Integral Abstraction
Conceptualizing Abstraction in the Quadrant Model
*This article is paired with Integral Theory and Metamodernism.
Prelude
Various concepts of “abstraction” can be mapped onto the Integral Quadrants framework. It is incredibly practical to juxtapose different domains of abstraction this way, since abstraction is a very equivocal word (‘open to more than one interpretation; ambiguous’). As you can see in the title image, there is a basic distinction between mental, physical, social, and material abstractions. This is important for differentiating between different concepts and ideas that employ the same word. And it is vital for understanding how a singular notion operates in all four quadrants differently.
A disclaimer is in order since I argue that a metamodern approach is post-Integral, which I discuss in Integral Theory and Metamodernism. There are problems with reducing analysis to the Integral and the AQAL framework — it is a good heuristic and guide, but not itself a matrix for deep social theory or critique. But it may also have other strengths and weaknesses I do not yet realize. At any rate, the quadrants are not a substitute for studying each concept on its own. Nevertheless, this article illustrates a fruitful crossover between Integral Theory and Abstraction hitherto unexplored. After all, the Integral Map is just an abstraction itself. As the great Ken Wilber wrote;
“Remember that the quadrants are just a version of first-, second-, and third-person realities? Well, the Integral Map and IOS are just third-person words, they are abstractions, a series of “it” signs and symbols. But those third-person words insist that we also include first-person direct feelings, experiences, and consciousness as well as second-person dialogue, contact, and interpersonal care. The Integral Map itself says: this map is just a third-person map, so don’t forget the other important realities, all of which should be included in any comprehensive approach.” — Ken Wilber, Integral Life
Middle English: from Latin abstractus, literally ‘drawn away’, past participle of abstrahere, from ab- ‘from’ + trahere ‘draw off’.
Introduction
The concept of “abstraction” is very important for everyone to understand, whether they realize it or not. We all do it implicitly, but to make it explicit improves learning outcomes. It is simple, yet hard to summarize it in all its complexity. Abstraction requires simplicity, which is a process of abstracting downward, but then detail is lost, so we must go back up.
Abstraction commonly refers to thinking, or the products of thinking; it is the process of distancing objects and ideas. Let me give a rudimentary example. Any concept is an abstraction: a country, a name, a color, a shape, a ball (standing in for all types of balls). These abstractions have properties, but aren’t real as such. They are the products of the thinking process of abstraction, that crystallize the essential information. The cartoon on the left is more abstract than the sketch on the right, but both are still abstractions.
For reasons that are not immediately obvious, abstraction is a vital concept across many fields from art to artificial intelligence, though it means slightly different things in each. See the Introduction to ‘Abs-Traction’ for a better primer on the various ways it is explored here. But to give one more example, consider the generic concept of an academic “abstract” itself; a long dense paragraph of written summary, often according to rigorous research protocols. It is called that, because the author has ‘drawn away’ the most basic elements from the complexity of the text, just as the cartoon has done.
Now we’re going to go from 0–60mph. Abstraction is ordinarily thought of as a mental process, not a physical one. However, when Marx introduced ‘commodity abstraction,’ everything changed:
“The view that abstraction was not the exclusive property of the mind, but arises in commodity exchange was first expressed by Marx in the beginning of Capital and earlier in the Critique of Political Economy of 1859, where he speaks of an abstraction other than that of thought.” — Alfred Sohn-Rethel, Intellectual and Manual Labour, 1978
So, now we have two categories of abstraction to play off each other: cognition and commodity. This is major progress from the one dimensional view, but Marx’s legacy has been complicated, and abstraction is still largely unappreciated. The dualistic approach implicitly dominates the contemporary social theories of abstraction, from Marx to Simmel to Sohn-Rethel, Geoff Sharp, Paul James, Ray Brassier and many more.
But what if we could we could go further still? The AQAL frame is very important here because it gives us 4 fields of reference rather than 2, which is currently the norm. In light of the Four Quadrants, dualistic abstraction then seems very limited. And most utilization of abstraction does so in one frame at a time, which is even more limiting. Perhaps it explains why much of the reasoning about abstraction appears to get stuck in perennial language games, such as this:
“Real abstraction does not refer to ideologies that arise on the basis of material exchange of goods, or the labor process that allows such exchange in the first place. Of course, Sohn-Rethel is interested in accounting for “the conversion of the real abstraction of exchange into the ideal abstraction of conceptual thought” (Sohn-Rethel, Intellectual and Manual Labor, pg. 68). But this “conceptual abstraction” or “ideal abstraction” is clearly derivative, a mirroring of the abstraction at work in reality itself at the level of ideas.” —Ross Wolfe, The Charnel House
Here, Wolfe places abstraction outside the thinking individual entirely, arguing that abstraction in the mind is secondary to abstraction out there. According to this, there is a social and material process of abstraction that precedes our cognitive abstraction. It is also called ‘abstraction’ because it is processing information via compression, simplification, and reductive algorithms. The first iterations of eyes that nature evolved just perceived light, and then shape and color. Early eyes were rudimentary forms of abstracting the sensory input. Physical bodies are extensions of this process just the same.
By using our mental abstraction to stare into the abyss, we can get but a glimpse of it; abstraction stares back at us.
Ultimately, in this formulation, abstraction exists before humans do; it is a process by which life evolves. When we get to the human level, there is no eluding the fact that abstraction is the basis of thought etymologically, procedurally, and materially. Benjamin Bratton elucidates abstraction as a process of sensori-motor mapping, grounding it in the physical first, as an evolutionary process he calls “computational abstraction”. This applies to all creatures to the extent that they map their surroundings to determine “food, friend, or foe”. To a degree Jordan Peterson considers abstraction as mapping as well (via Piaget), and scales up from ‘exploration’ to the creation of myth and philosophy. This is brilliant in its narrow context, but Peterson ignores other meanings and applications of abstraction, and is ignorant of critical theory and sociology more generally.
Fast forward to the information age, computers are also doing computational abstraction, and the accidental mega-structure of global civilization is eating itself alive, binging on our data and material resources. Meanwhile most people live life on autopilot, outsourcing our own critical faculties to AI. The collective intelligence does not know how to think about thinking. The world suffers from an epistemic crisis — a post-truth dystopia — because individuals are not taught how to think (abstract) together. Individuals and institutions alike suffer greatly from ignorance and knowledge gaps. We are largely oppressed by bad information. The systems that run our world are basically functional but equally misinformed as people, and with maligned priorities. This is a problem of abstraction, in every sense.
Abstraction is a prismatic concept that can address the meta-crisis, and this can be demonstrated somewhat by mapping it to the Four Quadrants. Integral Theory is an inherently abstract method, and also an intrinsically self-limiting one, so we must enter into abstraction but then always check back with reality:
“With Wilber, the level of abstraction is always so high that it is difficult to get down to the level of empirical details — where scientific questions tend to be settled.” — Visser, Science Has No Answer (2016)
Below is a generic map of the Four Quadrants, helpful for familiarizing yourself with the basic structure and contents of it. As admitted, the map itself is an abstraction, and as such we can conceive of things in each box as abstractions. The self, a thing, culture, and a network are all abstractions, but it doesn’t yet tell us anything about how they abstract.
Integral Abstraction
Three levels of definition:
Abstraction has the etymological roots ab- (away, from) and tract (draw off). Together, abstract means ‘to draw away’ (from the object) or ‘to withdraw (from the senses).
Abstraction is generally defined as a conceptual process of complexity reduction that highlights the essential properties or first principles of a given object or idea.
Abstraction is a manifold term differentiated across and within many fields, including math, computer science, linguistics, neuroscience, psychology, philosophy, and social theory.
— Parsed from Introduction to ‘Abs-Traction’
In the above definitions, all refer to the colloquial sense of abstraction as thinking. It’s what enables us to think of the other forms of abstraction. Below I propose a four-dimensional version in which thinking is merely one aspect, and in many cases a derivative one. Through Integral’s Four Quadrants framework, we can sort out four main categories of abstraction: mental, physical, social, and material. They correspond to subjective, objective, intersubjective, and interobjective: the Upper Left (UL), Upper Right (UR), Lower Left (LL), and Lower Right (LR). The objective and external forms of abstraction link to the etymological definition just the same as the internal.
Within each quadrant there are further distinctions between types of abstraction. But in short, I propose that mental abstraction (UL) refers to different interior individual mapping and thinking processes. This is the subjective experience of abstraction; physical abstraction (UR) is about exterior individual object properties, positions, and relations. It is embodied, but objective; social abstraction (LL) works through interior collective concepts such as art, values, language, culture, and politics; and material abstraction (LR) are the exterior collective ways our shared external reality is shaped by processes of abstraction. These cover a range of abstract processes that when viewed as a whole convey the awesome (and somewhat hidden) power of abstraction. Below the image, I discuss each quadrant in further detail.
Abstraction in the Four Quadrants
In the Upper Left (UL), Interior Individual, mental abstractions are thoughts, concepts, and the manifold thinking processes and cognitive developmental trajectories. It includes your identity, your visualizations, your deconstructions, and distillations. This type of abstraction is the main type most people will be familiar with.
For us to conceive of anything else, all other forms of abstraction are mediated through the UL abstraction. Your frame, and language itself, determines how you perceive reality. The abstraction of climate change operates in the LR, but our ability to comprehend it depends on our development and depth in the UL.
Linguistics and semiotics add another layer of abstraction to our social being. The term ‘vicious abstraction’ applies here as a common way of distorting communication, and applies in a double sense when distorting abstract concepts themselves. It is what your mind edits out when you misquote someone, or distort information.
Under this quadrant we can also abstract as a form of meditation, or ideation (imagination). The self is conceived and experienced in the UL, abstractly. One has direct access to this type of abstraction implicitly, and it becomes more explicit through education. Jordan Peterson waxes on this type of “reflective abstraction,” invoking the work of Piaget. Daniel Schmachtenberger also employs “abstraction” in is his descriptions of thinking:
“One of the things that’s so interesting is with our capacity for abstraction, we cannot just think about our experiential self of the moment but we can think about ourselves in abstract terms, we can think about time abstractly, deep past and deep future, right. And that is what allows us to actually understand evolution itself, it’s an understanding of deep past and fossil record and astrophysics. They give us a sense of the ability to abstract laws that of how that change occurs over time that allows us a deeper insight as to how we got here and then also the ability to vision a future fundamentally more beautiful and more interesting, and then be part of that creative process. So, it’s worthwhile just noting that our prefrontal cortex and our capacity for abstraction is a pretty new phenomena.” — Daniel Schmachtenberger @ Emergence (2016)
When doing it correctly/methodically, I show supporting evidence that Abstraction Will Make You Smarter, and Abstraction Will Make You More Politically Moderate; those are two introductory articles on abstract thinking.
The Upper Right (UR), Exterior Individual, physical abstractions are expressed in physical form, and embodied in physical objects. Ernest W. Adams describes “physical abstractions like colors, physical quantities, times, and places.” The brain, behaviour, and the science that studies them all fall into this quadrant. The neo-cortex is the part of the brain that evolved specifically to abstract. Therefore the bio-physical abstraction in the UR corresponds to the mental abstraction in the UL.
Throughout the levels in this quadrant, nature and reality can be studied and ‘abstracted’ (put into abstract scientific terms, made intelligible). The relationship between the UL and UR quadrants, between mind and body, is mediated through abstraction in this way. (The human) mind arises from the body (brain), and reflexively acts upon the body. This is a relationship I articulated in detail in Mindhack: Strengthen Your MetaPhysique: The Quantum Physical Fitness Revolution, where I explore some terms that help to bridge the mental and physical: ideokinesis, psychosomatic, and kinesphere.
In the Lower Left (LL), Interior Collective, social abstractions include abstractions such as art, values, history, language, archetypes, people, etc. This is the socially constructed inter-subjective reality where our ideas, worldviews, and narratives play out. The political state is recognized as an abstraction, an imagined community, a collective identity, as articulated in The Abstract Society and other political science literature, and yet it often is reified to dangerous ends (ie. dying for one’s country). Borders are often sites of human rights violations, depending on who you labeled as, and where you are going. This quadrant is our social realm, our shared reality, our meta-narratives.
Race is partially socially constructed, an abstraction, and racist discourse is also sanitized by coded language (hence, ‘abstracted’ in the literature), as discussed in Vicious Abstraction and Systemic Racism. In this way, vicious abstraction occurs both in the UL and LL, as individuals commit rhetorical blunders (whether on purpose or by accident), and meaning and truth are ‘lost in translation’ and mediated by social relations. This carries over into The Black Art of Abstraction, which discusses both a renaissance in abstract art combined with renewed social justice struggles.
This Quadrant is also where my critiques of Peterson comes in to play, for his misuse of conceptual abstractions. In The Detraction of Jordan Peterson, I point out his ‘vicious abstraction’ (distortion, omission) and vilification of common sociological concepts: postmodernism, marxism, feminism, social justice. Through abstraction, I show how Peterson’s own abstract approach and political project fails in the bottom two Quadrants.
The Lower Right (LR), Exterior Collective, material abstraction is a sort of Holy Grail, where abstraction is a process that acts upon matter/ material. This is the domain of the environment, economics, and ecosystems, where Marx’s notions of commodity abstraction, abstract money, and abstract labour operate.
“Still retaining the primary meaning of ‘abstrere’ or ‘to draw away from’, the abstraction of money, for example, works by drawing away from the particular value of things allowing completely incommensurate objects to be compared (see the section on ‘Physicality’ below). Karl Marx’s writing on the commodity abstraction recognizes a parallel process.”
“The state (polity) as both concept and material practice exemplifies the two sides of this process of abstraction. Conceptually, ‘the current concept of the state is an abstraction from the much more concrete early-modern use as the standing or status of the prince, his visible estates’. At the same time, materially, the ‘practice of statehood is now constitutively and materially more abstract than at the time when princes ruled as the embodiment of extended power’.[7]” — Wikipedia
Building on Marx, the theory of ‘constitutive abstraction’ develops a more advanced approach to meta-theory building and engagement, also operating in the UL Quadrant. Engaged Theory (“constitutive abstraction”) proceeds along four levels of abstraction, though I do not think it corresponds cleanly to the quadrant model: Empirical (doing), Conjunctural (acting), Integration (relating), Categorical (being).
Like in Minecraft (albeit virtual), material abstraction re-orders the material of the world by processes of removal and construction. The LR quadrant is our interobjective reality, so we should damn well agree on it what’s happening in it, but there is much mystification at work.
More of my articles that have focused on modes of abstraction in the LR; The Abstract Empire of Global Capital (financial abstraction) as well as the paired theories Evolutionary Globalization (autopoietic systems) and Systemic-Conspiracy as Social Pathology (abstraction of war) explain a lot of phenomenon in this Quadrant. Further, in The Abstraction of Water, “abstraction” is the term used for extraction of groundwater, but has even deeper connotations in the context of water politics.
Likewise in The Abstraction of Pollution, “abstraction” is used to describe the way pollution is obfuscated and the regulatory process is obstructed. I put both of these in the LR because they related to climate change. But in all of these topics, human thinking and decision making is involved, and thus rigorous abstraction in about all Four Quadrants matters.
Conclusion
The last quadrant, the LR, brings home the importance of abstraction in the UL. If we consider it all as one process, where the material, social, and physical conditions all affect our thinking, and vice-versa, then we realize we weren’t thinking as freely as we previously thought. Everything is contingent on everything else. We can experience a drastic expansion of awareness and change of mind (metanoia perhaps).
The Four Quadrants are conceptually distinct but inter-related domains of abstract processes. In truth there is one integrated reality. The article How to Humanize AI with Abstraction concerns all Quadrants, as it invokes so many different forms of abstraction: human thinking, computer science, social concepts, and the material resources engaged building AI platforms, and in the further reshaping of reality through AI.
My goal here has not been to try to teach Integral Theory. One can get that straight from the source — Wilber and his books — or the larger Integral community. I am not a proxy for these ideas, but this offers a useful way to frame and teach abstraction, and maybe teaches something about Integral as well. Insofar as it concerns a greater theory of abstraction, I think there is more to explore here. One could trace a theory of social cognition, epistemology, and knowledge through all the processes and entities related to abstract education, or lack thereof. Indeed, that is why social theorists pursue abstraction at all, but perhaps also get lost along the way.
But what is here is not yet a definitive theory of abstraction, it is a helpful guide to the different types. Integral has been criticized as lacking depth in the Lower Right Quadrant, the world of systems. Wilber pays well-intentioned lip service to the LR in the spirit of Deep Ecology, but lacks an understanding of the material politics at play. Perhaps this is a step towards what Michael Brooks calls ‘integral-marxism’. And in light of Marx’s theories of abstraction, we could consider this a part of what I call meta-marxism.
With all the complexity behind, I want to drift off to some much simpler Integral diagrams. For a great example of an abstract representation of Integral, check out this mind-map of Integral Education (includes education, theory, historical roots, practice). Below are some other abstract models from Integral Theory.
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