Category Archives: Metaphysics

fourfolds, Metaphysics

Four Primary Relations

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sq_four_ances

I’ve written previously about my fourfold Structure-Function (consisting of Structures, Functions, Actions, and Parts) and its association with four Modal Verbs (Must, Should, May, and Can). This resulted in the combined fourfold of Modal Things.

Here I present the next step: what it is that Structures Must do, what it is that Functions Should do, what it is that Actions May do, and what it is that Parts Can do.

Structures Must Maintain => Maintenance
Functions Should Perform => Performance
Actions May Occur => Occurrence
Parts Can Vary => Variance

The first column lists the four aspects of Structure-Function. They are loosely based on Aristotle’s Four Causes. Structures correspond to the formal cause. Functions correspond to the final cause. Actions correspond to the efficient cause. Parts correspond to the material cause.

The second column lists the Modal Verbs, the “modes” of each aspect. They are similar to deontic logic, two being more or less necessary and two being more or less contingent.

The third column lists the Actional Verbs, what it is that each aspect does in its modal way. One could also say these as mottos: “Structures must be maintained”, “Functions should be performed”, “Actions may have occurred”, and “Parts can be varied”.

The fifth column lists the four primary relations that correspond to each of the four aspects.

These four relations could inform a metaphysics, consisting of relations all the way down, all the way up, all the way back, and all the way forward.

Links:

http://plato.stanford.edu/entries/logic-deontic/

[*7.192, *8.40, *8.136]

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fourfolds, Metaphysics, Philosophy

Lucretius: On the Nature of Things

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But, now again to weave the tale begun,
All nature, then, as self-sustained, consists
Of twain of things: of bodies and of void
In which they’re set, and where they’re moved around.
For common instinct of our race declares
That body of itself exists: unless
This primal faith, deep-founded, fail us not,
Naught will there be whereunto to appeal
On things occult when seeking aught to prove
By reasonings of mind. Again, without
That place and room, which we do call the inane,
Nowhere could bodies then be set, nor go
Hither or thither at all- as shown before.

—  From On the Nature of Things by Lucretius

A book on the  rediscovery of  the ancient Epicurean poem “On the Nature of Things” by Lucretius has recently been published. “The Swerve: how the world became modern” by Stephen Greenblatt looks quite interesting. The fourfold above was inspired by the previous fourfold Spacetime. A very nice NPR review can be found below.

Further Reading:

http://www.npr.org/books/titles/140464239/the-swerve-how-the-world-became-modern

http://classics.mit.edu/Carus/nature_things.1.i.html

To Do:

Change swerving to veering.

[*7.18]

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fourfolds, Metaphysics, object oriented philosophy, Philosophy

Graham Harman’s Quadruple Object

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Graham Harman’s book The Quadruple Object is now available in English, and hopefully it will clarify some of the questions I have about his metaphysics. I have made an attempt at orienting his fourfold of real object, sensual object, real qualities, and sensual qualities with respect to the other fourfolds presented here. The fourfold object emerges from Harman’s analysis of Heidegger’s das Geviert.

Further Reading:

Graham Harman / Guerrilla Metaphysics: phenomenology and the carpentry of things

Graham Harman / Prince of Networks: Bruno Latour and metaphysics

Graham Harman / The Quadruple Object

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fourfolds, Metaphysics, ontology, Philosophy, Science

E. J. Lowe’s Four Category Ontology

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References:

E. J. Lowe / The Four-Category Ontology: a metaphysical foundation for natural science

http://en.wikipedia.org/wiki/E.J._Lowe

https://ndpr.nd.edu/reviews/the-four-category-ontology-a-metaphysical-foundation-for-natural-science/

Lowe, Edward Jonathan

http://www.informationphilosopher.com/solutions/philosophers/lowe/

[*4.94, *6.98]

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alchemy, Cartesianism, fourfolds, Metaphysics, Mind-Body Dualism, Philosophy

Arthur M. Young’s Fourfold Theory of Process

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I have recently come across the philosophical work of Arthur M. Young (AMY). This is an initial impression of that work since I have only read what is available from the web links below, and even then there is a great deal to digest. In addition, there is difficulty in presenting a summary of his theory because of similarities to my ideas as well as substantial differences. I am sure I will need to return to AMY’s theory after more consideration.

I have hinted at a correspondence between several double duals presented in this blog, but I have steered away from claiming that they are all linked to each other – that they are essentially equivalently exchangeable. AMY’s theory links the four elements, the four causes, Jung’s functions of the psyche, geometrical elements and transformations, as well as several other fourfolds into a cosmic theory of reality.

Some of these same fourfolds are present in my theory, and I am considering how others may be introduced. Some not mentioned by AMY are only mentioned in earlier entries on this blog, without presentation. However, from many of these same fourfolds I have reached substantially different conclusions from AMY. I believe this is because AMY’s theory of process is essentially dualistic, whereas my theory appears to be physicalistic, although one might also say it is a process and/or relational theory.

Below is a table of some of the correspondences for AMY’s theory of process:

Aristotle’s
Four
Causes		 Jung’s
Functions
of the Psyche		 Four
Elements of
Empedocles		 Geometric
Transform-
ations
Purpose Final Intuition Fire Rotation Spirit
Value Material Emotion Water Scale Soul
Form Formal Intellect Air Inversion Mind
Object Efficient Sensation Earth Translation Body

Below is a table of some of the correspondences for my theory:

Four Elements
of Empedocles		 The Here and
the Now		 Aristotle’s
Four Causes		 Duality of
Time and
Information		 Hjelmslev’s
Net
Fire Before Efficient Change time Substance
of content
Water After Final Bear time Form of
content
Air Above Formal Bear
information		 Form of
expression
Earth Below Material Change
information		 Substance
of expression

References:

Arthur M. Young / The Reflexive Universe

Arthur M. Young / The Geometry of Meaning

http://www.arthuryoung.com/barr.html

http://www.arthuryoung.com/4levels.html

http://www.arthuryoung.com/the2exc.html

[*6.84-*6.89, *7.78, *7.79, *8.2, *8.62, *8.63]

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fourfolds, linear logic, Metaphysics, Philosophy

Monism = Pluralism

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PLURALISM = MONISM

– From A Thousand Plateaus by Deleuze and Guattari

Jeffrey Bell’s blog entry about William James’ radical empiricism reveals relations between Hjelmslev’s Net and Linear Logic. To begin with, Hume was concerned with disjunctive relations (of expression) to the exclusion of conjunctive relations (of content). In addition, James sought the solution to the problem that consciousness (here content) has between the “one and the many”, one consciousness in relation to many consciousnesses. Unable to resolve this problem, James did not realize that conjunction can come in two modes, an additive one and a multiplicative one, a substance and a form.

The substance of content (here consciousness, agency, …) is constituted incrementally from choices between actions, either thoughts (thoughts-as-action) or actual actions (actions-as-action). This is additive AND. The form of content (essence, existence) is assembled by the ordering of those choices, a multiple choice of choices. This is multiplicative AND. These are the powers of AND.

However, Hume’s disjunction (expression) also comes in two flavors: additive and multiplicative (substance and form). It also has a problem with the “one and the many”. The substance of expression is either identity or generation (accident, substance). This is additive OR. The form of expression doesn’t seem like much in Linear Logic, but it is the very form of the logic, invertible with the connective tissue of the calculus (the comma). This is multiplicative OR. These are the powers of OR.

Content and expression are dual to each other, as conjunction is logically dual to disjunction. Is content the “subjective” and expression the “objective”? Is substance the “one” and form the “many”? Each is dual to the other, not distinguishable except by perspective. Perhaps these double duals are like a Mobius Strip, which only has one side, weaving in and out and forming a unity out of multiplicity.

Note that the elements of the double dual shown here are taken from the Protreptikos page “Monism and Pluralism”. The fourfold is made up of different “compositions in being”, each in two parts. There are many echoes to other double duals in these compositions, such as potency/actuality (existence) and substance/form.

References:

Gilles Deleuze and Felix Guattari / A Thousand Plateaus: capitalism and schizophrenia

http://schizosoph.wordpress.com/2010/08/11/monism-pluralism/

Further Reading:

https://en.wikipedia.org/wiki/Potentiality_and_actuality

Aquinas: Metaphysics

https://plato.stanford.edu/entries/aristotle-metaphysics/

https://plato.stanford.edu/entries/form-matter/

https://ndpr.nd.edu/news/form-matter-substance/

Matter and Form, Substance and Accidents

[*6.40]

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alchemy, fourfolds, Metaphysics, Space and Time

The Here and the Now

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Whosoever speculated on these four things, it were better for him if he had not come into the world —

  • what is above?
  • what is beneath?
  • what was beforetime?
  • and what will be hereafter?

— From the Mishnah (Hagigah 2:1)

All things have a root and a top; all events an end and a beginning. Whoever understands correctly what comes first and what follows draws nearer the Dao.

— From T’ai Hioh by Confucius

As above, so below.

— From The Emerald Tablet

I like these quotes because they show that Above, Below, Before and After are linked together. The first quote gives a warning about thinking about these concepts, but the second, encouragement. Above and below, or higher and lower, can be thought of as directions in space, but also as terms of hierarchy. Before and after can be thought of as directions in time, but also as beginnings and endings, causes and results.

Every individual is situated in space and time (see SpaceTime). Every perspective is due to expression and content (see Hjelmslev’s Net). Here is space, now is time.

References:

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

[*5.160, *6.30]

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alchemy, fourfolds, Metaphysics, ontology, Philosophy

The Four Elements of Empedocles

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Into this wilde Abyss,
The Womb of nature and perhaps her Grave,
Of neither Sea, nor Shore, nor Air, nor Fire,
But all these in their pregnant causes mixt
Confus’dly, and which thus must ever fight,
Unless th’ Almighty Maker them ordain
His dark materials to create more Worlds,
Into this wilde Abyss the warie fiend
Stood on the brink of Hell and look’d a while,
Pondering his Voyage; for no narrow frith
He had to cross.

— From Paradise Lost by John Milton


The Four Elements of Empedocles is one of the earliest ontologies. While not of special interest in itself (except of course to alchemy), other double duals are comparable to it, such as the The Here and the Now and Heidegger’s Fourfold. Additionally, it is interesting to remember that it was thought that the four elements were the primitives of which everything is composed; for example bone was fire, air, water, and earth blended in a certain proportion. I am unsure of the origin of the choice of the elements: why these four and not others?

Also, note that with respect to light transmission, the four elements can be arranged in the sequence of bright, light, dim, and dark. This is not to say that fire is “good” and earth “bad”, or that fire and earth are the most different from each other. Perhaps this distinction will have some meaning later.

[*5.188, *6.32, *6.56, *7.194]

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fourfolds, Metaphysics, Philosophy

Ken Wilber’s AQAL

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References:

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

https://malankazlev.com/kheper/topics/Wilber/Wilber_IV.html

http://tetrast4.blogspot.com/2008/12/wilber.html

[*5.190-*5.192, *6.58]

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fourfolds, linear logic, Metaphysics, Philosophy

Whitehead’s Criteria for Metaphysical Theories

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Note that consistency and coherency are considered rational, and that applicability and adequacy are considered empirical. This has importance for Heideggar’s Fourfold since the rational is revealed,  and the empirical is concealed. For Linear Logic, additive conjunction and multiplicative disjunction are reversible, yet additive disjunction and multiplicative conjunction are irreversible.

References:

Alfred North Whitehead / Process and Reality

Frederick Ferre / Being and Value:  toward a constructive postmodern metaphysics

Mark Graves / Mind, Brain, and Elusive Soul: human systems of cognitive science and religion

Paul Reid-Bowen / Goddess as Nature: towards a philosophical theology

[*6.12, *6.70]

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