In today’s post, I am looking at Batesonian abduction through the lens of George Spencer Brown’s Laws of Form (LoF). I have written about LoF here, here and here. Spencer Brown came up with an elegant algebra mechanism to capture the thinking process using a notation called as “mark”. I welcome the reader to explore the ideas in the links given above.
Laws of Form (LoF):
I will go through the basic calculations and notations needed for this post. I am going to use parentheses to capture the notion of the mark. For example, the distinction of an idea ‘A’ can be notated as:
(A)
The first principle in LoF is the Law of Condensation. This basically means that when an idea is repeated, it condensates into the original idea itself. For example, if I make a distinction of an apple, and I repeat the distinction again, I have not added anything new if the two concepts are identical to each other. The original concept remains the same. This is shown below:
(Apple) (Apple) → (Apple)
However, distinct ideas maintain their separation.
(Apple) (Orange) → (Apple) (Orange)
Through contrast and comparison of different ideas, we can achieve deeper understanding. This is shown below where we gain a better understanding of fruits in terms of Apples and Oranges:
(Fruits ((Apple) (Orange)))
Abduction:
With the basic notations of LoF out of the way, let us look at abduction. Abduction is a reasoning process introduced by Charles S. Peirce. It is a way of coming up with hypotheses to explain surprising or puzzling observations. It is different from induction (generalizing from observations) and deduction (deriving conclusions from general principles).
Peirce saw abduction as important in the context of discovery, the stage in science where new theories or ideas are generated. The modern notion of abduction has become more focused. Modern views of abduction often focus on finding the “best” explanation for a given observation. Peirce did not emphasize choosing the best hypothesis among many possibilities. He was more focused on generating hypotheses that could later be tested and refined. Peirce thought that while the hypothesis might be influenced by existing knowledge, abduction is still important because it leads you to consider new possibilities you have not fully explored yet.
For example, if a scientist notices that certain plants grow better near a specific type of soil, they might abduce the hypothesis that certain nutrients in the soil are helpful for growth. This hypothesis can later be tested through experiments and predictions.
Batesonian Abduction:
Gregory Bateson, the renowned anthropologist and cybernetician, developed a more nuanced interpretation of abduction. His approach emphasized understanding relationship patterns rather than linear cause-and-effect explanations. Bateson positioned abduction within the broader context of pattern recognition in networks, viewing it as a cognitive process for interpreting systemic patterns.
For Bateson, abduction was about seeing how different elements in a system relate to each other in a non-linear way. Instead of finding a single cause, Bateson was interested in contexts and feedback loops — how an element can be part of a larger dynamic pattern or system. Bateson, while acknowledging abduction as a method of forming hypotheses, placed it more broadly within the context of pattern recognition in networks. He saw abduction not just as a logical operation but as a cognitive process that helps us interpret and make sense of patterns in the world. For Bateson, abduction was related to the way humans and animals perceive and respond to relationships between elements in a ‘system’, not simply in relation to surprising observations or hypotheses.
Bateson asked in Mind and Nature:
What pattern connects the crab to the lobster and the orchid to the primrose and all the four of them to me? And me to you? And all the six of us to the amoeba in one direction and to the backward schizophrenic in another?… What is the pattern which connects all the living creatures?
His central thesis proposed that the connecting pattern is itself a metapattern—a pattern of patterns that defines the broader generalization of connectivity through patterns.
Bateson explained his take on abduction as:
Every abduction may be seen as a double or multiple description of some object or event or sequence.
The idea of double or multiple descriptions is very profound. In simple words, it is better to have multiple perspectives of a situation to have a better understanding of the situation. This represents a pluralistic framework. A simple example is the binocular vision we have. Each eye captures a slightly different image because they are located on opposite sides of the face. The brain combines these two images to create a single, three-dimensional perception of the world. Using our LoF notation, this can be described as follows:
(3-dimensional perception of the world ((Left eye image) (Right eye image)))
In terms of abduction, the brain “abductively” connects these two different descriptions (the views from each eye) to create a unified perception. The brain interprets the difference between the two flat images to infer depth – how far away objects are. This is similar to how abduction works by generating an explanation (in this case, the perception of depth) based on two related but distinct pieces of information (the two images).
The pluralistic aspect is the most important idea that I want to bring to the readers. In order to improve our understanding of a situation in complexity science or systems thinking or thinking in general, we should have epistemic humility and welcome different perspectives. Bateson also defined information as the difference that makes the difference. If the two descriptions are identical, we do not generate a new understanding. This would be very similar to being in an echo chamber. Now, this does not of course mean that you need to welcome ideas that are demonstrably absurd. The gist is that you need to be open to other perspectives and take a pluralistic approach.
Final Words:
The etymology of “abduction” means to lead away. It suggests leading away from our current knowledge to new explanations. It represents a movement away from what we already know. It is about being led away to new understanding.
A profound connection from Bateson’s Double Description suggests that real learning is not about accumulating single descriptions, but about developing the ability to see patterns across contexts. Using LoF helps us see why – the form (pattern((A)(B))) shows how understanding emerges from relationship rather than from things themselves. The Metapattern structure suggests that what we are really doing in double description is learning to recognize “patterns that connect” – metapatterns. This is why Bateson saw it as crucial for understanding complex situations like ecosystems or minds.
The LoF notation reveals something profound about abduction itself – it’s not just inference, but a leap to a new logical type. When we write (pattern ((A )(B))), we’re showing how abduction creates new knowledge by seeing across levels.
The use of LoF notation perhaps gives us a new way to look at things. I will finish with another example of improving our understanding utilizing a pluralistic approach. The paper, An update on Inuit perceptions of their changing environment, Qikiqtaaluk (Baffin Island, Nunavut) by Sansoulet, Therrien et al, offers an example of a pluralistic approach to understanding climate change, as it incorporates indigenous knowledge and perspectives alongside scientific observations. A LoF notation might be:
(climate-understanding ((scientific-models) (indigenous-knowledge) (economic-analysis)))
There are several examples in the paper that talks to the changes that the Inuit have seen as part of climate change. With respect to Inuit perceptions on climate change, including weather, climate impacts on the ice, and invasive/disappearing species, Inuit report the change in the ice as the main and most widespread change to have occurred in the last decades, with adaptation to this change being increasingly difficult and unsafe for hunters.
This integration of different ways of knowing exemplifies Bateson’s vision of abduction as a tool for understanding complex systems. It shows how the marriage of traditional knowledge and scientific observation can lead to richer, more nuanced understanding – exactly the kind of “difference that makes a difference” that Bateson emphasized. Through this lens, we see that addressing complex challenges like climate change requires not just multiple sources of data, but the ability to recognize and connect patterns across different domains of knowledge.
The application of Batesonian abduction and LoF notation thus offers not just a theoretical framework, but a practical approach to understanding and addressing complex challenges in our interconnected world. It reminds us that a nuanced and better understanding emerges from our ability to recognize and integrate the patterns that connect diverse ways of knowing.
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Linking up CS Peirce, Gregory Bateson, and G Spencer Brown around the idea of ‘Abduction’ and what CS Peirce (and, subsequently, John Deely) referred to as the ‘Semiotic Spiral’ which can be understood as an approach to understanding how reasoning plays into the scientific process of discovery that brings abduction, deduction and induction into a circular relationship, is really brilliant and, I think, quite powerful. There is an emphasis on the issue of how the relational approach plays into this in a powerful way. In fact, one might postulate that the relational is primary and the material derivative, which would be consistent with Peirce’s concept of ‘Synechism’ as a philosophical system based on the recognition of the fundamental role of continuity–as distinct from ‘Nominalism’ which is the dominant worldview that emphasizes the primacy of the material over the relational. This is a very important distinction which draws a line between the materialism on which reductive scientism is founded, and the idealism that Peirce proposed and has subsequently been promoted by Bernardo Kastrup as what he calls ‘analytical idealism’. However, I am not sure Peirce would be on board with Kastrup! Peirce proposed a ‘semiotic idealism’ or an ‘objective idealism’. What is now emerging as a very interesting ‘debate’ is that between Bernardo Kastrup and Rupert Sheldrake which can be tracked on Bernardo Kastrup’s blog at http://bernardokastrup.com/ and will be the basis for an upcoming online discussion being hosted by Alex Gomez-Marin, the Science Director of the Pari Center
( http://www.paricenter.com/ )…. on January 21, 2025… for more information about this presentation, see: https://paricenter.com/event/is-idealism-enough/ So that is a really good question! Is Idealism enough?? I would personally lean toward the position of Rupert Sheldrake on this debate, which I consider to be of fundamental importance at this inflection point in human history.
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Interesting as always.
Through abducting, one uses assumptions to formulate an hypothesis fitting one’s observations. We’ve trained ourselves – by using our brain – in finding the best fitting hypothesis in a situation- learning, experimenting, …. – and use this as a belief. We tacitly use Bayesian conditional probabilities.
P(H1∣E) := P(E)P(E∣H1)⋅P(H1) or P(H2∣E) := P(E)P(E∣H2)⋅P(H2)
It’s like learning to developing your taste – taste follows likelihood of f – in music, or even better, your taste of food. Your like “home cooking”. And it’s difficult to learn to appreciate another taste.
As Pierce also noticed: we tend to fixate our beliefs. After sometime, we don’t question our assumptions or hypotheses any more, but see everything confirming our belief. For instance “systems thinking”. We ignore that we’ve formulated an hypothesis.
Your brain uses these beliefs, patterns, tastes, likes, … to “predict” the future, so you’re better able to deal with them, when the facts happen. And vice versa, when you notices “like” it reinforces your patterns. This is how we like like like. (Thumbs up).
(Last week I asked participants in my workshop to remember the future and then work it out together).
When you dislike the facts, your beliefs kick in. One unlikes. And even worse, when your facts are fictions, – as all of our concepts are – you won’t like fictions (and beliefs) of others. So we use “taste” – disgust – to create and maintain distinctions between people.
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The point I wanted to make: every distinction is distinguished by someone. (Paraphrasing Maturana and Varela) So when making a distinctions, the distinguish-er is present. And one should add it in the distinction. I propose an eye <) (“eye see”)
So any distinction (apple) has be distinguished as an distinction by a distinguish-er. When it distinguishes itself, it can be written: <)(apple) (“eye see an apple’), because <)(apple)(apple) := <), you see,
<)(fruit(apple,pear,…). You can now “see” how a <) makes a distinctions. (fruit(apple,pear)) differs from <) (greengrocer)(fruit(apple,pear)) and a <) (fruit grower) (fruit(apple,pear)) and a <)(fruit-salade)(fruit(apple,pear)) and a <)(garbage can)(fruit(apple,pear)).
Also, interesting: <)(I<) and <)(I<))
So information can be written as: <) (difference, <)difference).
The pragmatic paradoxes become obvious to see. If not, consult the semiotic square by Greimas and Cortés. https://en.wikipedia.org/wiki/Semiotic_square
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Also playing into this debate is the work of two additional brilliant scientists and ‘theo-philosophers’. The more recent of these two is the theoretical biologist, Robert Rosen, who did seminal work on the distinction between living organisms and fabricated mechanisms in his books, ‘Anticipatory Systems’, ‘Life Itself’ and ‘Essays on Life Itself’. Rosen showed that living organisms are categorically distinct from fabricated mechanisms in at least two fundamental ways: (1) Organisms are closed to efficient causation while Mechanisms are open to efficient causation. (2) Organisms operate with ‘closed causal loops’ as a fundamental part of their relational model. As a result, while mechanisms are computable, algorithmic, simulatable, and strictly deterministic, organisms have none of these characteristics and, therefore, are categorically distinct from mechanisms and machines. Machines, as relational systems that admit to the mechanistic formalism, can be modeled as mechanisms whose relational model partitions into ‘states’ and ‘laws’ governing those states. The other of the two key folks whose work plays into this is the 17th century philosopher, Baruch (Benedictus de) Spinoza. In looking at the debate between Rupert Sheldrake and Bernardo Kastrup, they are clearly both idealists, but they have a very different approach to their idealism that centers on how the role of the Deity is to be understood. Does the Deity manifest the same form of reflective meta-consciousness as the finite human being does–which is Rupert Sheldrake’s position as I understand it–or does the Deity, being non-embodied, not share this capacity with the finite human, which, I believe, is Bernardo Kastrup’s position? This is a critical distinction between Kastrup’s analytical idealism and Sheldrake’s ‘spiritual’ idealism. I personally think that Spinoza, particularly in his final book, ‘Ethics’, has a great deal to contribute to this debate.
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I’m a big fan of both Spinoza and Rosen.
Trained as a bio-physicist I’ve always maintained that one should limit the concept of systems to human made (!) systems, like machines. If you can take out a part of a system and put it back, without changing the way it works, it’s a system. Living organisms can grow back some parts. (Also, we’ve got a very good word for self-organizing systems: organisms).
Spinoza postulated that (what we’re calling – JL) God is “Naturing Nature”, or ‘system’ generating ‘systems’. One cannot make a distinctoin between the concept of God and the concept of Nature. It’s evident from the story in the bible: Nature (itself) created nature, and human beings invented God, by naming. Of course, this induced the central (pragmatic) paradox of Life Itself. (I would have called her “herself”).
In idealism, the basic assumption consists of an idea of idea. We use ideas – being metaphors – to explain what actually happens. But like I said in my comment: when comparing two idealism with each other, the P(E), evidence, or the facts, disappear. The only things which are left are the likelyhoods. Which are beliefs, most of the time fixated.
The problems is not whether God(s) exists or not, the problem is it could be neither (nor exists, nor doesn’t) and both (exists and not exists). But not at the same time.
P(H1∣E) := P(E)P(E∣H1)/P(H1) and P(H2∣E) := P(E)P(E∣H2)/P(H2)
P(H1∣E)/P(H2∣E) := P(E∣H1)/P(H1) / P(E∣H2)/P(H2) := P(E∣H1)/ P(E∣H2) * P(H2)/P(H1)
“Black and blue
And who knows which is which and who is who
Up and down
And in the end it’s only round ‘n round
Haven’t you heard it’s a battle of words”
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