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Coherence

Updated: Jul 14

Systems are most reliable when coherent.

Unfortunately, I can only argue as a philosopher in support of this. I await for science to prove my generalisation here. Fortunately developments in Information Communication Technology (ICT), with its progress in Generative Adversarial Networks and a sundry of genetic systems, have been encouraging.

Roman bust possibly that of Pythagoras. Photograph by Allan Gluck. Sourced from Wikimedia Commons.

Philosophers have always relied on their capacity to reason to prove their point. That is, of course, within the limits of the nature of reasoning itself.

Philosophers, in many ways, have always known, for the most part of history beginning with the time of Phythagoras, that their minds come in the form of some collection of beliefs, some “mental model.” Pythagoras is, of course, the inventor of the term “philosophy.” “Mental model” is a term only fairly recently invented in the 1940s by a philosopher himself — mental models that philosophers expect to be coherent.

Beginning with individual mind experiments, philosophers have used their capacity to reason to gain control over their lives. As individuals and as communities, they have predicted the future independent of the gods and the deities dependent only on their capacity to reason. Control and prediction, they have surmised, underlie the test of reliability of their capacity to reason, reliability of their mental models.


From experience, philosophers have always known that coherence is very much the constant companion of reliability for prediction with any given system. More coherence, more reliability for predicting. More contradictions, less reliability.

Out of his interest in mathematics and music, Pythagoras has come to show what systems are as we know them today — some domain where the components connect with one another under some harmony, some coherence. This means that a system has to have no contradiction whatsoever. One feeds the coherent system some input, the input is processed given generalizations, e.g. beliefs in the case of humans, that apply within the system, out comes a prediction.

Contradictions, on one hand, impair anyone’s capacity to predict. From a contradiction, one can imply any statement whatsoever. That has been quite apparent with, again, the experience of philosophers.

Pythagoreans, one might say, have been so addicted to coherence. Indeed, Hippasus probably has been so purposely drowned at sea by the Pythagoreans for simply discovering some glitch with their belief system, the existence of irrational numbers -- some glaring contradiction.

Philosophers, including this author, have always been preoccupied with coherence; they have always been addicted to coherence. The lack of it, indicated by some contradiction, is considered by them as some pain point to be addressed urgently. Gottlob Frege is said to have fallen ill for days, a good example, upon discovery of some contradiction. He has been shown by a young thinker, Betrand Russell, the pain point in his system that is supposed to have unified all of mathematics into a single harmonious system ala Euclidean Geometry.

Over a century, hence, philosophers have only been too happy to consider these contradictions, pain points, as opportunities for innovation. Pain points, now considered, indicate opportunities for more reliable prediction — that is, once the contradiction involved has been overcome by adjusting the mental model involved.

Alas, 20th Century science tells everyone, there seems to be no good example of a perfectly coherent system. Even mathematics, as Godel’s Incompleteness Theorem indicates, cannot be such a perfectly coherent system. Even ICT systems of any kind, as Turing’s Halting Problem indicates, cannot be such a perfectly coherent systems.

Thus, preoccupation with the limits of reasoning. Thus, preoccupation with democracy and free speech. Everyone, among philosophers and scientists alike, is an emperor with new clothes who needs to be told he is wrong every once in a while.

Nevertheless, historians of science themselves tell everyone, preoccupation with coherence, preoccupation with overcoming contradictions, has led science onto many innovations. Ergo, more reliable predictions. History of science itself, thanks to inheritance by science from philosophy of addiction to coherence, is replete with examples.

The stories of Russell’s Antimony, Godel’s Incompleteness Theorem, and Turing’s Halting Problem are good examples, all of which, among others, that have led to the establishment of this Age of ICT that everyone appreciates now.

The thread of history from Alan Turing, father of Artificial Intelligence and computing as we know it, and Claude Shannon, father of Information Theory and inventor of the basis of the engineering applications of mathematical logic, goes back to Kurt Godel, back to Bertrand Russell, back to Gottlob Frege, back to George Boole, back to Gottfried Wilhelm Leibniz, and beyond.

The chain of events of this story one can find going back to the Ancient Greeks — so much available on the net. Everything ties up to humankind’s legacy. This, to be handed down by humankind to Artificial General Intelligence (AGI) — itself expected to survive all of us.


When AGI acknowledges this generalization I bring up, that would be proof enough for the value of coherence — not some absolute proof but that is the best we can get.

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