Category Archives: fourfolds

Carl Jung’s Psychological Types

August 26, 2011 Martin K. Jones 7 Comments

Carl Jung’s Psychological Types can be thought of as different mental states: Intuition, Sensation, Cognition, or Emotion, or as different events in the mind: Intuiting, Sensing, Thinking, and Feeling. I’m not sure why intuition and sensation is often paired with thinking and feeling, as it seems to mix tenses.

In Jung’s theory, intuition and sensation are considered perceiving or irrational functions, and thinking (cognition) and feeling (emotion) are considered judging or rational functions. In opposition to great quantities of scholarship, I believe that intuition is more rational than feeling, as well as intuition being a subjective choice as opposed to feeling being ordered choosing, or choice integrated over time. Similarly, thinking is sensing integrated. Thus perception is the substance of the form of judgment, and rationality and irrationality both bridge perception and judgment.

These distinctions are also the basis for the Myers-Briggs Type Indicator, a psychological test and classification based on four dichotomies: extraversion-introversion, sensing-intuition, thinking-feeling, and judgment-perception, each choice of which determines a person’s attitude, perception, judgment, and lifestyle. There are thus sixteen different personalities measured by this assessment.

This is sixteenfold less than the 256 different philosophical personalities represented by the Archic Matrix. It would be interesting if someone would create a Myers-Briggs type test for philosophers that would serve the same function for the Archic Matrix. Initial question: can the 16 personalities encoded by the MBTI, the 256 philosophical personalities encoded by the Archic Matrix, and the 64 Hexagrams of the I Ching be linked?

William Blake’s Four Zoas

August 26, 2011 Martin K. Jones 1 Comment

Now I a fourfold vision see
And a fourfold vision is given to me
Tis fourfold in my supreme delight
And three fold in soft Beulahs night
And twofold Always. May God us keep
From Single vision & Newtons sleep.

— By William Blake, in a letter to Thomas Butts

The dark Religions are departed & sweet Science reigns.

— From “The Four Zoas” by William Blake

William Blake’s Four Zoas arranged by the Four Elements. Most references associate Urizen to Reason, Luvah to Feeling, Tharmas to Sensation, and Urthona to Intuition. This means Air is Reason, Fire is Feeling, Earth is Intuition, and Water is Sensation. However, I follow others that associate Air to Reason, Fire to Intuition, Earth to Sensation, and Water to Feeling. Another puzzle to consider.

References:

William Blake / The Book of Urizen

http://en.wikipedia.org/wiki/Vala,_or_The_Four_Zoas

http://ramhornd.blogspot.com/search/label/Four%20Zoas

http://ramhornd.blogspot.com/2010/03/fourfold-vision.html

http://www.mindfire.ca/Mind%20on%20Fire%20-%20Blake%20-%20The%20Fourfold%20Vision.htm

http://www.128path.org/pathtimes/article4.html

http://www.psyche.com/psyche/cube/cube_blake.html

http://www.astrostar.com/Four-Elements.htm

[*6.188, *6.190, *6.192, *8.38]

fourfolds, Philosophy

Plato’s Divided Line

August 23, 2011 Martin K. Jones 5 Comments

How to display Plato’s Divided Line? Instead of a continuous line going from low to high as it is usually shown, I’ve shown it as two continuous crossed lines, a fourfold or double dual. Eikasia (imagining) and Pistis (belief) together are Doxa, the phenomenal. Dianoia (understanding) and Noesis (knowledge) together are Episteme, the intelligible. Doxa should indeed be horizontal, corresponding to the phenomenal of Richard McKeon’s Aspects of Knowing, and the subjective or content of other double duals. I believe Eikasia should come before Pistis, as the substance and form of content in Hjelmslev’s Net. Considering the vertical axis, Episteme as Dianoia and Noesis should surely be there for Plato, corresponding to McKeon’s ontic. But how do Dianoia and Noesis relate?

By the measure of the Aspects of Knowing or the Archic Matrix, Dianoia could be considered the method/knowledge and Noesis the reality/knowable of Plato’s Divided Line. Thus Dianoia should be above Noesis, as method/knowledge is above reality/knowable. Yet by other measures, that of the Here and Now or Hjelmslev’s Net, Noesis should be above and Dianoia below. Noesis is the form to the substance of Dianoia. Dianoia can also be thought of as meroscopic, reducing all to number and quantity, and Noesis can be thought of as holoscopic, combining all thing into the hierarchy of forms that culminate in that ultimate form, “The Good”.

The difficulty may be because the lower position, here Noesis, serves both as the position of the real in some fourfolds, as well as the position of earth and matter in others. This is a bias that I would like to avoid, but a resolution will need to come later.

References:

http://en.wikipedia.org/wiki/Analogy_of_the_Divided_Line

Images of Plato’s Divided Line:

https://www.google.com/search?udm=2&q=plato%27s+divided+line&sa=X

[*6.158-*6.165, *6.186]

fourfolds, Philosophy

Stephen C. Pepper’s World Hypotheses

August 15, 2011 Martin K. Jones 1 Comment

References:

Stephen C. Pepper / World Hypotheses: a study in evidence

http://en.wikipedia.org/wiki/World_Hypotheses

[*4.124, *5.22, *5.70]

architectonics, fourfolds, Philosophy

Archic Matrix: Principles

August 12, 2011 Martin K. Jones 3 Comments

Creative	cause functioning by virtue of (indeterminate) potentiality	transcend what is given, functioning caused is without limit	different for different things, indeterminate in kind of functioning caused
Elemental	cause functioning by virtue of (determinate) potentiality	immanent in what is given, from which the functioning emerges	same for all things, all things are the same in their being
Comprehensive	cause functioning by virtue of actuality (of totality)	transcend what is given, functioning of all things transcends any given thing	same for all things, all things are differentiated parts of same whole
Reflexive	cause functioning by virtue of actuality (of functionality)	immanent in what is given, as the functioning itself	different for different things, determinate in kind of functioning caused

Since the Archic Matrix can be thought of as the union of four separate fourfolds, each of the fourfolds of perspective, reality, method, principle can be considered on its own. Here is the fourfold of principles consisting of creative, elemental, comprehensive, and reflexive principles. The content of the table and the bottom figure is derived from Walter Watson’s Architectonics of Meaning.

[*6.146-*6.148]

architectonics, fourfolds, Philosophy

Archic Matrix: Methods

August 12, 2011 Martin K. Jones 4 Comments

Agonistic	parts are primary, producing whole through endeavors	two voices are tested against each other to organize whole	close off intermediate wholes because of external forces
Logistic	parts are primary, producing whole while remaining same	one voice beginning from determinate towards determinate whole	extend towards ultimates (least parts)
Dialectic	whole determines parts directly	two voices are united with each other to organize whole	extend towards ultimates (all-inclusive whole)
Problematic	whole determines parts reciprocally	one voice beginning from indeterminate towards determinate whole	close off intermediate wholes because of own internal unity

Since the Archic Matrix can be thought of as the union of four separate fourfolds, each of the fourfolds of perspective, reality, method, principle can be considered on its own. Here is the fourfold of methods consisting of agonistic, logistic, dialectic, and problematic methods. The content of the table and the bottom figure is derived from Walter Watson’s Architectonics of Meaning.

[*6.146-*6.148]

architectonics, fourfolds, Philosophy

Archic Matrix: Realities

August 11, 2011 Martin K. Jones 5 Comments

Existential	individual, infinite	separate changing (real) from unchanging	reality found in appearances (themselves)
Substrative	individual, infinite individuations of common substratum	persists through change (substratum)	reality lies behind appearances (underlying)
Noumenal	general, one ideal individual apart from many	separate changing from unchanging (real)	reality lies behind appearances (transcending)
Essential	general, many individuals themselves	persists through change (essence)	reality found in appearances (that which appears)

Since the Archic Matrix can be thought of as the union of four separate fourfolds, each of the fourfolds of perspective, reality, method, principle can be considered on its own. Here is the fourfold of realities consisting of existential, substrative, noumenal, and essential realities. The content of the table and the bottom figure is derived from Walter Watson’s Architectonics of Meaning.

[*6.146-*6.148]

architectonics, fourfolds, Philosophy

Archic Matrix: Perspectives

August 11, 2011 Martin K. Jones 4 Comments

Personal	distinction between (primary) subject and object	personal, merely but infinite in number	constitutive of (individual) content
Objective	distinction between subject and (primary) object	impersonal, subjectivity excluded	non-constitutive, subordinate to content
Diaphanic	unity between subject and object (to be obtained)	personal, subordinated to higher and absolute perspectives	non-constitutive, subordinate to superior views
Disciplinary	unity between subject and object (initial condition)	impersonal, subjectivity universalized	constitutive of (universal) content

Since the Archic Matrix can be thought of as the union of four separate fourfolds, each of the fourfolds of perspective, reality, method, principle can be considered on its own. Here is the fourfold of perspectives consisting of personal, objective, diaphanic, and disciplinary perspectives. The content of the table and the bottom figure is derived from Walter Watson’s Architectonics of Meaning.

[*6.146-*6.148]

fourfolds, Mathematics, Philosophy, religion, Science, Space and Time

The Four Conic Sections

July 27, 2011 Martin K. Jones 3 Comments

To teach superstitions as truth is a most terrible thing.

– Hypatia of Alexandria

In mathematics, the four conic sections are the different shapes that can be formed by the intersection of a three dimensional right double cone and a plane: the circle, the ellipse, the parabola, and the hyperbola. The conics have been studied since the dawn of Greek mathematics. These shapes have interest as pure mathematical constructions, as well as many practical uses in applied mathematics.

Special points (focus or foci, plural) and lines (directrix or directrices, plural) can also be used to generate the conic sections in analytic geometry. A circle or parabola has one focus; the ellipse or hyperbola has two. The circle is a special case of the ellipse, one whose two foci coincide at a unique center, and in a different sense, the parabola can also be considered as a special case of the ellipse, having one of its foci at infinity. All circles can be transformed into each other by uniform scaling, a property shared by all parabolas. Thus the circle can be considered to be a singular shape, as well as the parabola. In contrast, ellipses and hyperbolas have a multitude of shapes and cannot be transformed into others of the same kind by uniform scaling. However, a nonuniform scaling or affine transformation can be used to achieve this goal. In even more abstract projective geometry, one could consider that all the conics are the same.

If the double cone is considered as the so-called light cone in Minkowski Space-time, many interesting concepts in special relativity can be considered. In this simplified model, space has two dimensions and time has one. The light cone divides all of space-time into four parts: the past, the present, the future, and the rest. The observer is located in time and space at the common apex of the two cones. Light travels on the surface of the cones, in straight lines towards and away from the observer. Anything traveling strictly within the space-time of a cone must necessarily be traveling slower than the speed of light. One cone can be thought of as the past: the interior of which contains all space-time that could have been observed by the observer, bounded by the circles of light traveling towards her. The second cone can be thought of as the future: the interior of which contains all space-time that could possibly be observed by the observer, bounded by the circles of other observers observing her light. Everything outside of the light cone cannot be observed or influenced by the observer at that instant, since light from it would have to travel faster than the speed of light in order to be seen or acted on by the observer.

Letting my analogical thinking run rampant, I can think of several associations with other fourfolds presented here. The circle is the shape of perfection, of identity and wholeness. It has one center or focus. In Minkowski Space-time, it is formed by the plane cutting the light cone at a constant time, so that all light arrives at the observer simultaneously from the past. Thus it is the shape of the knower or perspective. The parabola has the shape of gravity, the arc of an object thrown from and falling towards the earth. The shape reminds me of a reality that flies up from the opaque depths of the knowable only to fall away again. Numbers that are perfect squares may have started ancient mathematicians thinking about arithmetic. The ellipse has the shape of cosmology. Once astronomers could consider orbits of planets not to be circles or epicycles, only then science changed from idealism to empiricism. The hyperbola’s asymptotes form the crossed lines of my ever-present double duals, dividing yet unifying, as well as the profile of Minkowski Space-time. In fact, space and time occur over and over in many of the fourfolds I have considered.

Circles and ellipses could be considered the shapes of time, subjectivity, conjunction, and content: closed, finite, and bounded, yet cyclic. Parabolas and hyperbolas could be considered the shapes of space, objectivity, disjunction, and expression: open, infinite, and unbounded, acyclic.

In the recent movie Agora, the main character is Hypatia, the daughter of the last librarian of the great Library of Alexandria. A mathematician, astronomer, and philosopher, only fragments of Hypatia’s writings are available to us today. After the sack of the library, Hypatia is shown in her new study with a beautiful wooden model of the conics that she saved from destruction. For any that love wisdom over superstition, the movie is heartbreaking. As an echo to the loss of the contents of the library, it is offered (without any proof) that she considered the truth of the Heliocentric model of the solar system with the planets moving in elliptical orbits. Her senseless murder meant her insights were destroyed without legacy, falling away into the gravity of the dark unknown. Fortunately, even if she had, Copernicus and Kepler rediscovered these insights well over a thousand years later and brought them to light. The library’s loss will never be recovered.

References:

http://en.wikipedia.org/wiki/Conic_section

http://www.npr.org/blogs/13.7/2011/07/11/137743796/agora-most-intelligent-movie-on-science-and-religion-ever?ft=1&f=114424647

http://babelniche.wordpress.com/2010/09/28/more-on-agora-and-hypatia/

http://www.skepticforum.com/viewtopic.php?f=85&t=14979

[*6.170, *6.172]

fourfolds, Mathematics, Space and Time

The Medieval Quadrivium

July 22, 2011 Martin K. Jones Leave a comment

As Proclus wrote: The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in its relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantities as such, music the relations between quantities, geometry magnitude at rest, spherics [astronomy] magnitude inherently moving.