The Power of Three: Ternary Logic, Triolectics, and Three Sided Football

Binary thinking seems to be a plague visited upon mankind, locking our minds into grooves that oscillate between the extremes of yes or no, true or false, love or hate, good or evil, left or right, black or white, communism or capitalism, utopia or oblivion, leaving little room to explore variances on the spectrum between polar opposites. This habit creates false dilemmas when all the available options get reduced down to just two. Entire fields of possibility are left unexplored.  When our minds identify with just one pole it tends to create fundamentalist antagonisms towards people and institutions whose thinking centers on the opposite pole.  When we ignore the vast terrain of middle ground that lies between, like ignoring the experience of those who live in the flyover states between the coasts, we miss out on many nuanced realms of meaning. The worst aspect of binary thinking is probably the deleterious effect it has on our ability to imagine what may yet be possible.

            Polarities do exist, and they often exert tremendous tugs at one another, as in the polarities of magnets, of male and female. When the polarities in question are political or religious in nature it animates the animus and people tend to slip into acrimony. The increased animosity between liberal Democrats and conservative Republicans over the past decade or more is a case in point. On some deep level I think they subconsciously get off on this attraction to each other. The foaming mouth of a fundamentalist Christian denouncing heavy metal, role playing games, and gay sex is as often as not projecting their shadow side onto the object of their hate. By the same token an angry anti-gun activist may harbor secret wishes to wield destructive powers over others. Is there a way out of these twin blind alleys of diametrical opposition? Can we find healing from our collective bipolar disorder?

            I think there is a way and it can be found at the fulcrum, the center point of the scales, the point of perfect balance and integration between two opposing poles. We can take steps towards moving to that fulcrum by exploring philosophy, in the form of ternary logic and triolectics, and by playing games designed for three teams, in this case Three-Sided Football.
​
            In the past philosophy wasn’t just a way for academics to get tenure. Serious contributions to philosophy and science came from engaged citizens who weren’t tied to publishing and pushing papers on regular basis just to keep their position. As “dollar dollar bills y’all” became the name of the academic game, theories seem to have become increasingly harebrained, existing only within the phantasmal realm of a mirrored echo chamber. Universities continue to flounder,  and the study of philosophy, including the philosophy of science, is a suitable pastime for those downwardly mobile dandies who don’t want to get their hands dirty on mudlarking expeditions, but would rather get lost in thought as they drift about as aspiring flâneurs. They will have to be willing to dirty up their minds, however, as mind is not separate from nature, as the Cartesian dualists would have people to think.

Charles Sanders Peirce (1839–1914) was an American philosopher, mathematician, logician and scientific thinker. His father, Benjamin Peirce, was also of scientific bent, and was a professor of astronomy and mathematics at Harvard University. Growing up in an environment of high intellectual achievement honed Peirce’s considerable natural gifts, and a career in academia was almost a given for him, if he hadn’t scandalized the prim and proper minds at Johns Hopkins University. His teaching job there was terminated without warning due to the fact that he was living in sin with his second wife, Juliette Annette Froissy, a.k.a. Juliette Annette Pourtalai, before the divorce from his first was official. Juliette also happened to be Romani, and her heritage was another mark of prejudice against the couple. This fall from the graces of higher learning left him unemployable at other universities. He ended up eking out a living by writing for scientific journals, crafting entries for Century Dictionary, and doing intermittent work for the U.S. Coast and Geodetic Survey. When his father passed away he was left with enough inheritance to buy a farmhouse on property near Milford, Pennsylvania, where the couple was able to remain independently poor. Their poverty was not quite genteel, but it did allow him to be extremely prolific in his writing, much of which is still unpublished. He often had to write on the reverse of manuscript pages because he was at times unable to afford fresh paper.

            As the university system implodes, those who have an interest in philosophy, science, or other academic pursuits could do worse than follow Peirce’s example, and continue to study, write and publish as independent scholars.

 Thinking in terms of threes seemed to be natural to Peirce. Triads, trichotomies, and groupings of threes are found throughout his work.  His system of logic consisted of three parts: speculative grammar, speculative rhetoric, and what he called critic.  He also sketched out a formal system of math based on triadic logic. Peirce is also credited as the philosopher who kick-started the contemporary study of semiotics, or the general study of signs and signification, representation and meaning. Peirce defined a sign as being triadic, composed of three parts, these being the sign vehicle, the object and the interpretant.

Peirce had suffered from the painful effects of facial neuralgia, a condition he had since his teenage years, which may have been partially responsible for the couple’s relative social isolation. Yet out of his suffering came the gift of his prodigious thinking and his obsession with logic. Peirce believed that some propositions in logic are neither true nor false.  He rejected the Principle of Bivalence that states that any proposition can only be false or true. This provided the motivation he needed to pursue triadic solutions.

In his concentrated thought Peirce was led to create a triadic logic of induction, deduction and abduction. Induction is an inference that is probable, while deduction is a type of inference where the conclusion is supposed to follow necessarily from the premise. In a deduction it is impossible for the premise to be true and a conclusion to be false. Abduction is the process of inference by which a hypothesis can be generated and formed. This term is also sometimes called retroduction, and can be further defined as a way for researchers to conceptualize that requires them to identify those circumstances the concept cannot exist without. Peirce took these even further than logical argument forms and used them as the basis for truth-seeking that he called “scientific method.” In his thought, induction, deduction and abduction become the three phases of scientific inquiry.

Just as philosophy contributes to the practice of science, so too can it contribute to the practice of art. Enter Danish painter and philosopher Asger Jorn (1914–1973), a co-founder of the Situationist International. In the early 1950s, after convalescing in a sanitorium where he was being treated for tuberculosis, Jorn wrote the text Held og hasard (“Luck and Chance”). He submitted this to the University of Copenhagen, which he hoped would approve it as a thesis. The text, however, was too unconventional. In it he argued that alongside the two dominant modes of thinking, philosophy and science, there was a third, valid alternative: an artistic mode. As per the title, he also wrote extensively on the role of luck and chance in all manner of situations.

            In Jorn’s text he speculated on how humans first learned to walk, and cited Erik Nyholm, who believed the first humans were apes who had learned to sing, due to a new jaw structure that allowed for more movement of the tongue, which in turn allowed for the creation of new sounds. Singing became an incitement to dance, and dancing distinguished early humans from other animals. Singing and dancing apes learned to walk by first learning to dance on their hind legs. From this perspective, Jorn suggested that game playing is a way to enter new stages of evolutionary change. The inclination towards pleasure and fun is an incitement to new behaviors. Games are also very often subject to the role, or roll, of chance, which brings about novel experiences.

            Peirce had also been an advocate of chance and its role in evolution. He thought that chance, what he termed Tyche, or Tychism, “must give birth to an evolutionary cosmology, in which all the regularities of nature and of mind are regarded as products of growth.”
            The Situationists espoused many interventions to break people away from the trance of the society of the spectacle. Games were used to break apart the rigid binary of work time and leisure time. They strove to show how play was not just a way to spend “free time” in the off hours away from office, factory, or cashiers register, but a way to transform existing energies and put them to use on life giving activities.

Asger Jorn had long been smitten with Hegelian and Marxist dialectics. While the dialectic method of philosophical argument can be traced back to Plato, and was used under the rubric of medieval logic, it was given a new lease on intellectual life when G.W.F. Hegel made it a core aspect of reality itself. Karl Marx and Friedrich Engels then got a hold of it and further retooled it into dialectical materialism. As communism spread, the idea of dialectical materialism became a major part of the intellectual ecology of the era, and Jorn was among those who became enamored.

Jorn, however, saw many restrictions in dialectical materialism. As a writer, philosopher, and theorist he tinkered on it, blending in his own ideas, and attempted to extend it with insights from quantum physics. What he came up with was Triolectics, a playful rebuke. In time, due to a thought experiment in his book Natural Order, it became the basis for Three-Sided Football.

Jorn came up with the game of Three-Sided Football (TSF) as an outgrowth of his writings on Triolectical Materialism. These were first written about in his pamphlet, “De la méthode triolectique dans ses applications en situlogie générale” (“The Application of the Triolectical Method in General Situology”) published by the Scandinavian Institute of Comparative Vandalism.  According to the members of the team Strategic Optimism Football, triolectics “went beyond linear transfers of energy, constructing spatio-temporal fields of possibility and negotiation. Not oppositional but superpositional – contradictions resolved by blending multiple simultaneous potentialities.”

For Jorn, Three-Sided Football was just a thought-experiment, a way to play with the philosophy behind Triolectics. In Natural Order, he wrote,

"Three teams meet on a six-angled plane instead of a rectangular one… First of all one wants to quickly discover that it is impossible to control who of the two enemies attacking is shooting the goal. It becomes necessary to turn the rules around… so that the victorious side is the side that has best defended themselves, and where the fewest goals have been let in. The victory has become defensive and not offensive... It will not at all be an exciting match... a third force can in this way neutralize a tension between two forces. That is why two-sided opponents are always aggressive or attack-minded, while three-sided are defensive. Whether this in itself marks a transition from dialectic to complementarity, I would like to leave unsaid. ... There are in these observations absolutely no political suggestions. I am only searching to find out what is actually going on… Whether a triangular relationship is static or constant, that would depend on whether there is an increasing tension. In that case this might lead to a real explosion, whereas the possibilities in the two-sided relationship are cancelled out by the two-sided fight’s neverending energy use.”

Such insights from Triolectics could be useful to those who want to escape the state of advanced rigor mortis that seems to be the inevitable byproduct of the forever culture war.

In the 1990s a number of post-Situationist groups began to bubble up in the UK and Europe. Psychogeography and détournement were the prime interests. In the writings of the Situationists they had found a still valid critique of art and the leftist politics artists so often kept as bedfellows. At an anarchist event in Glasgow in 1994 Jorn’s football thought-experiment descended from the Platonic realm of ideas, and the first actual games were played. Since then it has been played at different locations around the world. A World Cup for three-sided football was even organized at Jorn’s hometown of Silkeborg, Denmark.

 The game is pretty much played the way Jorn sketched it out. The winner of a TSF match is the team who gives up the fewest goals. If your team scores zero goals, it can still win, as long as the other teams gave up more goals than yours. The three teams play on a hexagonal pitch with three goal areas. Instead of splitting the time of the game into halves, it is played for a duration of three twenty-minute thirds. As the teams strive to concede as few goals as possible, various alliances are formed and dissolved in swift and fluid formations. With its roots in philosophical anarchism, the rest of the rules are flexible in the extreme, and a number of variations are played within the small TSF community.  

The members of the Strategic Optimism Football team contend that the playing of the game teaches a way of strategy that removes two-sided oppositions. “Strategy is no longer the illusion of mastering a totality. Rather it is the negotiation of undecidables that removes both the binary fixity of formal Aristotelian logic and the teleology of dialectical change at once. One is presented not with the binary and fixed categories construed by media-imposed ideology. Rather one can glimpse an externality – the larger matrix of general emergencies that contain and triangulate the particular emergency.”

 As the world struggles to find solutions for our many crises and predicaments, ternary logic and triolectics can help individuals and communities escape from the rat race of us-against-them, and develop defensive survival strategies. For those of us who seek liberation from political binaries, and the Cartesian binary thinking that has divided humanity’s experience and made it somehow apart from nature, we could do much worse than to spend time playing games of ternary logic inside our heads, and games made for three teams with our friends. If we engage with our fellows in an interplay of imagination, we might just catch glimpses of the futures that lie beyond oblivion or utopia.

RE/SOURCES:

Illuminating more than just these brief snippets of the deep thoughts of Charles Sanders Peirce and Asger Jorn is beyond the scope of this essay. They are all worth digging into for those who want to explore further. Reading and contemplation are among the cheapest of pastimes, especially if you access material through your local library system. In my original sketch of this essay I had included information on the three-sided chess variant. It didn’t end up fitting in the space allocated here. Readers may find it easier to organize a three-sided chess match than a three-sided football match, but the philosophical underpinnings differ.
 
The Art Story. “Asger Jorn: Danish Painter and Scholar” <https://www.theartstory.org/artist/jorn-asger/>

Bateson, Gregory.  Steps to an Ecology of Mind. New York, N.Y.: Ballantine Books, 1972.  Bateson’s essay “The Cybernetics of ‘Self’: A Theory of Alcoholism” is contained within this quintessential collection of his work that traverses across the disciplines of anthropology, psychiatry, evolution and genetics, systems theory, and ecology.

Burch, Robert. “Charles Sanders Peirce.” The Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.). Stanford, Calif.: Metaphysics Research Lab, 2022. <https://plato.stanford.edu/archives/sum2022/entries/peirce/>.

Colapietro, Vincent M. Glossary of Semiotics. New York, N.Y.: Paragon House, 1993. A useful text for anyone interested in semiotics. It contains many definitions of the abstruse terminology employed by Peirce.
Information Philosopher (website). “Charles Sanders Peirce” and “Gregory Bateson.”  <https://informationphilosopher.com/solutions/philosophers/peirce/>, <https://informationphilosopher.com/solutions/scientists/bateson/>. The Information Philosopher website, hosted and written by Bob Doyle, is a massive resource on philosophy and science as seen through the lens of information analysis. 

Jorn, Ager. The Natural Order and other Texts, trans. Peter Shield. New York, N.Y.: Taylor and Francis, 2017.
Peirce, Charles Sanders. The Essential Peirce, eds. Nathan Houser and Christian Kloesel. Bloomington, Ind.: Indiana University Press, 1992.

Rasmussen, Mikkel Bolt, and Jakob Jakobsen, eds. Cosmonauts of the Future: Texts from the Situationist Movement in Scandinavia and Elsewhere. Brooklyn, N.Y.: Autonomedia, 2015.
Strategic Optimism Football (website). “Triolectical Materialism and the Beautiful Game of Three-Sided Football.” <https://strategicoptimismfootball.wordpress.com/2015/01/07/triolectical-materialism-and-the-beautiful-game-of-three-sided-football/>

Parks, Tim. “Impossible Choices,” ed. Nigel Warburton. Melbourne, Australia: Aeon,  Jul. 15 2019. <https://aeon.co/essays/gregory-bateson-changed-the-way-we-think-about-changing-ourselves> A biographical essay on Bateson and his work. 

.:. .:. .:.
This essay originally appeared in 2022 in an issue of New Maps as part of my Cheap Thrills column.

.:. .:. .:.
​
The  writings presented here will always be free, but you can support my work by passing the essays on to others, and sharing the links to other sites and telling your friends.  I have also set up a Buy Me A Coffee page, which you can find here if you would like to put some money in my rainy day coffee jar. You could also buy my book if you want to support me.

☕️☕️☕️ 

​
Thank you to everyone who reads this and helps support the universalist bohemian art life by keeping me caffeinated and wired.