What happens when the fourfold of Noether’s Theorem is spliced together with the fourfold of Pauli-Jung? Both have Space-Time and Matter-Energy. The former has Conservation and Symmetry, and the latter has Causality and Synchronicity.
I had to remind myself that Conservation means consistency (of matter or energy) through time (and space), and Symmetry means consistency (of form) through space (and time), so in some sense they are dualistic.
Combined, one has the three axes of dual concepts, represented above.
What happens if one combines the four classical Greek (Western) elements with the five classical Chinese (Eastern) elements? Air is in the former and not the latter. Wood and metal are in the latter and not the former.
I’ve left out the Aether (the Fifth Element) of the West because I follow Empedocles, and I see that the five classical Japanese elements have those four and Void as well. But, I’m just looking at material and tangible elements.
One might consider Wood and Metal to be derivatives of Earth, but let’s consider them to be distinct for this exercise. So, maybe six elements!
In his unpublished book “A General Theory of Value”, architect Michael Benedikt argues for a information-theoretic account of value, defining value as follows:
The theory of value offered in this book revolves around three propositions: first, that positive value is attributed to that which preserves or creates more life; second, that “lifefulness” is characterized by a particular quantity and combination of complexity and organization; and third, that in the case of human societies and minds, achieving this optimal quantity and combination of complexity and organization depends on the quality and flow of information among people, and between people and their less-animate environment—plants, animals, buildings, places, things.
It is fascinating that the things that are alive and the products of these lives obtain the highest calculated value of “complexity and organization”.
In order to begin to quantify value, a measurement of the complexity and a measurement of the organization of an entity or system is required. It is worth noting that “not organized” does not mean “complex”, nor does “not complex” mean “organized”. Thus complexity and organization are independent of one another.
Above I have schematized Benedikt’s “Ω Plane”, which consists of two axes, organization and complexity, ranging from disorganized (chaotic) to organized, and simple to complex. “Δ Ω” is simply the measure of the increase in both complexity and organization, and points the way to “value”.
Generously, Benedikt has made his unpublished book available on his web site for all to read.
Michael Benedikt / A General Theory of Value (unpublished)
In “A General Theory of Value”, philosopher Ralph Barton Perry argued for a naturalistic account of values, defining value as “any object of any interest.”
From 1946 to 1948, Perry gave a Gifford Lecture, which later was enlarged to became his book “Realms of Value”. The Gifford Lectures are purportedly about “natural theology”, but many normative subjects have been addressed in them.
Above I have diagrammed Perry’s eight “realms of value”, although I have changed morality to ethics. I have also paired them up to give a fourfold, which doesn’t seem too erroneous.
Custom and Art
Economics and Science
Politics and Law
Religion and Ethics
I’m disappointed that Knowledge is missing from his list, but I could eliminate some of his choices and rearrange a bit to make room for it.
Ralph Barton Perry / A General Theory of Value: its meaning and basic principles construed in terms of interest
Ralph Barton Perry / Realms of Value (Gifford Lectures)
No permanence is ours; we are a wave That flows to fit whatever form it finds: Through night or day, cathedral or the cave We pass forever, craving form that binds.
― Hermann Hesse, The Glass Bead Game
“The Glass Bead Game”, also known as “Magister Ludi”, is the last full length book by German author Hermann Hesse. His works include many thoughtful and interesting stories, detailing the main character’s personal development and spiritual growth. Hesse won the Nobel Prize in Literature in 1946, and his books saw a resurgence of popularity in the 1960’s and 1970’s in the US.
“The Glass Bead Game” is special to me because it describes, although vaguely, a fictional game that is cultivated and played in a future idyllic setting of intellectual devotion, although the larger world is certainly a post-apocalyptic one. All human knowledge is the subject of the game, and the play somehow links mathematics, music, science, cosmology, history, poetry and literature and everything else accepted as higher learning for the imagined cultural time and place.
Is the book sexist because it describes the cloistered society of the game as being restricted to boys and men because of ability, or the idea that men are less distracted from intellectual pursuits without women around? The book is either a product of its time, or perhaps of the political setting in its fictional future. Interestingly, the main character, along with three other character’s lives shown in short stories said to be written by the main character himself, are easily associated with Carl Jung’s theory of psychological types. This is the meaning of the figure above.
Several individuals and groups have tried to imagine how the actual game or any “glass bead game” (GBG) could be played, and there are scattered links on the web, many broken over time and neglect. I agree that analogy and metaphorical thinking are key points to any GBG, as well as the other pillars of attributes nicely discussed in links below.
Connection (or Affinity)
Cogitation (or Contemplation, Thought)
Formalism (or Rules)
Iconicity (or Representation)
Syncretism (or Objectivation, of Culture or Civilization)
(Some attributes have been substituted by thesaurus for word length.)
… For although in a certain sense and for light-minded persons non-existent things can be more easily and irresponsibly represented in words than existing things, for the serious and conscientious historian it is just the reverse. Nothing is harder, yet nothing is more necessary, than to speak of certain things whose existence is neither demonstrable nor probable. The very fact that serious and conscientious men treat them as existing things brings them a step closer to existence and to the possibility of being born.
Everything is dual; everything has poles; everything has its pair of opposites; like and unlike are the same; opposites are identical in nature; but different in degree.
— From The Kybalion by The Three Initiates
There are trivial truths and the great truths. The opposite of a trivial truth is plainly false. The opposite of a great truth is also true.
— Niels Bohr
I have mentioned the alchemical notion of the “Marriage of Opposites” several times (here and here). When opposites marry, what happens as a result? Do they cancel one another out, leaving just a boring average as result? Do they explode in a fiery conflagration, like matter and anti-matter releasing energy? Or do they create a new thing, something that is greater than the sum of their parts?
If opposites annihilate each other, what is the result, emptiness or a void? It is often said that nature abhors a vacuum (“horror vacui”), but I think it is far more true that the mind does. In dualistic thinking, everything that is not one thing must be its opposite. Not good is bad, not happy is sad, not black is white.
In classical logic, the Law of the Excluded Middle says that for any proposition “p”, either it is true or its negation “not p” is true. Thus, “p or not p” is necessarily true, a tautology. Similarly, their combination “p and not p”, cannot ever be true, and so is necessarily false. If one can assume “not p” and derive a contradiction, then “p” must be true (reductio ad absurdum).
In intuitionistic logic, one cannot deduce “p” simply from the falsity of “not p” (that is, “not not p”), one must actually prove that “p” is true. So “p or not p” may still be uncertain, if we don’t know how to prove “p”. However, “p and not p” is still false, based on the falsity of “not p”.
In the viewpoint of Dialetheism, it is offered that there are truths whose opposites are also true, called “true contradictions”. Dialetheisms cannot exist in formal logics because if “p and not p” is true, then you can deduce anything you want and your logic breaks down. Nonetheless, much thought through the years has been dedicated to dialetheisms and their ilk. Please see the recent work by philosopher Graham Priest.
When one considers something and its opposite at the same time, how can you reach an agreement between them? In magnetism, opposite charges attract and like charges repel. All too often, opposite viewpoints vigorously repel each other instead of reaching a happy medium. Each viewpoint considers the other “false” and so they push away at each other, instead of meeting halfway in compromise.
If there is empirical evidence supporting one viewpoint and not the other, and both parties can agree to it, then problem solved. But if viewpoints are more like ideologies, and one side shows evidence that the other side dismisses, what then? Are we only left to agree to disagree? That doesn’t seem like a long term solution.
In this blog I have insinuated but not stated explicitly that a marriage of opposites can often be achieved by combining it with another pair of opposites. Rather than meeting in the middle to a void or an annihilation, one can reach the other side by “going around” the danger, by way of intermediates. Much like Winter reaches Summer by passing through Spring and Summer reaches Winter via Fall, this type of structure is found everywhere in human thinking.
In fact, many systems of pluralistic philosophies are built on fourfolds instead of dualities. For example, see the work of Richard McKeon, specifically this paper.