Archive for the ‘Philosophy’ Category

The Fourth Way

April 20, 2019

“The Fourth Way” is the title of a 1957 book by Russian esotericist P. D. Ouspensky that is supposed to be about the self-development methods of the mystic/philosopher/teacher G. I. Gurdjieff. Ouspensky was a student of Gurdjieff for a significant part of his life until there was a parting of the ways. This book was published after Ouspensky died in 1947. A substantial amount of it is constructed in questions and answers, as a teacher might answer their student’s questions.

Ouspensky’s first book in 1909 was about the fourth dimension, which was much in the public consciousness in the first few years after Einstein published his theory of special relativity. His second book was titled “Tertium Organum”, or the third canon of thought, after Aristotle’s first and Francis Bacon’s second. Ouspensky’s third book “A New Model of the Universe” continued in this way, linking science with spirituality, or at least consciousness.

What is a person or what are the aspects of a person? Is a person a machine? A physicalist thinks that a person is their body, and the mind is what the brain does. A dualist thinks that a person has a body as well as a separate mind, but we know that the mind is dependent on the body for operation and it can be diminished by injury, neglect, or abuse. There are other aspects of the person, such as the emotions or “heart”, which are somewhere between the body and the mind.

And if you search on the web, “soul” or “spirit” are often shown in images along side body, mind, and mood, but these terms are imprecise. Sometimes soul is defined as spirit, sometimes spirit as soul. It is difficult to determine what is meant by them, but they are usually of a higher-order nature than the physical or mental or emotional. It is usually what remains the same for a person, the still point of a changing self, regardless if that endures after death.

  • Body
  • Mind
  • Mood (Heart or Emotions)
  • and Spirit?
  • or Soul?
  • or Balance?

Various schools of spiritual people concentrate on the control and discipline of different aspects of the self: the physical for the Fakir, the mental for the Yogi, and emotions for the Monk. These are the first three historical ways for self-development, but they require separation from the normal social world, and neglect the other aspects of the self. The Fourth Way was said to require no extreme separation, and to develop body, mind, and mood in a balanced way.

Gurdjieff thought that most if not all people were machines because they were “asleep at the wheel” (my metaphor), the wheel being the control of their own consciousness. Similar to the practice of lucid dreaming, these teachings (also called “the work” or “the system”) purported to develop the conscious self into something much more than ordinary awareness. This aware self would have access to all sorts of abilities that remain hidden or dormant in most of us.

The Fourth Way is also said to be the way of the “sly man”, but to be sly is to be crafty, cunning, and tricky. If you are sly you are deceitful or a charlatan, dishonest and evasive, a “rogue”. You take advantage of people, or you game the social system. Are there any truth to these teachings, or were they merely a way that Gurdjieff found to make an easy living? If not, why call it the way of the “sly man”? On the other hand, who doesn’t want to develop their best selves in the most efficient and clever way?

  • Fakir: Physical
  • Yogi: Mental
  • Monk: Emotions
  • Rogue: Balance or ?

I also read that “sly man” is a translation of the French “le ruse”. The idea behind this name is for a person that takes advantage of opportunities in their normal life to development their awareness, rather than just their attitude towards others. And so it’s a posture towards the broader world, not just towards people. If I had a short word to substitute for “rogue” in the above diagram, I might do so, to prevent the negative impression I might be giving. But the term “rogue” is probably less offensive that it used to be, so I’ll keep it for now.

Yet people do love to be deceived. They love to be entertained, and they love a good story with charismatic characters. They also love to hear what they want to hear. Perhaps that’s all these teachings really were and are. And yet, many artists, writers, and thinkers have embraced the ideas of this fourth way. Certainly to enhance one’s consciousness is a positive thing to do, or to eliminate erroneous or harmful thought, or to “know thyself”. Socrates taught that “the unexamined life is not worth living”. Perhaps there is some worth to these teachings after all, but a person may have to determine this for themselves.

Further Reading:

Tertium Organum online:

Some videos to entertain found by searching for “fourth way” and “sly man”:

[*10.168, *11.48]



Noether-Pauli-Jung, V2

April 10, 2019

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. And if Space-Time and Matter-Energy are both divided into Space and Time and Matter and Energy, one obtains this eight-fold.

Causality means that some action or cause in time (say a process) of things in space can have an effect (another process, say) on different things in space, and Synchronicity means that different events (say processes) separated in space can have non-causal relationships between them.  Conservation means the consistency of a quantity of matter or energy or matter-energy through time, and Symmetry means the consistency of a measure of a structure or form through space.

I am reminded of my fourfold Four Bindings, consisting of Chains, Grids, Blocks, and Cycles. Causality and Synchronicity are Chains (or non-chains for the latter) Space and Time are Grids (or flexible meshes), Matter and Energy are Blocks (or chunks of stuff), and Symmetry or Conservation are Cycles (of the group-theoretic kind or the equivalence class kind or just loops).

Further Reading:

This is a reworking of a previous six-fold diagram that I believe is served better as an eight-fold.

[*10.68, *10.155, *11.55]


An Eightfold Metaphysics

February 1, 2019

If one juxtaposes the fourfold Space-Time-Matter-Energy with the fourfold Structure-Function-Part-Action, one sees that there are several relations between them. These are simple common-sense relations, not modern-physics types of relations. Below they are listed by Space-type relations and Time-type relations.

Space is required for the extension of Structures.
Matter constitutes Structures.
Parts in an arrangement make up Structures.

Structures extend and are organized in Space.
Matter is located in Space.
Parts occupy Space.

Time allows the expression of Functions.
Energy is required for the operation of Functions.
Actions in a sequence constitute Functions.

Functions have duration and reoccur in Time.
Energy requires and is dependent on Time.
Actions take place within Time.

Several analogies are also evident in this diagram.

  1. Space : Structures :: Time : Functions
  2. Space : Parts :: Time : Actions
  3. Space : Matter :: Time : Energy
  4. Structures : Parts :: Functions : Actions
  5. Structures : Matter :: Functions : Energy
  6. Parts : Matter :: Actions : Energy

Notice that analogies 1.-3. are “contains” relations, and 4.-6. are “part of” relations. One obtains the nesting of entities:

Structures > Parts > Matter
Functions > Actions > Energy

I suppose that any analogy could be shown in a figure like the one on the right (or even written as A / B // C / D) or with the two squares side by side, and that sets of four or six analogies that overlap could be nicely shown as above. If so, I wonder what can be gained by such representations? Probably individually not so much but with overlaps I think it would be interesting.

Further Reading:

The study of parts and wholes relations is called Mereology.

[*10.157, *11.26, *11.34]



The Rosetta Stone of Arthur M. Young

January 27, 2019

In his book “The Geometry of Meaning”, Arthur M. Young developed a system which he called his “Rosetta Stone” because he claimed that it associated mental attributes to some physical measurements, giving a kind of map to mind-body dualism. In the above diagram the expressions and names of these twelve objective values or physical units are shown. Examine the list below to see the twelve subjective values or mental attributes (shown in parentheses) that Young ascribed to them.

I’ve rearranged the sequence of these somewhat because I don’t quite understand the reasons for the organization Young gave them. I’ve also relabeled the units using the more standard derivative notation L’ = dL/dT, L” = d^2 L/ dT^2, etc. His notation is given at the end of each line below in parentheses for comparison (essentially he removes the d’s from the derivatives, writing dL/dT as L/T, which seems confusing to me when then multiplied by L).

Given the measurement Position or Length (L), Moment is Mass (M) times Position giving ML, and Moment of Inertia is Moment (ML) times Position giving ML^2. Velocity (L’), Acceleration (L”), and Control (L”’) have similarly related pairs of values by multiplying each by M and by ML. This gives four sets of similar expressions differing by their common derivative. I should have probably named the 1st set to be 0th, 2nd set to be 1st, 3rd set to be 2nd, and 4th set to be 3rd after the order of the common derivative.

  • Position (Observation): L
  • Moment (Significance): ML
  • Moment of Inertia (Faith): ML^2
  • Velocity (Change): L′ (L/T)
  • Momentum (Transformation): ML′ (ML/T)
  • Action (Impulse): MLL′ (ML^2/T)
  • Acceleration (Spontaneous act): L” (L/T^2)
  • Force (Being): ML” (ML/T^2)
  • Work (Fact): MLL” (ML^2/T^2)
  • Control (Control): L′′′ (L/T^3)
  • Mass Control (Establishment): ML′′′ (ML/T^3)
  • Power (Knowledge): MLL′′′ (ML^2/T^3)

How does Young justify associating, for example, the mental attribute “Faith” with the physical unit “Moment of Inertia”? It seems to have something to do with his original cyclic order of these twelve measurements and the associations he gives them to the Astrological Signs of the Zodiac. This mapping is not shown but can easily be found in the links below.

Further Reading:

Arthur M. Young / The Geometry of Meaning

The only early entry in my blog without a leading figure (and poor tables as well):

[*7.78, *7.79, *8.2, *11.38]


The Law of the Instrument

November 16, 2018

Sometimes I wonder if I overdo this fourfold thing. The law of the instrument says something like “if all you have is a hammer, everything looks like a nail”. Dividing things up into four parts, or bringing four things together into a whole, is the belabored theme of this blog. Fourfolds are my hammer, and what a nice hammer it is!

When my father was in a nursing home, he had a roommate for a period of time that would just draw houses continuously. Not nice architectural renderings either, but houses like a child would, where you can see three sides of it at once (the front and both sides). I might be doing that one day, endlessly drawing fourfold diagrams in endless fourfold permutations.

Speaking of hammers, Martin Heidegger also wrote at length about them in regards to equipment or instrumentality. He contrasted a working hammer that was “ready-to-hand” to a broken hammer that was “present-at-hand”. The working hammer recedes into the background of its ready utility, but the broken hammer, being useless, is merely present in pieces.

The notion of science as negative enterprise was raised by Heidegger since scientific investigation only gives you the present-at-hand, and not the smooth extension of ability that is ready-to-hand. I disagree, because how can you fashion a hammer in the first place or repair it if you aren’t full cognizant of its constituents and construction?

I realize that some worthwhile analyses are made by this approach to technology. For example, few are able to construct or repair modern automobiles or smartphones. In a sense, that should make Heidegger happy, since most are using this modern equipment with no clue as to how they work. And if they wear out or break or become obsolete, they are too costly to repair or upgrade and are sent to the scrapheap. But I say this tongue-in-cheek.

Heidegger’s “tool analysis” is the basis for much of his later writings, specifically concerning “das Geviert” (simply meaning square). If tool analysis is itself a tool, what happens when you apply tool analysis towards itself? Does one get an infinite fractal of fourfolds, ascending and descending, approaching and receding?

Further Reading:,_everything_looks_like_a_nail

Look at this painting!




The Question Concerning Technology

November 10, 2018

“The Question Concerning Technology” by Martin Heidegger is not an easy read. This short essay is full of unusual terms and phrases. I think part of the reason for this is Heidegger’s style of writing, and part is the capacity of the German language to build compound words easily. Thus in the English translation you have several hyphenated words like “standing-reserve” and “bringing-forth”. Of course, difficult terminology seems to be typical for Heidegger, but there are also many words taken from classical philosophy that have special meanings, which Heidegger was well versed in.

In this essay we first learn that our question is really a questioning and will be a process that “builds a way” to understanding, so initially we are more interested in the journey than the destination. The way that is desired is towards a “free relationship” between an “open” human existence and the “essence of technology” (essence being what a thing is, as if we can know exactly, so finding out is part of our journey). Second, we are told that the essence of technology is not technological, so to try to find what this essence is by using more technology is to be in an “unfree” relationship with it.

Third, our question concerning technology is really asking what technology is. A common and “correct” definition is that it is both a means to an end, and a human activity. The former is the instrumental aspect of technology, and the later is the anthropological aspect. But Heidegger does not think that these two aspects are the complete or “true” ones, and so our questioning leads us to inquire as to the essence of instrumentality. For that, we turn next to consider the general causes of things and their effects, and so on to examine the classical Four Causes of Aristotle.

Readers of this blog will be familiar with the Four Causes, as I have mentioned them frequently. I consider them an important paradigmatic four-fold, and have tried to develop a more modern version of them with my four-fold Structure-Function. However, Heidegger was no friend to modernity, and his treatment of the Four Causes and the remainder of his essay shows that plainly. But let us continue on with our journey before we spoil our quest. As a reminder, here is a quick list of the Four Causes:

  • Efficient Cause – causa efficiens – Logos
  • Material Cause – causa materialis – Hylos
  • Formal Cause – causa formalis – Eidos
  • Final Cause – causa finalis – Telos

By thinking about causes in this way, can we discover the essence of causality? Heidegger explains that what causality is involves the things responsible for the bringing about of other things or what kinds of things a thing is indebted to in order for it to occur. (Others have argued that instead of causes another good name is the four “becauses”, i.e. the reasons for or the explanations of things). Note that Heidegger uses the terms responsibility and indebtedness to give the Four Causes (what I consider to be) a normative aspect.

Heidegger presents to us a silver chalice as an example of how to think about the the Four Causes in relation to Greek thought. Hylos (or hyle) is the material we start with, Eidos is its form or aspect, Telos is responsible for bringing together both (but not as aim or purpose but as bounds or context), and all three are indebted to… Logos? Heidegger now departs from how Aristotle was understood to view the causes named after him, and says so himself, in order to argue that these four ways of responsibility and indebtedness are really what these causes are all about.

To be continued… maybe…

Further Reading:

Notes for Further Writing:

Interesting articles on Shintoism and Heidegger:

Interesting article on language and technology (tool-making) arguing that they are related: The structure of language mirrors the methodological structure of tool making:

A nice symmetric view of the Four Causes as things undergoing changes is shown in:

Boris Henning / The Four Causes, The Journal of Philosophy, Vol.106, No.3 (March 2009), pp. 137-160





The Archic Matrix

September 13, 2018

Now that I am presenting sixteen-folds, let me briefly return to a subject I’ve mentioned previously. The Archic Matrix of Walter Watson and David Dilworth is a four-by-four matrix representing different aspects of the “personalities” of philosophers, determined by their writings. It is adapted from the Philosophical Semantics of philosopher Richard McKeon.

The four aspects of the Archic Matrix (also called Archic Variables) in this diagram are Perspective (upper left), Reality (lower left), Method (upper right), and Principle (lower right). The archic variable Perspective can have values Personal, Agonistic, Existential, and Creative, and similarly for the other three variables.

Each of the values of each of the variables is conditioned by one of the variables. For example, Personal is only conditioned by the Archic Variable Perspective, even though it is already a value of that variable. The value Agonistic is conditioned by the Archic Variable Method, Existential by Reality, and Creative by Principle.

Whereas the Myers-Briggs Type Indicator is a two-by-four matrix giving sixteen different combinations for its four personality “variables”, each having two values, the four-by-four Archic Matrix has four values for each of four variables and so gives 256 different combinations. It would be interesting if someone mapped the larger scheme into the smaller.

Further Reading:

Archic Matrix: Perspectives

Archic Matrix: Realities

Archic Matrix: Methods

Archic Matrix: Principles


The only work that seems to mention both the Archic Matrix and Myers-Briggs is as follows:

Mondo Secter / The Architectonics of Culture: A Critique, Modification, and Extension of Hofstede’s Study of Societal Culture with a Chinese-Based Typology, Ph.D. Dissertation, Simon Fraser University, August 2003

Secter is elsewhere mentioned to be completing an adaption of this dissertation (albeit long ago), called “The Architectonics of Culture and Personality: Six Core Dimensions of Who We Are”. It would useful to know anything else about this work. Updates, anyone?

[* 10.151]





Hannah Arendt: The Human Condition and the Life of the Mind

June 22, 2018

In her book “The Human Condition”, philosopher Hannah Arendt discussed the vita activa, the active life:

  • Labor
  • Work
  • Action

In “The Life of the Mind”, she wished to present the vita contemplativa, the contemplative life:

  • Thinking
  • Willing
  • Judgment

Unfortunately, she died just as started working on Judgment, so that aspect was just outlined with notes.

The differences between the active and the contemplative can also be thought of as the practical versus the theoretical. This pair of triplets is not easy to turn into a troika of duals.Further Reading:

[*9.98, *10.102]





Six Types of Philosophers

June 18, 2018

I have mentioned fourfold classifications of philosophers before, most notably the Philosophical Semantics of philosopher Richard McKeon (which is similar to the Archic Matrix of Walter Watson and David Dilworth). These are actually sixteen-fold classifications, since each of four attributes have four types.

Instead, consider this six-fold classification by Justin E. H. Smith:

  • Curiosa – Particularist
  • Sage – Systematist
  • Gadfly – Social Critic, Commentator
  • Ascetic – Disciplinarian
  • Mandarin – Academic, Professional
  • Courtier – Bureaucrat, Institutionalist

In addition, here is another diagram of this same classification scheme.Further Reading:

Justin E.H. Smith / The Philosopher: A History in Six Types, Princeton University Press, 2016.




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:



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