State of the Form

Introduction

State, condition and form are almost synonymous. Is the form of a thing its state? But while it is hardly possible to speak self-reflexively of a form of form, there are states of states. States are usually system states, comprehensive descriptions of a thing. However, when we speak of a good or bad state, a stable or unstable, imaginary or magical state, these are states in which a state can be. When it becomes possible to describe imaginary and magical states, logic opens up to areas that have been suppressed and excluded by modern science and have led to the separation of the logic of science from myth, religion and art. It finds its way into a new state.

This work is based on the largely unknown mathematician and psychologist George Spencer-Brown (1923-2016), who distinguished states of this kind in his Laws of Form in 1969. If we ask what distinguishes a form from a state, it is the figures of the form. Speaking of the figure of a state does not capture what the state is about, but it can describe mathematically what a form is: Its schema. And conversely, the energy of the form shows in what way a state goes beyond a form: forms must be in certain states for their energy to be effective. All in all, the figures, states and energy of the form result in the dynamics of the form. Instead of asking for a multivalued logic, it is asked for a logic in states of different orders. - An earlier version was presented at the Laws of Form 2024 Conference in Liverpool, which took place on August 7-10, 2024, adapted variants at the Hegel-Kreis Tübingen on July 17, 2024 and at the Philosophical Colloquium of the Akademie für Ältere in Darmstadt on September 23, 2024. This resulted in many suggestions for continuing the topic. I owe further comments to Manuel Bachmann, Matthias Hauer and Werner Surek.

Examples In physics, the state of a particle describes which properties it possesses and which values were measured for these properties. The term 'State function' is ambiguous: it can mean both a state variable and the respective value that was measured. Quantum mechanics speaks of quantum numbers: Each particle is determined by its dimensions, e.g. the electron by four quantum numbers: The shell on which it runs around the nucleus; within the shell, its orbital; the angular momentum; the spin, which is comparable to a magnetic attraction. A particle is completely described by its state. For quantum mechanics, the trajectory of a particle is not a curve that can be observed in space and time, but the sequence of transition probabilities to change from one state to the next. Thus, with the physics of the 20th century, the state has taken on an overarching meaning. This has not remained limited to physics, but has also led to a completely new understanding in all other areas, including questions of culture and politics, to describe systems, recognize their development possibilities and enable action.

The building condition of a house and the state of health of a living being are typical examples from everyday life.

There are not only states of solid objects such as a house or a body: thermodynamics describes macro-states such as the volume, pressure and density of flowing systems, their energy and their information content. Biology adds macro-states such as the ability of self-preservation (e.g. repair mechanisms in the case of mutations) and self-organization (autopoiesis).

In this sense, we can speak of the state of one's own life or the state of a social order, the human condition (conditio humana). This is not merely a metaphor for transferring the idea of states from physics and technology to other areas, but can be defined in each case for itself and has given the relevant sciences such as sociology, psychology, political science, but also comparative literature etc. completely new possibilities for their theory formation (e.g. when a certain raw material of literary processing is in the states of a text, a film or a performance and switches between them).

Spencer-Brown asked about the common logic of all these examples and spoke of states within the logic. This did not exist in traditional logic and mathematics: there were only two possibilities for a form of judgment, a figure of reasoning or a mathematical proof: They are true or false, but to speak of states was only conceivable in order to emphasize certain stages of development and to remedy deficiencies, for example when a proof idea is initially in the state of a sketch, a program code in the state of a pseudo-code, until the only valid state is reached in which true and false can be clearly distinguished.

In addition to 'true' and 'false', there are sometimes attempts to add further truth values such as 'uncertain', 'undecidable' or 'unimportant'. But are these values like 'true' and 'false'? An uncertain value means that it has not yet been possible to determine a value with certainty. Obviously, 'uncertainty' is not a third value, but a provisional state in which the determination of a value has not yet succeeded or is incomplete. The situation is similar with the other proposals for additional values.

Spencer-Brown's Laws of Form have therefore been taken up primarily by systems theory, while philosophy, which remains within traditional logic, can do little with them to this day and largely ignores them. As far as I know, there are only important contributions within Hegel research that have taken up Spencer-Brown's idea.

Everyday language provides further examples of imaginary or magical states. Art and dreams deal with imaginary states. Since the separation of magic and science at the beginning of the modern era in the 16th century, these two areas have become increasingly alien and almost incomprehensible, and it is only since Freud and new art movements such as surrealism and film art, such as dream logic, that people have been asking about logics that differ from scientific logic and lead to a new understanding of logic. A similar question can be asked in mathematics: Do the imaginary values of mathematics have to do with imaginary states? Is a distinction to be made between a natural and an imaginary state in numbers, each of which can take on different values? Although everyone intuitively understands what a magical state is, it is not immediately clear how it relates to other states. Some authors, such as the mathematician Georg Cantor or the psychologist C.G. Jung, hoped to revisit suppressed traditions of occult, hermetic and magical thinking and use them to clarify open questions in their science.

Spencer-Brown's concern is already evident in his early work on probability and the patenting of a lift control system (automatic control of a passenger elevator). He emphasizes conflicts that cannot be resolved within traditional logic and its two-valued nature of true and false, existing and non-existing. When it comes into internal conflict, logic enters a new state that can be paralyzing or fruitful. With the imaginary, Spencer-Brown does not introduce an additional value that stands alongside the previously known values, but rather a new state in which new types of values can be determined.

Spencer-Brown's Laws of Form systematically show a development of states: Initially, he defines a form as the distinction between a marked and an unmarked state. In the further course, the unmarked state transforms into an imaginary, unstable, virtual and finally a mentally creative state. The unmarked state proves to be far more than the mere negation of the marked state. It contains the “formal seeds” (LoF, 101) from which further development can emerge and lead to new states.

In a word: Can the understanding of states of form lead to an exchange between magic and science, which was interrupted in the 16th century, and inspire both?

Possible consequences: In all conversations about both imaginary numbers and Cantor's stages of infinity, I have experienced how difficult it is to understand their special character. For me, understanding them as states of a new kind of order is the answer with far-reaching implications for logic, mathematics and philosophy.

The patenting of the Lift Control System

I want to start with a practical example: In 1965, Spencer-Brown filed a patent for an electronically controlled lift control system with which an elevator operator can be replaced by an automatic machine (Spencer-Brown, 1965a and b). An elevator cannot change direction everywhere, but only when it is on a floor. A conflict arises when it is requested from above and below at the same time. Where should it go first? The solution is to add a memory that only contains one value: The last movement was downwards or upwards. If there is a conflict, the elevator continues in the direction it has already taken. At the latest when it reaches the top or bottom floor, there can only be one clear request, so that it can turn around and serve the requests from the other floors. (This system is rigid and cannot, for example, react to emergencies when an injured person needs to be transported urgently).

This solution abandons Boolean logic. There are 3 variables, each of which can take two values, and therefore result in a total of 2³, i.e. 8 cases: Call 1 for requests from above, Call 2 for requests from below and the memory. Call 1 and 2 each receive the value 0 if there is no request and the value 1 if there is a request. The memory shows the direction of the last movement: 0 stands for 'last moved upwards' and 1 for 'last moved downwards'. As a result, the new direction is determined and the memory is updated.

This looks like a truth table. The following illustration is taken and revised from Spencer-Brown's patent applications (Spencer-Brown 1965a, 7; Spencer-Brown 1965b, 2).

Case	Call 1 ↑	Call 2 ↓	Memory	Movement	Memory new
1	0	0	0 (↑)	idle	0 (↑)
2	0	0	1 (↓)	idle	1 (↓)
3	0	1	1 (↓)	↓	1 (↓)
4	0	1	0 (↑)	↓	1 (↓)
5	1	0	0 (↑)	↑	0 (↑)
6	1	0	1 (↓)	↑	0 (↑)
7	1	1	0 (↑)	↑	0 (↑)
8	1	1	1 (↓)	↓	1 (↓)

The table is to be read line by line: In case 1, there is neither a call from above nor from below, and the last movement was upwards. The elevator stops and the memory remains unchanged. Case 2 is almost identical: Again, there is no call from above or below, but the last movement was downwards. In this case too, the lift stops and the memory remains unchanged.

In cases 3 and 4, there is no call from above, but there is a call from below. The last movement was up or down. In both cases, the lift moves downwards. The movement is entered in the memory.

In cases 5 and 6, there is a call from above, but not from below..

In cases 4 and 6, the lift changes its direction of movement and the entry in the memory is changed.

Cases 7 and 8 are critical, as they show the conflict when there are calls from below and above at the same time, but the lift can only be moved in one direction. In these cases, the memory decides: If the elevator has already moved upwards, it will continue to move upwards (case 7), and vice versa if it has already moved downwards (case 8).

It is crucial to understand that the memory does not introduce a third truth value, as suggested by a multi-valued or non-Aristotelian logic. Instead of introducing a third value, first-order and second-order states are to be distinguished in the lift:

– The 8 cases are first-order states. They describe the respective state of the system.

– In turn, two second-order states can be recognized in the 8 cases: Uniqueness (in cases 1 to 6) and Conflict / Dilemma (in cases 7 and 8).

The solution to the conflict/dilemma in cases 7 and 8 is not a third value that can be read off the system, but a new, independent axis (dimension, degree of freedom) must be introduced for it, which in turn has only two values: 0 or 1 (in this example: 'last went up', 'last went down'). It was Spencer-Brown's engineering idea to add a memory to the elevator and to introduce a rule as to how the conflict is resolved with the value entered in the memory. Many other solutions are certainly possible, but like this solution, they require an additional mechanism.

The solution patented by Spencer-Brown is not accidental, but intuitive: even if the elevator stops at every requested station and only then continues in one direction or the other, it is intuitive to speak of a momentum that Spencer-Brown's solution takes up. It can be assumed that nature proceeds in a similar way in comparable conflicts, for example when a decision has to be made about the direction in which a hand is to be moved or a blood pressure is to be shifted.

Mathematically, this solution corresponds to a coordinate cross on which the values 0 and 1 are also entered on the x-axis and y-axis, but with different meanings. The new axis is imaginary in relation to the original axis. In this example, it has arisen from the engineer's imagination and uses a value that cannot be read off currently but can be recalled from memory. From a philosophical point of view, we can say with Hegel: Call 1 and Call 2 belong to the sphere of being (what is in the present moment) and thus to traditional logic, whereas memory as imagination (recollection and memory of how it was) belongs to the imagination and the sphere of the mind. (cf. in Hegel Enz §§ 452-454, 461-464; TWA 10.258-262, 277-283).

The machine knows no history. It is set up by the engineer and behaves according to predetermined rules. It is slavish to them (parasitic) and incapable of any creativity of its own. For Spencer-Brown, this results in a second-order conflict: how can we move from an automatic (formal, parasitic) logic to a creative logic?

The two second-order states distinguished in the lift system (solvable, dilemma) became the two states with which Spencer-Brown begins the Laws of Form: the uniquely solvable state is marked, whereas the conflict state is open and unmarked within the given environment. In order to find a solution, it is necessary to go beyond the given system. In this example, this is the extension of the system by a memory. With the resolution of the conflict through the imaginary value, the way is also found how the juxtaposition marked - unmarked can in turn be led further into the distinction between real and imaginary states, etc., until Spencer-Brown is able to describe his own path in retrospect with the note to chapter 11 and distinguish between the mental states 'parasitic' and 'creative'.

The conflict described with the elevator shows the elementary form and with it the logic of how a conflict can occur and be resolved. This method is already formalized and can be adopted for far more complex conflicts if they are traced back to their elements and worked through from there. This even applies to conflicts that arise in antinomies and moral conflicts, as will become clearer below.

Note: This view of Spencer-Brown's patent goes back to a work published in 1998 by a group of authors led by Kreinovich (Kreinovich et al., 694-695). I owe the reference to Peiyuan Zhu. Their work is in the tradition of probability and evidence theory, i.e. questions that Spencer-Brown also started from (Spencer-Brown 1953, Spencer-Brown 1957).

Second-order states with Spencer-Brown

Spencer-Brown wants to bring logic as a whole into a new state: From a frozen, traditional, formal state to a state of creativity. Creativity is a mental state that is not brought about from outside by a deus ex machina, but rather arises step by step from the fundamental questions of logic when it encounters paradoxes and antinomies of its own accord and has to ask itself how it got into this state and how it can leave it again.

This requires a change of mindset: the goal of creativity cannot arise from a leap out of uncreativity, but there must be an impulse from the beginning that is already creative, even if it only leads in the final stage to a full understanding of creativity. Creativity is a cyclical concept, just as it is, for example, for sin and morality: sin came into the world through sin (Kierkegaard, 31), and only those who already have morality will find morality (Hegel, TWA 3.464). The task is to blow up and stir up the given state of logic by means of suitable forms or in more old-fashioned terms: to inspire (begeisten). This happens in the Laws of Form through a change of meaning in which states of different kinds are presented and emerge from one another. At each stage, pairs of different first-order states occur (e.g. marked or unmarked, stable or unstable), and at the same time each stage shows self-referentially what state the state is in at that stage (second-order states), until the state of mentality is reached at which it is parasitic or creative (LoF, 102).

Spencer-Brown already announces this in the introduction to his work:

“What is encompassed, in mathematics, is a transcedence from a given state of vision to a new, and hitherto unapparent, vision beyond it. When the present existence has ceased to make sense, it can still come to sense again through the realization of its form.” (LoF, xxiii)

Each stage shows a vision of what is meant by the respective state, which goes beyond itself until the final vision is reached with the 11th chapter and its coda.

– marked - unmarked The sensual stage. At the first stage, the elementary states of each form are seen and differentiated with the senses: As a demonstration, Spencer-Brown chooses the elementary sign , which he introduced and from which it is easier to see what is inside or outside than from the Sheffer line. All other signs can be constructed from this sign.

At this level, “spaces, states or contents” (LoF, 1) mean the same. For the sensory distinction between inside and outside, it would have been sufficient to speak of spaces and their contents. If they are also referred to as states, everyone understands what is meant: Being-in-something and being-outside-something. This encourages us to go beyond the difference between marked and unmarked and is a first mental activity: the inside is not only a space, but also a state of being marked by a boundary.

Spencer-Brown initially deliberately leaves open whether and which of these two states stands for existing or non-existing, for true or false. These distinctions will only result from the further course of the transformations of these two states

Understanding this is the greatest difficulty and requirement in order to find one's way into the train of thought of the Laws of Form: If, for example, the inside is marked as colored or as true, this does not mean that the outside - as Boolean logic claims - must be the opposite of this, i.e. black and white or false. It only means that the outside is not marked and it remains open whether and how it can be marked. It can certainly be black and white or false, but after closer observation it can possibly also be colored or true, or it can be in a completely different state in which no color or fixed truth value such as true and false can be spoken of.

The consequences of this unusual type of logic are discussed in more detail with probability theory and there with the distinction between probability and evidence (see Kreinovich et al.). The same applies there: If, for example, I know with a probability of 70% that it will rain tomorrow, this does not mean that there is a probability of 30% that it will not rain. It only means that there are good reasons that say with a probability of 70% that it will rain, while it remains open what else can occur and influence the weather. It is possible that completely different, unexpected events will occur that were not taken into account in the weather forecast. Evidence is used to assess whether this is the case. A distinction must be made: The probability statement of 70%, and the evidence that the calculation on which it is based is correct. - This misunderstanding shows elementarily how much the theory of probability runs counter to common perception and is counter-intuitive, because we have become so accustomed to the two-valued logic of existent and non-existent.

– imaginary The level of understanding (Verstand) and imagination. The distinction between marked and unmarked cannot be strictly maintained. Within the bivalent, marked state, conflicts arise whose solution must lie outside the marked state in a space that is an imaginary state compared to the marked state. This appears magical to some and a blind coincidence to others. The solution can no longer be seen with the senses, but requires imagination and understanding. It is necessary to inquire into the reason that led to the conflict (according to Hegel in his Science of Logic on Contradiction, TWA 6.64-70).

Spencer-Brown's solution was based on three insights:

– In mathematics, the mathematician, physician and astrologer Gerolamo Cardano (1501-1576), who was active during the Renaissance, introduced imaginary numbers that go beyond the realm of real numbers. Cardano worked on simple arithmetical problems for which there is no solution in the realm of natural numbers. Are there two natural numbers a and b such that their sum a + b = 10 and their product a · b = 40? Anyone will realize by trial and error that two such natural numbers do not exist, but Cardano succeeded in designing new (imaginary) numbers in his imagination that lie outside the realm of natural numbers but are also cyclic (in today's notation: and ): Although these numbers are not on the real axis and leave the realm of sensuality, their addition results in the directly recognizable natural number 10, and when they are multiplied, a new complex number is found in a rotary motion, which in turn lies on the real axis and results in the natural number 40. This is the archetype of the re-entry considered by Spencer-Brown (see the article on Imaginary numbers, Tydecks 2017).

– Frege defined terms by their courses-of-value (others translate: value-range). To put it graphically, this is the graph of a function. For example, the temperature curve and the blood pressure curve are value curves that describe the state of health. In some rocks, fault lines can indicate the course of geological changes. For Frege, the course-of-value is the extension of a concept. We only know about a thing what we can read off and generalize from its course-of-value. He hoped to show that every concept can be determined by its course of value, i.e. descriptively.

– From Wittgenstein's point of view, the course of value can be seen as an example of a propositional sign. This is an unusual and misleading expression: it does not refer to punctuation marks such as points, commas or question marks, but in the same way that a course of values describes a concept, a sentence or a related group of sentences can describe a concept. While the courses of value meant by Frege are sensually vivid, sentences can be used to describe concepts for which there are no visible or otherwise measurable quantities and their courses of value, such as the concepts 'soul' or 'worry'. They can only be made comprehensible with words, stories and possibly images of typical situations. If a sentence describing a term is itself taken as a unit, we can speak of a propositional sign: the sign of something that shows itself in this sentence. In a literal sense, this is a sign that encompasses the statement of a sentence in an image (icon, imago) and stimulates the imagination to understand it (WTLP, 3, 3.1, 3.12). A sign shows more in itself than can be said in words. Thinking further, this leads to the question of whether a language is conceivable whose signs have a far greater expressive power than the language we know. The science fiction author Samuel Delany explored this in a playful and creative way in his 1966 novel Babel-17. He gives the following example: If there is no distinction between I and you in a language, or between different genders, this shapes our thinking in a fundamentally different way than we are used to. This applies, for example, to the formal language of logic and programming languages. Conversely, the idea of a language can be designed that can stimulate our thinking far more than the languages we are familiar with. Similarly, in music, the question is asked whether there are unique melodies that immediately change the state of the listener (according to Helmut Krausser in his 1993 novel Melodien with examples such as the Miserere by Gregorio Allegri, probably composed in the 1630s).

Spencer-Brown recognized the inner connection: If not only real-valued functions (“single-valued functions”) and their graphs are considered as by Frege, but also functions in the realm of imaginary values, then their oscillating graph shows the solution of conflicts such as Russell's antinomy and other paradoxes (LoF, 97). As an example, he uses the oscillator function to name the value progression of 'true' and 'false' in the liar paradox: if the sentence “this sentence is false” is true, it is false, and if it is false, it is true, and so on (LoF, 60f). The liar paradox is neither true nor false, nor does it assume any of the other proposed truth values such as 'uncertain' or 'unimportant', but it is in a different state that can only be described by the oscillating graph of a function that runs in the domain of imaginary numbers. The circular and hyperbolic functions, such as the oscillator function, are represented mathematically using Euler's formulae with imaginary numbers.

The imaginary state is certainly not identical to the unmarked state, but emerges from it in a precisely defined way. Traditional mathematics reduces the question of imaginary numbers and their states to the introduction of a new calculus (the algebra of complex numbers with its own algebraic operations) and does not see the idea that Spencer-Brown is concerned with. Spencer-Brown shows how the imaginary state provides a new view of the unmarked state.

– Stable and unstable states Physical and technical view. The decisive factor is the memory function. When is it possible to rely on memory? This only applies in stable states. There is always an unknown residual instability, which physics and technology try to determine using perturbation theory and technology assessment. The unmarked state becomes the unstable state. Instability arises when the rule is disturbed and changes. (LoF, 64). Only in the stable state can the same rule be applied continuously and memory be trusted.

– Possible (virtual) and real states Developmental idea. States of different centrality.

However, unstable states are not only states of uncertainty and unpredictability, i.e. they have a deficiency. Only from unstable states can something new emerge. “All that is not information, not redundancy, not form and not restraints—is noise, the only possible source of new patterns” (Bateson, 418)

This is how the unstable state becomes the space of possibilities. This is where the “formal seeds” lie. For Spencer-Brown, they are “in a less central state” (LoF, 101). These are obviously states of different potentiality (virtuality) (see Leibniz and Gödel).

– mental states (parasitic, creative) Thinking like this requires imagination and creativity. Spencer-Brown gives the last section of chapter 11 the title Coda. There, another change of meaning occurs: The marked / unmarked or stable / unstable states become “various states of mind which we put upon ourselves” (LoF, 68). What can be meant by this becomes clear in the note to chapter 11, when a distinction is made between parasitic and creative (LoF, 102).

Is the term 'parasitic' suitable? With polemical intent, it means that the parasite is completely dependent on its host, lives from its power, energy and creativity and can only parasitize on it. This also applies to science when, on the one hand, innovators violate the existing rules and find themselves exposed to harsh criticism, while on the other hand, conservatives can feed off what innovators have introduced before them. “All applied science is seen as drawing sustenance from a process of creation with which it can combine to give structure, but which it cannot appropriate.” (LoF, 102)

I would like to add the distinction between paralyzed states and states full of energy. It can be used to describe phenomena that are of immediate political relevance today, when entire societies fall into a state of polarization and mutual blockade. Conversely, it is the question of the energy of form that can be used to describe states of form in which we can speak of openness and stimulation.

– Second-order states Overall, there is an insight into second-order states: the different states in which a state can be. Is there an energy that leads from one second-order state to the next? Is this second-order energy the measure with which the entire process stimulates and fuels its observer and their mental activity?

Epigenetic landscapes (Mons philosophorum)

What is the relationship between first-order and second-order states? Is there a state in which the two emerge from each other? This is shown by a diagram that is, so to speak, the propositional sign of the state of form. It does not have to be newly designed, but can be taken from a historical development that led from Gödel, Turing, McCulloch and Pitt to both the theory of cellular automata and the introduction of epigenetic landscapes, a new type of evolutionary theory by Waddington in 1957 (see the presentation of the historical development by Tara Abraham).

Epigenetic landscape. Source: Huang 2012, 151

The image of an epigenetic landscape goes back to Waddington's earliest work on epigenetics (Waddington, 29). While the progressions along the streams show how development is controlled by genes, the influences of the contour lines show how epigenetics can alter genetically controlled behavior. This representation has since been transferred to the description of other biological processes such as the development of cancer and tumors..

At this point, it must be sufficient to give a few hints as to how this image can be used to describe the states of form:

– The basis are cellular patterns and their transitions, whose formal foundations can be described with the Laws of Form. These are first-order states.

– The patterns are entered in a space that is spanned by a real and imaginary axis. The complex-valued courses of values mentioned by Spencer-Brown can be visualized in this space.

– The flow curves correspond to the respective marked state. What lies beyond the contour lines remains unmarked. The contour lines are the conflict lines. It is not possible to decide along the contour line into which valley the descent will take place. From the perspective of a valley, what lies beyond the contour lines is open.

– Attractors show blockages and the parasitic mental state. The movement only circles around itself and is unable to recognize any alternatives. Everything is in a state of drying up and dissolution. In contrast, a water cycle must be added, which is not shown in this diagram: the streams and lakes of the attractors soak the ground until the water rises within the mountain, causing the streams at the top of the mountain to gush and bubble. This is the state of natural reproduction and fertility. If the mountain is seen in its vitality, we can speak of the Mons Philosophorum, the flourishing mountain, an alchemical image that the founders of modern science such as Newton and Leibniz certainly knew and were more or less consciously guided by, even if, as far as I know, it cannot be explicitly proven in their published works. I see related ideas in Spencer-Brown when he talks about enlightenment.

This drawing was created as part of work on the development of tumors and cancer. Every living organism continuously undergoes numerous mutations, which in most cases damage and impair the control mechanisms (the information stored in the proteins and genetic material), but which can also lead to revolutionary innovations. No progress without the risk of failure. This can lead to the development of independent life processes within the body that can damage and kill the host body, or improve its life process, such as the viruses that protect an embryo from the mother's immune system. The attractors develop a momentum of their own in relation to the surrounding overall flow.

This image applies not only when marked and unmarked states can be distinguished on the sensory level, but also on the meta-level, when the history of scientific theories and their development processes in turn correspond to the image of an epigenetic landscape.

Related topics at LoF24

Catjects and third-order states

Is there a simpler representation for the third-order state? This could be the catject, an expression proposed by Dirk Baecker, which combines the pair of opposites subject - object in a new way and connects them with the prefix kategoreia (Baecker 2024b). Dirk Baecker spoke at LoF24 on video about the relationship between Spencer-Brown and Leibniz's monadology (see Baecker 2024a). This is a philosophical foundation of his concern to introduce a new concept into philosophy and systems theory in the form of catjects. The catjects substantiate the form of a movement named with the letter X, which begins with a something, leads across the boundary of its marking into its other and, in a context designated with n, leads back from the other to the something, whereby both the other and the something as well as the character of this movement change reciprocally in the course of this movemen

The description (marking) of a Something can be understood as a first-order state (marked state), its system state. The description of the relationship of a something to another and the common situation (the context n) leads to the second-order state. This is the state in which the system state (the first-order state) is, the relationship between the marked and unmarked state. The overarching movement that leads from the first-order state to the second-order state and back again is the third-order state.

For me, the epigenetic landscape (Mons philosophorum) is the paradigm of the third state, when first-order and second-order states not only balance each other fruitfully (or, on the contrary, dry up, exhaust), but also mutually enliven and flourish.

With the catject, a simple diagram was invented for this complex process, which goes back to Spencer-Brown. Spencer-Brown had introduced the form (LoF, 65). An area marked with the content of variable a changes to an unmarked area designated by variable b. This movement returns to variable a and changes it. In the catject, the variables a and b are left open. This results in a general form comparable to the cross and the re-entry independent of variables. Additionally, the context is added. The context can also be an observer, whereby it can be assumed that both the observer changes the observed through his observation, as well as being changed by the observed, and that the course of the observation itself continues to be developed in interaction with the observer and the observed.

Baecker emphasizes: Leibniz saw the divine bond as a third-order state (Baecker 2024a, 2, 12). All monads communicate with each other via God, who gives the system its ability to speak and whose activity is responsible for it all going well. Systems theories such as Luhmann's adopt this figure, but understand communication directly as a third-order state and are convinced that they can manage without a divine bond (without a God understood as a deus ex machina) (Baecker 2024a, 24). For them, communication ensures its own success (autopoiesis).

From the perspective of sociology, sociality is the paradigm of a catject that is to be understood from the movement of delimitation of independence and dependence (Baecker 2024b, 72)..

The members of a sociality are independent in themselves. Their state can initially be described as a state of mutually independent system elements (first-order state). When they recognize their relationships to other elements, they recognize their interdependence. Independence can only be understood in contrast to dependence (second-order state). This insight returns to independence and allows both independence and dependence to be seen in a new light, as well as the relationship between independence and dependence. - Consequently, the context in which independence and dependence recognize their interrelationship could be added.

The state of the economy and its literatures (Samuel Delany)

Robert Kiely (born 1987), a writer and literary critic who grew up in Ireland, came from London. He portrayed the science fiction author Samuel Delany (* 1942) (* 1942), who wrote very successful novels in the 1970s, distributed in Germany by Bastei-Lübbe, which is generally considered to be pulp fiction. He often mentions and quotes Spencer-Brown as well as other philosophers in his novels. He dedicates some of his work to the feminist SF author Joanna Russ (1937-2011), whose novels Alyx (1968) and The Female Man (1975) are worth mentioning.

Robert Kiely makes clear reference to the Marxist tradition in several contributions and has published his own poems and a text on the Scottish poet Peter Manson (* 1969).

While searching for the texts by Delany and Russ on Wikipedia, I came across an article by Ken James (* 1932) on Delany and Spencer-Brown. With Delany, James gives an inventive interpretation of Spencer-Brown. Delany asks why Science Fiction (SF) literature has flourished since the 1950s. Just as Spencer-Brown looked for the arithmetic that preceded and justified Boolean algebra, he asks about the social change that precedes SF and shows itself in the enthusiasm for this new genre. He sees it in the development of the economy from a barter economy to a money economy to a credit economy (James, 191). In times of the barter economy (I would rather say goods economy), the thing itself counted.

Goods economy: When differences of opinion arise, everyone turns to the matter at hand and seeks clarification there. The matter decides. Appeal to the cause. Everyone works on a life's work, a thing they have created that will outlast their lifetime. This can be a successful life that many people remember, or a great work of art, such as a great novel. It is valid in its own right, regardless of the various opinions and criticisms of how it is received and viewed. Frege emphasizes in a famous example that the morning star and the evening star are identical because they are the same thing, the planet Venus. Husserl wants to get back to the matter and, in an epoché, exclude everything that can only be explained from a certain point of view and does not belong to the matter. The language models developed after 1950, which led to ChatGPT and comparable applications, want to free the key terms (tokens) in texts from all grammatical elements and recognize the semantic networks that exist between the tokens, i.e. between the things meant by the different words.

Monetary economy: With money, relationships become the focus: What is my good worth compared to others? The focus is no longer on what is exclusively mine, but on who is best able to network and realize themselves in elective affinities (chemism). It is no longer the profession (or the vocation for a profession), but the ability to find the right partners without ever committing oneself to them as to a good, but to constantly develop the network of relationships dynamically. The responsibility and sense of responsibility for certain things and partners recedes behind the intention to let everything and oneself run in a free-flowing network and to be able to live oneself out in ever new facets. Happiness is experienced as flow. This is one of Delany's most important themes. For him, the network of partners expands into a network of genders. No one wants to be tied down to a specific, inherited gender in their life, but instead dreams of a society and a life in which there is not only a network of partners, but also a variety of genders in which everyone can move in their different life contexts and switch between them without having to commit to anything. Anything goes.

Credit economy: The monetary economy still sees money as something that can be hoarded, compared and spent. However, the creation of money opens up completely new possibilities, which Goethe already refers to in Faust (Faust II, Act 1, appearance of the Emperor and his entourage in the pleasand landscape garden): Mephisto recommends to the Emperor, who is suffering from a shortage of money: 'Simply print money, put it into circulation, and you will see how it will be accepted, traded with and the economy will flourish, if only everyone believes in the future.' Money creation emerged with the ever-increasing spending on wars and has prevailed since the decoupling of the dollar from gold in 1971 and has since led to a completely new economy. However, this is not about economic theory and economic history, but about the associated change in the way of thinking and culture. With credit economics, teleology replaces the relational thinking of elective affinities and chemism: teleology is used to examine purposes whose realization lies in the future. This once again puts the economy, science, culture and thinking in a completely new state. It goes so far that, since 1928, quantum physics has been predicting and observing antiparticles whose behavior can only be explained by the future, meaning that time appears to run backwards but is actually circular. The imaginary state is in turn shifted into a new state with the circular perspective from the future. It is similar with cultural phenomena. During Robert Kiely's lecture, I understood for the first time that and why the question of genders and possible future forms of life is more than just a fashion that is only attractive to a certain milieu.

Delany adopts Spencer-Brown's approach and at the same time criticizes it where Spencer-Brown, in his view, remains stuck in the economy of goods. Spencer-Brown places mathematics and formal language at the center. He looks to arithmetic and the two axioms that he has formulated as the basis for understanding Boolean algebra. In contrast, Delany valorizes natural language. Delany and his predecessor, the feminist author Joanna Russ, relativize the male view of things, for which the female view is only a variant. Instead of relying on the hard facts of a matter, Delany advocates the Analytics of Attention, which does justice to the respective situation and the images that emerge from it. Reflection is no longer merely a tracing back of images to the things that were depicted. Since then, a new understanding has been gained of the extent to which the future determines the economy. This is taken up by SF. They design possible models, numerous alternatives and abandon the point of view of a way of thinking for which, in the end, it is the thing that counts. When an image (model, future design, utopia) is created of a thing, it is no longer secondary, but changes the thing. Kiely sees initial points in Spencer-Brown's second book, Only Two Can Play This Game, which was published in 1971. It was a focal point at LoF24, in which Spencer-Brown wants to break away from a purely male perspective and describes failed love stories, for example. This book is on the borderline between a philosophical and a literary work.

States of Conversation (Florian Grote)

Florian Grote is Professor of Product Management at the private CODE University of Applied Sciences in Berlin. He transfers Maslow's hierarchy of needs (from the elementary physical needs such as breathing, food, sleep, reproduction to the level of self-actualization and its visions) to the corporate organization, especially in startup companies (the physical work level, productivity, communication, as well as the common vision) and emphasizes the interaction of the five levels: It is not enough to describe what system state a company is in (turnover, number of employees, employee surveys, etc.), but it is also about the relationship and balance between the different levels.

Building on this, he presents an extended language model that analyzes the question structure and recognizes whether questions are only being asked in a certain direction. This is not only evident in management consulting (what questions do a company and its departments ask a team of consultants), but applies to all conversations. The language model should be able with its answers to take better account of previously neglected aspects and make the conversation as a whole more comprehensive and balanced. For example, questions are often only asked one-sidedly at the material level about how turnover can be increased, or at the communication level about how networks can be better promoted within the company, or whether the company has visions with which it can address its customers. However, the aim is to promote the interplay of all levels

States of Conversation:

– System state: what is being talked about, in what language, what words are being used, who is talking, how long is being talked about, various statistical evaluations of linguistics

– Dialogue ability: are the speakers able to listen to and respond to each other, do they have a feeling for the conversational situation. Is it just monologuing and working through scientifically proven, empirical knowledge, or is there harmony between several voices as in a choir and a music group?

– Creativity: does something new emerge from the system and the dialog, is a mood for innovation or conservatism fostered in the conversation and can it develop?

Sigle

LoF = George Spencer-Brown: Laws of Form, New York 1972 (Julian Press) [1969]; siese.org

TWA (Theorie Werkausgabe) = Georg Wilhelm Friedrich Hegel: Werke in 20 Bänden. Auf der Grundlage der Werke von 1832-1845 neu ediert. Red. E. Moldenhauer und K. M. Michel. Frankfurt/M. 1969-1971

WTLP = Ludwig Wittgenstein: Tractatus Logico-Philosophicus, Side-by-Side-by-Side Edition; Online
zitiert wird nach dem Nummerierungssystem und nicht die Seitenzahl

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