Graham Harman’s Quadruple Object

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


E. J. Lowe’s Four Category Ontology


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

[*4.94, *6.98]


John R. Searle’s Epistemological and Ontological Senses of Objective and Subjective


John R. Searle / The Construction of Social Reality



Kolb’s Learning Cycle

There seems to be many different so-called learning cycles, but I think Kolb’s matches my other double duals most closely.

David A. Kolb / Experiential Learning : experience as the source of learning and development


[*6.38, *6.88, *6.134, *8.93]



The Four Basic Electronic Components

A fourfold has recently been in the news. The physical realization of the memristor completes the four basic electronic components, along with the resistor, capacitor, and inductor. Theorized to exist since 1971, the memristor may revolutionize computational devices.




A Story for Everyone

Wouldn’t it be nice if everyone had a common story we could all learn and share? A story about who we are, what we are, and maybe even a little about the how and the why. Could it be told in such a way that each of us could accept it as our very own? A film and companion book coming out soon will attempt just that, titled Journey of the Universe.

Previous books by Loyal Rue and Brian Swimme have tried to achieve this ideal. Swimme is involved in this new movie, and is the narrator. Rue’s book is a personal favorite. Astrophysicist Eric J. Chaisson has written many books on this topic. Their common theme is evolution, expanded from the biological to encompass the cosmos. Cosmic evolution, if you will.

Evolution merely means change over time, i.e. transformation. Most people agree that things have changed over time, but many disagree on how much, how long, and how come. How can we decide what information to accept, and what to reject? The great unifier of human knowledge is science, yet science is often disparaged even while making the modern world possible. Partially, I’m sure, for that very reason.

Different cultures have had their own creation stories since the very beginning of humanity. Many have said that a large part of being human is the impulse to tell and the need to hear stories. All narratives are built from atomic parts that answer questions: who, what, how, and why. Or, to cast them into modal verbs: may, can, must, and should. Who may? Intention or agency: the characters. What can? Chance or contingency: the setting. How must? Structure or necessity: the plot. Why should? Obligation or responsibility: the theme.

Would a story simplistic enough for everyone to accept be so dilute as to be worthless? All life as we know it requires water, and pure water is ultimately ‘diluted’. But water is certainly not worthless. Daniel Dennett calls the concept of evolution the ‘universal acid’, an alchemical alkahest. Can we replace the corrosive acid in his metaphor with sustaining and nurturing water?

Loyal Rue / Everybody’s Story: Wising Up to the Epic of Evolution

Brian Swimme / The Universe Story: From the Primordial Flaring Forth to the Ecozoic Era–A Celebration of the Unfolding of the Cosmos

Daniel Dennett / Darwin’s Dangerous Idea: evolution and the meaning of life

Eric J. Chaisson / Epic of Evolution: seven ages of the cosmos

Marjolein Groefsema / Can, May, Must and Should: A Relevance Theoretic Account, in Journal of Linguistics, Vol. 31, No. 1 (Mar., 1995), pp. 53-79


J.-Y. Girard’s Linear Logic

Linear logic is a substructural logic invented (or discovered, if you’re a Platonist) by logician Jean-Yves Girard. Many other logics can be embedded into it, including classical and intuitionistic logic, so in a sense it is a “logic behind logic”. Linear logic can be partially derived from the rejection of the structural rules of weakening and contraction, the first of which adds arbitrary propositions and the second reduces duplicated propositions to single occurrences. Due to these changes in the logical rules, logic is transformed from being transcendental (truth transcends its use) to pragmatic or materialistic (truth is restricted by use). Therefore linear logic can be given a “resource interpretation” that makes it a logic not of truth but of things: producing and consuming, giving and taking, pushing and pulling, like the desiring machines of Deleuze and Guattari (see Hjelmslev’s Net).

The fragment of linear logic I show here is called MALL, for Multiplicative-Additive Linear Logic. The two exponentials that interconvert additive and multiplicative operations are not shown, which also allow for the weakening and contraction rules to be reintroduced.

Note that the two additive operations allow for propositions to be created and destroyed and the two multiplicative operations contain exactly the same propositions. One could say the additive operations allow for change, and the multiplicative operations allow for bearing. In the resource interpretation, note that additive disjunction () is creative and additive conjunction (&) is destructive. Both additive conjunction (&) and multiplicative disjunction () are reversible, whereas additive disjunction () and multiplicative conjunction () are irreversible.

Linear logic was a major inspiration for naming this blog “Equivalent Exchange” (see Introduction), since it is a logic of production and consumption. Linear implication, written as A –o B (and equivalent to A B), can be thought of as exchanging A for B.

Linear logic has also been adopted as the logic for “radical anti-realism”. How can it have both a physicalistic interpretation, and yet describe an anti-realism more radical than ordinary anti-realism? I will need further study to understand these claims.




The Tetralemma and Semiotic Square

The Tetralemma is a list that is supposed to exhaust all logical possibilities. Something is either X, or not X, or both X and not X, or neither X nor not X. Nagarjuna’s Fourfold Negation expresses a paradox by negating the Tetralemma, and asking what is not X, nor not X, nor both X and not X, nor neither X nor not X.

The Semiotic Square is an analytical tool to explore relationships between two semiotic signs, usually considered opposites of each other. The S1 and S2 in the figure are the signs in opposition, so that S2 is the dual of S1. S1+~S2 (S1 and not S2) would be X, ~S1+S2 would be not X, S1+S2 would be both X and not X, and ~S1+~S2 would be neither X nor not X.


[*4.84, *5.182]


Richard McKeon’s Aspects of Knowing

Richard McKeon’s system of Philosophical Semantics arises from the sixteen pairwise and ordered relations between his four aspects of knowing or cognates: knower, knowledge, the known, and the knowable. These sixteen relations can be sorted in four groups of four elements each: methods, interpretations, principles, and selections.

Between knower and knowledge, and between the knowable and the known, arise the four methods of two each: the universal and the particular.

  • From knower to knowledge, the operational method.
  • From knowledge to knower, the dialectical method.
  • From the knowable to the known, the logistic method.
  • From the known to the knowable, the problematic method.

Between knower and the known, and between the knowable and knowledge, arise the four interpretations of two each: the phenomenal and the ontic.

  • From knower to the known, the existential interpretation.
  • From the known to knower, the essential interpretation.
  • From the knowable to knowledge, the entitative interpretation.
  • From knowledge to the knowable, the ontological interpretation.

Between knower and the knowable, and between knowledge and the known, arise the four principles of two each: the meroscopic and the holoscopic.

  • From knower to the knowable, the actional principle.
  • From the knowable to knower, the simple principle.
  • From knowledge to the known, the comprehensive principle.
  • From the known to knowledge, the reflexive principle.

Between each of the aspects of knowing with itself, arise the four selections.

  • From knower to itself, the perspectival selection.
  • From knowledge to itself, the transcendental selection.
  • From the knowable to itself, the reductive selection.
  • From the known to itself, the functional selection.

Each method can be associated with a discursive process: operational with debate, dialectical with dialogue, logistic with proof, and problematic with inquiry. Each method is also associated with a mode of thought which in turn has two moments and one dependency or assumption: the operational method is debate by discrimination and postulation dependent on chosen theses, the dialectical method is dialogue by assimilation and exemplification dependent on changeless models, the logistic method is proof by construction and decomposition dependent on indivisible constituents, and the problematic method is inquiry by resolution and question dependent on discoverable causes.


Richard McKeon / On Knowing–The Natural Sciences

Richard McKeon / Freedom and History and Other Essays: an introduction to the thought of Richard McKeon

Sadly, the following pages are no longer available:

[*4.47, *5.184-*5.187, *6.20, *6.106]



Arthur M. Young’s Fourfold Theory of Process

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:

of the Psyche
Elements of
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
Four Causes
Duality of
Time and
Fire Before Efficient Change time Substance
of content
Water After Final Bear time Form of
Air Above Formal Bear
Form of
Earth Below Material Change
of expression


Arthur M. Young / The Reflexive Universe

Arthur M. Young / The Geometry of Meaning

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


Every Fourth Thing

How to Be a Stoic

an evolving guide to practical Stoicism for the 21st century

The Chrysalis

"For man has closed himself up, till he sees all things thro' narrow chinks of his cavern" -- William Blake

  Bartosz Milewski's Programming Cafe

Category Theory, Haskell, Concurrency, C++

The Inquisitive Biologist

Reviewing fascinating science books since 2017


Every Fourth Thing


Derek Wise's blog: Mathematics, Physics, Computing and other fun stuff.


integrating 4 binary opposites in life, learning, art, science and architecture


integrating 4 binary opposites in life, learning, art, science and architecture

Playful Bookbinding and Paper Works

Chasing the Paper Rabbit

Antinomia Imediata

experiments in a reaction from the left

Digital Minds

A blog about computers, evolution, complexity, cells, intelligence, brains, and minds.

philosophy maps

mind maps, infographics, and expositions

hyde and rugg

neat ideas from unusual places

Visions of Four Notions

Introduction to a Quadralectic Epistomology

Explaining Science

Astronomy, space and space travel for the non scientist


Every Fourth Thing

Illustrated Poetry

Art by Marcy Erb

Ideas Without End

A Serious Look at Trivial Things

Quadralectic Architecture

A Survey of Tetradic Testimonials in Architecture

Minds and Brains

Musings from a Naturalist

Why Evolution Is True

Why Evolution is True is a blog written by Jerry Coyne, centered on evolution and biology but also dealing with diverse topics like politics, culture, and cats.


Four-fold thinking4you

Multisense Realism

Craig Weinberg's Cosmology of Sense

RABUJOI - An Anime Blog

Purveyors of Fine Anime Reviews and Ratings Since 2010


Between Subject and Object

The Woodring Monitor

Every Fourth Thing


Every Fourth Thing


Every Fourth Thing

The n-Category Café

Every Fourth Thing


Every Fourth Thing


Sometimes those Sticking their Heads in the Sand are Looking for Something Deep


Online Home of Christopher Vitale, Associate Professor of Media Studies, The Graduate Program in Media Studies, Pratt Institute, Brooklyn, NY.




Explorations in the Paradoxes of Meaning

Object-Oriented Philosophy

"The centaur of classical metaphysics shall be mated with the cheetah of actor-network theory."

Objects & Things

objects & things, design, art & technology

%d bloggers like this: