Mathematical paradoxes in chaotic societies

Mathematical discourses are certainly peculiar for a large variety of things, but I think that the main two are: their foundations and their structure. At the beginning of every dissertation, there is in fact a moment in which the participants have to agree about some principles—the so called axioms—that can never be contested. They can be the formalisation of some common “truth” (such as “every number has its own successor”) or, in general, propositions that have no reason to be thought false in the framework of the topics in question. On this fundamentals the entire building of the conversation—the so called theory—is raised, following a set of rules that, thanks to the initial agreements, are perfectly aligned with the intents of all the parts and can only point to formally correct and thus, in this sense, true conclusions.

In this picture the concept of paradox seems to have no room to grow up—and this is true, but it doesn’t mean that its inspection thus has no value. In fact, a lot of mathematical effort was and is made by the scientific community in the analysis of “bugs” of the mathematical language, for example in order to discover some of its properties and maybe empower and expand its capabilities. With this in mind, it is clear that no collision can arise in a conversation based on this principles, even when a paradox is encountered: a mathematical paradox is just a nonsense proposition derived from an incorrect use of the rules of the theory but a perfectly reasonable one outside of the theory itself, thanks to the transparency of the ways that were employed altogether in order to obtain it.

I find interesting the employment of this formalism for the description of social mechanics, because while it is obvious that human relationships are neither transparent nor exact, I think that we can nevertheless link them to what we said in the first two paragraphs.

Paradoxes are quite common in our everyday social life. We often experience situations in which facts don’t resemble what it was said about them or, analogously, talk with people that affirm something clearly in contrast with their background or promises. Moreover, things can be inconsistent not only “with respect to themselves” (like contradictory people) but also with other elements of the reality. Why does this happen? A temporary answer can be found in the axiom- theory framework described above: everybody base their existence on a set of— moral, aesthetic, etc.—principles, because there is no other way to exist, but this set differs in its elements from person to person: every person has their own set of “axioms” from which they—rigorously!—derive all the theories of their life, and this personal starting point constitutes the source of all the ambiguities and collisions of the case. Without the discussion and agreement of the principles typical of the mathematical discourses, it is clear that all the successive propositions have an high probability of being in contrast, because they are based on rules that point in different and sometimes even opposite directions.

I would like to conclude this first article with an anecdote told to me by the fabulous Glory Mary, a friend of mine and editor of this metazine. The last two thousands years of human emotions seem to tell us that we decide most of our personal axioms when we are young. Maybe because we feel the reality more intensely or maybe because we let the very first principles encountered enchant us, but that’s it. For this reason, and due to the fact that parents and their sons have often quite a lot distant youth, the former and the latter typically end to have quite different fundamentals on which all the following events find a pretext—for example in fashion style. During a rebel, punk moments of her life, Glory Mary one day came back to home with a custom, all-painted pair of jeans with a giant Garfield on her leg. It was a supercool fit for her... but not for her mother. And that’s it, the story is already finish, because the existence of those pair of jeans ended that day, in a sad litter basket that the mom of Glory thought it belongs to. And we cannot blame her: what a paradox! A jeans with paint on it in the 80s...

words by STEFANO MARTIRE

visuals generated with AI Lexica Stable Diffusion inspired by Yuval Noah Harari & Glory Mary

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