Category Archives: Philosophy

fourfolds, Philosophy, semiotics

Hjelmslev’s Net

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“God is a lobster, or a double pincer, a double bind.”

— From A Thousand Plateaus by Deleuze and Guattari

Linguist Louis Hjelmslev developed a semiotic model which elaborated Saussure’s two part signifier and signified into the double dual of the substance of content, the form of content, the substance of expression, and the form of expression. Contents are “formed matters”, and expressions are “functional structures”. Both are further separated into a substance and a form. The original signifier can be considered the form of expression, while the original signified can be considered the form of content. The two types of forms are like a net of warp and woof (why else a net?), dividing an undifferentiated unformed matter (Earth, purport) into two types of substances.

Deleuze and Guattari cast this net from Hjelmslev’s use in language into universal application by way of examples in geology and biology: sedimentation/folding and molecular genetics. The two planes of content and expression are the First Articulation and Second Articulation, respectively, the first of which “chooses or deducts”, and the second of which establishes “functional, compact, stable structures”. In their geology example, the First Articulation is the process of sedimentation, and the Second, folding. Generally, the two substances deal with territorialization, deterrritorialization, and reterritorialization, and the two forms are concerned with coding and decoding (and recoding?).

Additionally, there is talk of the molar versus the molecular (as continuous/discrete or unity/multiplicity?) but the molar is not form, nor is the molecular substance, nor vice versa. The First Articulation moves from molecular substances to molar forms; the Second Articulation moves from molecular forms to molar substances. How confusing! What does it all mean? One could spend a lifetime lost in these fun-house reflections!

I propose that the four basic logical operators of Linear Logic are in correspondence to the double articulation of Hjelmslev’s Net.  Content is Conjunction, Expression is Disjunction, Substance is Additive, and Form is Multiplicative. Content and Expression is Substance or Form; Conjunction and Disjunction is Additive or Multiplicative.

References:

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

Manuel De Landa / The Geology of Morals: a neo-materialist interpretation http://www.t0.or.at/delanda/geology.htm

Luke Feast / The Science of Multiplicities: post-structuralism and ecological complexities in design http://researcharchive.vuw.ac.nz/handle/10063/142

[*3.170, *4.46, *4.88, *4.112, *4.146, *5.70, *5.174, *6.10]

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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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Cartesianism, Computation, fourfolds, Space and Time

The Duality of Time and Information

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The states of a computing system bear information and change time, while its events bear time and change information.

— from The Duality of Time and Information by Vaughan Pratt

The most promising transformational logic seems to us to be Girard’s linear logic.

— from Rational Mechanics and Natural Mathematics by Vaughan Pratt

References:

Vaughan Pratt / The Duality of Time and Information http://boole.stanford.edu/pub/dti.pdf

Vaughan Pratt / Time and Information in Sequential and Concurrent Computation http://boole.stanford.edu/pub/tppp.pdf

Vaughan Pratt / Rational Mechanics and Natural Mathematics http://chu.stanford.edu/guide.html#ratmech

 [*5.170]

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epistemology, fourfolds, Philosophy, Space and Time

Aristotle’s Four Causes

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Material: That from which something is made.

Efficient: That by which something is made.

Formal: That into which something is made.

Final: That for the sake of which something is made.

— from Aristotle for Everybody by Mortimer Adler

“Happy is he who can recognize the causes of things.”

— Virgil

Aristotle’s Four Causes is likely the most familiar of all the double duals that I will present. The causes are closer to being “becauses” since they are usually thought of as the reasons or explanations for things. Why not call them the four prepositions?

The standard example of the four causes is what is needed for the building of a house. A house is built by the craftsmen, from the raw materials, into the form shown on blueprints, for the homeowner to live in. This and other usual examples are concerned with the making of something.

Formal and final causes have gotten the short shift since the beginning of the scientific revolution. Francis Bacon stated that the only scientific reasons for things were the efficient and material causes. For those critical of materialism this is often termed mere “matter in motion”. Matter can be thought to exist in space, and motion in time. Where does form or finality exist? I will say in space and time as well.

References:

Max Hocutt / Aristotle’s Four Becauses, in Philosophy, Vol. 49, No. 190. (Oct., 1974), pp. 385-399.

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

http://plato.stanford.edu/entries/aristotle-causality/

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

http://faculty.washington.edu/smcohen/320/4causes.htm

Notes:

John Sowa’s Thematic Roles: initiator, resource, essence, goal.

http://www.jfsowa.com/ontology/thematic.htm

[*4.112, *5.73, *5.162, *5.168, *7.47]

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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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alchemy, anime, logic, Philosophy, semiotics

Introduction

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“Humankind cannot gain anything without first giving something in return. To obtain, something of equal value must be lost. That is alchemy’s first law of Equivalent Exchange. In those days, we really believed that to be the world’s one, and only truth.”

—Alphonse Elric, in the first opening to Fullmetal Alchemist

The concept of Equivalent Exchange introduced in the anime quoted above inspired the title of this blog. “To obtain, something of equal value must be lost.” Though this term was recently coined, the concept is a familiar one and has been around for a long time. It is found as guides, rules, and laws in philosophy, religion, and science. For example:

  • Do unto others as you would have them do unto you.
  • Don’t take more than you give.
  • Give and you shall receive.
  • What goes around comes around.
  • There’s no such thing as a free lunch.
  • You get what you pay for.
  • You get what you deserve.
  • An eye for an eye, a tooth for a tooth.
  • You scratch my back, and I’ll scratch yours.
  • Energy is neither created nor destroyed.
  • Every action has an equal and opposite reaction.
  • Yin and yang.
  • Karma.

I’m sure many more can be listed. I invite my readers to submit them.

These are all conservation laws: total value is maintained, even while it changes hands. And they certainly seem to be “conservative”:  all things being equal, they usually hold.

That being said, this blog isn’t specifically about “equivalent exchange”, except for hopefully obtaining the value of knowledge for the effort expended. Instead, I hope to explore a common thread that runs through philosophy, logic, and semiotics in the form of “double duals” (which themselves seem to have the property of equivalent exchange), with the goal of understanding and classifying different philosophical subjects and systems, exploring the nature of pluralism, and enhancing dialogue between opposing viewpoints. The image of the Tower of Babel in the title banner was chosen because public discourse has become fragmented and even broken.

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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fourfolds, Metaphysics, object oriented philosophy, ontology, Philosophy

Heidegger’s Fourfold (das Geviert)

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We are too late for the gods and too early for Being. Being’s poem, just begun, is man.

— From Thinker as Poet by Martin Heidegger

“Every man makes a god of his own desire.”

— Virgil

Note that Heidegger’s Fourfold is a perfect schema for the Tower of Babel: while mortals strive to join the earth and sky, the gods undo their efforts by turning their unity into multiplicity.

References:

Graham Harman / Tool-Being: Heidegger and the Metaphysics of Objects

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

http://culturalstudiesnow.blogspot.com/2011/05/martin-heidegger-building-dwelling.html

http://avoidingthevoid.wordpress.com/2009/10/28/heating-up-the-transmutations-of-media-beings-part-1/

Also:

Andrew J. Mitchell / The Fourfold: Reading the Late Heidegger (Studies in Phenomenology and Existential Philosophy)

Martin Heidegger’s Gods

[*6.2, *6.3, *6.56, *6.62, *9.163]

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