Archimedes' triadic proof of the trisection of an angle.
"Mathematics, semantics and pragmatics properly applied to 'The highest probability, of the highest possibility, is the only possibility', creates an absolute wisdom logic and truth, when thoroughly explicated, by isomorphically uniting the triadic ancient mathematicians and philosophers, with the modern triadic mathematicians and philosophers". me
"One of the metaphysical principles of the Pythagoreans is called the Triadic Principle or the Law of Mean Terms. It is based on the idea that there can be no meeting between opposites, and therefore, for there to be a Harmonia, or Union, of the opposites, there must be a Mean Term, which has something in common with each of the Extremes. The Mean Term both connects the Extremes, but also keeps them separate by occupying the gap between them. Therefore, as we will see, Mediating powers are also Separating powers"... John Opsopaus
"...Therefore, another mean is required to unite the original mean with each of the extremes. As a consequence, the advancing Pythagorean analysis of Reality discovered an ever-proliferating family of triads. This is avoided by a more profound version of the Triadic Principle, called the Principle of Continuity. It recognizes that there is a continuum or spectrum from one extreme to the other. The proliferating triads are simply finer divisions of the continuum". J.Opsopaus
63 years of wandering in the wilderness of senses and intellects has brought me to the above title, to describe my brand of “Pragma”, the old Pythagorean name for pragmatic operations of mind and society. This post will be about the eclectic ontological geometry of a priori perception and action, or the simple/complex mechanics and actions of mind and nations___A priori, as it is about first actions, first.
Many have read and studied the varied fields of knowledge, accepted or rejected certain schools of thought, and may have come to certain conclusions or not. This matters not, as I plan to take you where you’ve most likely, never been. We’ve all read or heard the words of the thousands of master-minds of recorded history, whether mathematician, philosopher, scientist, spiritist, theologian, linguist or whatever___but, have we truly seen what we’ve witnessed? I say no, we’ve a lot deeper to trek___The forest is very thick.
Just look at perception, our first action. It first sees hunger and discomfort. A few days later perception opens its eyes for the first time, and an amazing fact takes place, by no intentional action of the individual___perception starts mathematically mapping the surrounding world, totally passively to the individual, yet most isomorphically perfectly matching the outside images, to the inside images of natural instinctual, self-functioning, perception and memory. This is the eclectic ontological geometry of passive perception on autopilot. Before we as individuals even decide to will objects into perception, nature has implanted our minds/brains/memories with the natural given ground, or I could say the a priori given ground of perception, and the natural given ground of nature, man and the universe, have passively entered and first started the natural induction processes.
Do we have any idea how complex the maths involved, in this earliest stages of development truly are? I’m not only talking about the image mapping transference maths/actions required, but we must realize perception herself, must possess all the ‘arithmetic’ ability potentials of these first feats, before we even leave the womb. Think about it. Perception can geometrize all these images, dimensionalize them, isomorphically map them exactly as seen, and all without the slightest error of representation. Just try personally to exactly draw/paint what you, as an adult see, on canvas. How close can you come to exactness? I think you’ll quickly get the complex picture, if I just recommend you do a simple thought trick. Picture a triangle in your mind’s eye. Zoom it small and then large. Do the same with a circle. Now the same with a square. Don’t cheat buy looking at the next few sentences. Stop, and repeat this several times. Now, take note. What did you see? Plato’s Forms?(he maybe interpreted it too metaphysically, but I think we’re mature enough scientifically to differentially see the reality of his Forms and Archetypes as scientific abstractions, and the same goes for the Pythagoreans, to our interpretations of their metaphysics and mysticisms)___Intuitionistically formed by the natural given scientific abstract perception. Was the triangle a perfect equilateral triangle? Was the circle a perfect circle? Was the square a perfect square? I’m willing to bet they were, as I’ve performed this thought experiment with many others, and the answers were always the same___perfect figures___but why and how? You didn’t even participate in making them perfect. The mind of perception worked alone, after you thought of the general term, and perception passively did the geometric/dimensionalizing/zooming perfection(that’s a bunch of isomorphic maths)___You can’t even do it free-hand on a piece of paper, yet passive perception can function as near ‘arithmetic’ perfection. IMO, this is why the early Greeks were so amazed with geometry, and no early school exceeded the depth of the Pythagoreans at geometry, and the earliest algebras they produced, as witnessed by the Pythagorean theorem, which btw relates directly to the golden ratio/mean/variable by way of Kepler’s Pythagorean triangle, built upon the golden ratio geometry, and all constructed with just a compass and straight edge. The above is why math is our superior a priori essence agent, and must be mentally maintained so, to truly and fully interpret logic and intuition’s facts of the actionably intelligent world of pragmatics, and its kissing triadic cousin, semantics.
As far as I can find, the Pythagoreans were the first to state ideas of “Pragma”, and it meant ‘operations’ of minds and systems, just as Peirce(basing his ideas on the early Greeks) interpreted it many years later in the pragmatic maxim. ; “Consider what effects that might conceivably have practical bearings you conceive the objects of your conception to have. Then, your conception of those effects is the whole of your conception of the object”. I have restated this as per the title as, “The Triangle of Triadic Wisdom, to Actionable Intelligence”, by joining Pythagorean thinking and Charles Sanders Peirce’s thought concepts. The Pythagoreans defined a triadic principle as the necessary “mean term” between opposites(they just didn’t possess the isomorphic/morphic knowledges and maths, we now do, though they did have morphic as a concept, yet not fully applied to their triadic system). This triadic structure of early Greek thought lasted until the later years of Aristotle, after Plato had died, when he then headed Greece down its dyadic Alexandrian road of destruction___Aristotle tried to eliminate the triadic___the most important perception element___from his system of pseudo-logics, and the empire’s reign of Alexander(Aristotle’s student) only lasted for eight years of senseless war, then divided and later fell to the Romans___Dyadic ostracism of the triadic___Not so good…
The Pythagoreans accepted three systems of thought and logic, 1.Monadic, 2.Dyadic, and 3.Triadic, which lasted up through Socrates and Plato’s eras(may have needed improvement, but not ostracism). It can be represented by a simple equilateral triangle, labled at its points 1.Intuition, 2.Arithmetic(Top), and 3.Logic, corresponding to the first three above. All three of both number series can contain triad trees, under triads, under them, while all three are also isomorphically interchangeably/inter-relational as to perception’s mechanics of chosen and unchosen “I” actions, as they all exist inside the perception agency of mind, as agents in the periphery of perception, to be inferred in by induction as needed. It may look complex at first, but it isn’t. Just consider any one agent, say intuition, being monadic in operation, meaning universal, can eclectically ontologically view and act with the other two agents, logic and math, and all their triadic tree sub-agents, through transductions, inductions, deductions and abductions___just simple isomorphic psychological/philosophical transferences. We do it all the time___every day___every second. It’s just the a priori mathematics of nature involved is stupendously superior to our feeble intelligences. And don’t take this as super-natural, as it’s not___It’s just a priorily naturally given mathematical complexity, just as is the given universal mechanics, and its related/constructed quantum mechanics, and Einstein’s field theories and maths.
I’m just trying to point out the fact, that if you want your mind to function properly, after the 2000+ year ostracism of one of its necessary entities, the triadic mechanics of perception, then simply adopt Hammurabi’s Code, “Know thyself, and the truth will set you free”. Many think it’s about transcendence, and nothing could be further from the truth. It’s about transc(i)ndence, not transcendence. It’s not about going or thinking above to the raw ego, it’s about going in and down to the senses in co-operation with the logic and math agents, fully understanding the eclectic ontological habits of all the people, and not just your chosen group. Most all the world’s great thinkers were eclectic ontological polymaths, not simple dyadic particularists, the world is so over-full of. The ‘Houses of Wisdom’ at Baghdad and Tehran clearly show this through history, as we would have no access to the ancient Greek wisdom, if it weren’t for the eclectic polymath ‘men of wisdom’ of these interim schools of thought, maintained through the early Dark Ages to the early Middle Ages, by wise men and women who truly cared. The world is really short on giving them the credit they deserve. There were hundreds, possibly thousands, working even by candle-light for more than a malenium, transcribing the Greek and other important early texts.
Now since I mentioned earlier the triadic triangle of thought, you may have noticed intuition being the included middle term of what Aristotle excluded with his interpretation of the pseudo-logics of the syllogismic logic. Aristotle was a brilliant ethicist, there’s no doubt about that, but after this early mathematical period under Plato’s Pythagorean mathematics school tuteledge, which is surely reflected in Aristotle’s Ethics, and Plato died, Aristotle drifted away from the Pythagorean method of using math to secure intuitive thought soundly within their triadic system, by banishing it to the scrap-heap of history, for about 2300 years, except in the Byzantine Empire era, and later in Peirce’s era, and lately with such authors as Bakhtin, Hintikka, Chiasson, Pietarinen, my-self and many, many recent others, re-investigating the history of our true “Triadic Utens” thinking, processing, and perceiving processes. Well, it’s been a long time since the Pythagoreans tried to develop a thorough school of thought, but It’s about time we started re-realizing the dynamic importance of this basic fundamental mechanics of the true geometry of our very own triadic a priori perception. We’ve been historically mind-crippled long enough!
Now many, especially the dyadic only crowd, would argue till the cows don’t come home, that the triadic can not function as math or logic, but they’d be wrong, as we’ve already, about 100 years, been using the intuitionistic maths and logics of L.E.J. Brouwer and many, many others in more fields of math, logics and computers than I could possibly list. So, I think it’s about time more dyadic analytic, continental, foundationalist and coherentist philosophers awoke from their pseudo-philosophic fallacy___The Aristotle/Frege/Saussure/Russell/Wittgenstein/Carnap/Quine/Chomsky seduction___and joined the real new world of truth to logical pragmatic actions, mathematical facts, and intuitive interpretations of. What do you think…?
Realize, intuition and logic function fine, when guided by the mathematical facts of practical and intelligent world actions… My next post will be about those practical and intelligent real world actions, it’s titled;
Flying Money___“Big Strong Dollar, Make Big Weak Nation…!”
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