Pure Logic Is An Illusion. Axiomatics Means Choice, Thus Heresy.

The problem with pretending that there is something as pure logic is that any logical system involves axiomatic choices, and those, in turn, are a matter of emotions, feelings, proclivities, inclinations, and, generally sentiment, thus emotion. 

This initial axiomatic choice is even more basic than Second Order Logic Incompleteness theorems (which say that, given an axiomatic and basic arithmetic, one will still have to make further emotional choices down the logical road, beyond the initial axiomatic system).

It is not easy to find good and complete axiomatics. Euclid had five axioms, but he took for granted other axioms or operations which he used, but did not mention as the axioms they were. For example that a line divided the plane. With his fifth axiom, the parallel axiom, Euclid disappeared non-Euclidean geometry, which existed before and allowed to compute the size of the Earth, distance of Moon and Sun, etc. so Euclid, in one sense, shrunk minds.

In other words, a logical system will be as smart as what we want to do with it… An emotional will, so to speak. Emotional wills can be pretty stupid, as when religious fanatics want to kill everybody. The most famous case in history happened during the Crusade against the Albigeois in France when the legate of the Pope was asked how to distinguish good Catholics from heretics, and he replied: “Kill them all, God will recognize his own!”

In the European Middle Ages, the basic emotion in the matter of civilization among most people is that they owed the world to “God”. Later that emotion was overwhelmed by the realization that attributing fascism to a Dog in the sky, had been a collective illusion to make possible the rule of the few. The USA is presently undergoing such a transformation, as the belief in “God” is collapsing… in no small part due to its subconscious connection to the established order… which is entirely correct, same as Feudalism and God.

We know enough about neurology in 2021 to understand how neurology is driven and built, by emotions. Emotions are fundamentally resting upon topology, in a sense more fundamental than Category Theory itself (wild hunch on my part!)

A basic failure of old fashion thinking has been to claim that emotion should not influence logic, and, thus, does not influence logic in systems of thought which are advanced enough. That is true in a restricted sense in engineering, technology and some scientific theories… even then the question of why this particular fields have been elaborated and why they are used, arises, unavoidably

Pure logic is an illusion. Axiomatics means choice, thus heresy [1]. 

No saddles for Euclid. So not only did Euclid not ride horses, I presume, but he ignored the computation of the size of the Earth made contemporaneously by Phytas of Marseilles (and generally attributed to Erastothenes, who was born 70 years later, from anti-French racism)

Patrice Ayme


P/S: I used “Axiomatics” with an s, the plural, in analogy with “Mathematics”. Thus it is a mild neologism.. But if there is such a thing as “mathematics”, there is certainly such a thing as “axiomatics”, the former being deduced from, and varying according to, the latter…


[1] Latin hæresis, “school of thought, philosophical sect.” The Latin word is from Greek hairesis “a taking or choosing for oneself, a choice, a means of taking; a deliberate plan, purpose; philosophical sect, school,” from haireisthai “take, seize,” middle voice of hairein “to choose,”

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