A General Theory of Value, Part 2

March 20, 2018

What is value?

In his unpublished book “A General Theory of Value”, architect Michael Benedikt argues for a information-theoretic account of value, defining value as follows: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Generously, Benedikt has made his unpublished book available on his web site for all to read.

Further Reading:

Michael Benedikt / A General Theory of Value (unpublished)



A good resource for reading about information:


Also see Cesar Hidalgo’s excellent “Why Information Grows”.

Cesar Hidalgo / Why Information Grows: The Evolution of Order, from Atoms to Economies


[*7.132, *10.86]



A General Theory of Value

March 16, 2018

What is value?

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.

Further Reading:

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)




On this blog: The World Values Survey


Another “General Theory of Value” available on the web:

C. L. Sheng / A Utilitarian General Theory Of Value


[*10.74, *10.75]


The Glass Bead Game

March 6, 2018

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.

  • Analogy
  • 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.)

Further Reading:

Hermann Hesse / The Glass Bead Game










… 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.

[*8.138, *10.82]


The Marriage of Opposites, Part 3

March 2, 2018

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.

Further Reading:















A Game of Fourfolds, Part 5

February 24, 2018

In this fifth installment of our ongoing series, I propose that a game could be played by making a set of equally sized and shaped triangular tiles with simple words or phrases on them. The triangles are all isosceles right triangles, also called monoboloes, so that two of them joined along their long edge would be a square, and four of them joined at their right angles would be a larger square. Figures of two tiles joined along any edge of equal length are called diaboloes, three are called triaboloes, four are called tetraboloes, and in general the figures are called polyboloes (or also polytans, after the Chinese tangram puzzle).

The words or short phrases on the monoboloes would need to be chosen judiciously so that each word has a matching opposite. (A list of such pairs of opposites or duals can be found at my previous fourfold game post.) This is so that a square diabolo could be formed from opposites, and a square tetrabolo could be formed that makes some conceptual sense. In fact, the game play would require that tiles should only be played and joined if there was a rational or explainable reason for their combination.

For example, “Water” and “Fire” could be aligned along their long edge as well as a short edge, whereas “Earth” and “Below”, not being opposites, could only be aligned along a short edge. Opposites could also be aligned “corner” to “corner” (where corner is the 90 degree angle), if there is a supporting tile between them.

During game play, the players alternate playing tiles from their hand onto the table, or pick tiles up from the table and place them back in different positions. Obviously the rules of play would need to be specified in more detail, as well as a method for scoring so that a player could “win”. Or, as a game of solitaire, perhaps winning is just maximizing the number of tiles played onto the table, or the illumination of concepts brought about by the play.

I might also consider that the flip-side of a monobolo is the same word but perhaps having white letters on a black background or colored differently to distinguish it from the “front”. And would the flip-sides all be of the same color? As I have shown various fourfolds on this blog, I have tried to orient them in a common conceptual “direction”, although that is often not clear to me or agreed upon by others of similar temperament. Perhaps they could be the same color if they metaphorically point this same way.

Also, by design and by construction, the monoboloes could be considered “Words”, diaboloes could be considered “Thoughts”, triaboloes could be considered “Actions”, and tetraboloes could be considered “Things”. This would be more in line with the hierarchy given by Richard McKeon’s 1972 lectures on Aristotle’s “Topics”. Words, thoughts, actions, and things are called “commonplaces” by McKeon, or a “place within which inquiry about meanings that are about things that are covered by that meaning can take place”.

The association of these tiles with tangrams is an interesting one. The standard tangram set consists of two small tans (unitans?), three bitans (square, midtan?, and paratan?), and two tetratans that form larger tans (bigtans?). I wonder if there is a standard nomenclature for these pieces, because mine seems rather silly.

I used to have a tangram set when I was a child and even still have an old Dover book by Ronald C. Reed “Tangrams: 330 puzzles”. It’s nice to see that it’s still available on Amazon. Of course the arrangement of the pieces in tangrams is much more flexible than what I’m proposing here for my game so really they are very little alike.

Further Reading:




Richard McKeon / Disciplines, Arts, and Faculties: Invention and Justification: Topics, Lectures given at University of Chicago 1972. (Taped, Transcribed and Edited by Patrick F. Crosby, by private communication)


Possible names for tile combinations:

  • Unit, Solitary, Unitary, Simple, Singular, Singleton
  • Binary, Duplex, Dual, Twofold, Bipartite
  • Triple, Threefold, Ternary, Trinity, Tripartite
  • Quaternary, Quadruple, Tetrad, Fourfold, Quadripartite



Fourfold Physicalism

February 17, 2018

It is not enough for a wise man to study nature and truth, he should dare state truth for the benefit of the few who are willing and able to think. As for the rest, who are voluntarily slaves of prejudice, they can no more attain truth, than frogs can fly.

— From Man a Machine, by Julien Offray de La Mettrie

Further Reading:







Structures are built from parts.
Parts are reductions of structures.
Functions are assembled from actions.
Actions are the constituents of functions.

[*8.132, *9.104, *10.10]


Enlightenment Now!

February 15, 2018

I want a new enlightenment and I want it now! One replete with:

  • Humanism
  • Reason
  • Science
  • Progress

Or, at least I can read the book.

Further Reading:

Steven Pinker / Enlightenment Now: The Case for Reason, Science, Humanism, and Progress


Pinker’s twitter feed:




Seven Sermons to the Dead, P2

February 14, 2018

Here with inadequate description is another fourfold of entities from Seven Sermons to the Dead.

  • The Pleroma: The spiritual universe as the abode of gods and of the totality of the divine powers and emanations.
  • The Creatura: The living world, subject to perceptual difference, distinction, and information
  • Abraxas: The supreme power of being transcending all divinities and demons and uniting all opposites into one
  • Philemon: Jung’s spiritual guide, the narrator

Further Reading:






Seven Sermons to the Dead

February 11, 2018

Four is the number of the principal gods, as four is the number of the world’s measurements.

One is the beginning, the god-sun.

Two is Eros; for he bindeth twain together and outspreadeth himself in brightness.

Three is the Tree of Life, for it filleth space with bodily forms.

Four is the devil, for he openeth all that is closed. All that is formed of bodily nature doth he dissolve; he is the destroyer in whom everything is brought to nothing.

— Carl Jung, from Seven Sermons to the Dead

Further Reading:






Every Fourth Thing

January 29, 2018

And thence retire me to my Milan, where
Every third thought shall be my grave.

— Prospero, from The Tempest

Every single action.

Every other word.

Every third thought.

Every fourth thing.

Further Reading:

Things, Thoughts, Words, and Actions

On Things, Thoughts, Words, and Actions


I should have ordered this fourfold by 1: words, 2: thoughts, 3: actions, 4: things, as per Richard McKeon. But, I have my reasons.