, since they are full of surprises. Let’s wait and see.
(The picture, showing a Greek vase painting of some ships, is from https://fr.wikipedia.org/wiki/Fichier:NaveGreca.jpg. It hints at the nautical context in which the ideas surrounding the deity of Proteus probably emerged.)
 The form of that piece, the more or less philosophical dialogue between mythological figures, was inspired by a book written by Cesare Pavese. I have tried my hand on this form a few times before, see https://asifoscope.org/?s=Leuco&submit=Search.
“Die Philosophie der Stoa und ihre allegorische Mythendeutung nutzte die Proteus-Gestalt und deren Verwandlungsfähigkeit zur Veranschaulichung der schöpferischen Veränderungen der Elemente im Kosmos“, see https://de.wikipedia.org/w/index.php?title=Proteus_(Mythologie)&oldid=163306022. The wikipedia article referes to “Georg Pfligersdorffer:Studien zu Poseidonios. Wien 1959, S. 120ff“ as a reference for this and states that even Francis Bacon picks up this interpretation referring to “Sapientia veterum c. 13”. I have not checked these claims but it does not matter for our purpose here.
 Although this is not a Greek word – it is a pseudo-Greek neologism -. Moreover, there is no rule forcing us to import grammatical forms from a source language along with a borrowed term. So even if “proteon” was a Greek word, we could still use a plural “proteons”, just as we use “kayaks” as the plural of “kayak”, although the Inuktitut word “qajaq” from which it has been borrowed, has the plural form “qajait” (as far as I can tell from my very limited knowledge of that language).