At the heart of the pursuit of knowledge lies a principle, an axiom, worth examining. This is the principle of non-contradiction. Since Aristotle established it as the primary axiom of knowledge, it has been taken for granted, as a given, but is in reality merely a circular argument or even a simple norm of democracy elevated to the status of a fundamental principle.

If we return to Aristotle's texts, especially Book Gamma of his metaphysics, we notice that he struggles to find a solid argument on which to base this principle. It is perhaps even because of the nebulous nature of its foundation that Aristotle deemed it wise to make it the first axiom of all knowledge, like an infallible weapon against the sophists. The principle is stated as follows:

"It is impossible for the same to belong and not belong at the same time to the same thing, and from the same point of view and all the other specifications we could add, whatever they may be added against dialectical difficulties. »

Aristotle, Metaphysics, Book Gamma 1005b 17-23

We will see in this article that the principle of non-contradiction is in itself more of a postulate, or an arbitrary choice, than a truth valid at all times and in all places: I would even say that it is an artifact of language that leads us, through words of negation and terms of polarity, to believe that there are statements that do not hold up. And it is precisely in a democracy that the value of a statement is scrutinized all the more because there is an election and a crowd of citizens to judge us: moreover, because certain positions are opposed.¹It is useful to have a grounds for accusation of disqualification to use against one's opponent. Logically, then, few candidates are willing to relinquish such a weapon by denouncing it: the game, where one must be very careful not to contradict oneself in order to avoid being accused, is more of an enterprise of mass invalidation than a quest for knowledge.

Have we ever acquired knowledge through the principle of non-contradiction? No. It's a disqualifying principle that leads us to believe a statement is necessarily false if it's contradictory. It's a negative principle in every sense of the word. Could "the set of sets that do not contain themselves" contain itself and not contain itself at the same time? This famous Russell paradox cuts to the heart of the matter: like any resolution of a paradox, it leads us to re-evaluate our thought patterns and our worldview.

In this instance, I find in the concept of a hollow truth a positive principle of knowledge. A hollow truth is defined by a statement that is necessarily true because the antecedent of a material implication is false. If I say, "When it rains, I take out my umbrella," but it never rains, the statement would be true. However, a hollow truth is grounded in logic! It is when we apply it in "real life" or in natural language that it seems absurd to us. Yet the principle of non-contradiction operates in the opposite direction: it is not grounded in logic, but in "real life" it seems self-evident. (Isn't that what we could truly consider paradoxical?) The question addressed in logic here is: can A imply ¬A without ¬A implying A, and can this truth serve as a basis for knowledge? If I can convince you of this, then the non-contradiction is logically refuted because the contradiction would then be valid. In my view, Russell's famous "father of dogma" would then be resolved. Indeed, if the set can contain itself without that which it contains containing itself, the paradox ceases to be one. If that which it contains does not contain itself, then the set contains itself while simultaneously not containing itself, without this being false; we will be on the right track.

A standard for discussion, not a principle of reason

Right away, upon reading the definition of non-contradiction in the introduction, we can see an error in the principle. When he says, "and all the other specifications that we might add, let them be added against dialectical difficulties," all he is saying is that one must make a rhetorical, even sophistical, effort to "contradict," not what, but the one who seems to contradict itself. There is an infinite regress here. "And all the other specifications we could add" is virtually an infinite number of specifications. Language is such that it is not possible to enumerate them all: if it is not time or point of view, it could be the level of abstraction, modality, etc.

It is a total war, where every possible aspect of the relationship between one thing and another is called to the front lines to defeat the Socratics' main enemy: the Sophists, who delivered opposing arguments, capable of convincing the masses of one opinion and then its opposite. Non-contradiction as a principle is Aristotle's weapon against sophistry. However, this does not mean that all contradictions are worthless.

For example, the statement 'Aristotle is still very much alive despite being dead' is not invalid. As a philosopher, in this respect alone, his work is dead in that there will never be any new Aristotelian works, and in many ways, what he said is "outdated," in that we have adopted philosophies other than his in many respects, particularly concerning biology. But his philosophy is still very much alive in the sense that we apply his law of non-contradiction as a sacred text. His philosophy, as transmitted in his texts, is still very much alive. His philosophy belongs to both the living and the dead. It is his ghost that makes the paradox of set theory a "problem." It is his theory of non-contradiction as a principle of knowledge that leads us to believe in proof by contradiction, or even to have named it as such, as absurdity.

When he says "and all the other specifications that we could add that they be added against the dialectical difficulties He shamelessly points out that it is precisely the defenders of this axiom who add the parameters by which the same cannot belong to the same thing. Thus, Aristotle engages in both metaphysics and non-metaphysics simultaneously. The book is called "Metaphysics.". The passage on the axiom of non-contradiction follows directly from those on being qua being, and is the first axiom of knowledge. However, in stating the principle, he quickly enters into dialectical debate.

He himself admits that this axiom cannot be proven, because it would have to be done for every statement, which would be an infinite task. If it has to be done for every statement, then there is no logical proof, in the sense that the cogito is a logical proof of a first principle. And so, non-contradiction is neither a law nor a principle: it is a norm. A rule adopted when public debates in the Assembly present opposing viewpoints: when the time comes to establish a law, either it is established, or it is not; it could not be established without establishing it. Either one goes to war, or one does not. Far from being metaphysical, this law seems more like a political construct.

A contradiction is a necessary statementfalse lie

A contradiction, as a necessarily false statement, is itself a necessarily false statement. (Proof) For example, the following statement is contradictory: "I couldn't arrive on time because I left too early." However, it turns out to be completely true: "The subway broke down between two stations, and I had to wait for hours to be evacuated by a rescue team, but if I had left after the breakdown was announced, I could have taken a taxi." It is therefore true that by leaving too early, our anti-hero got himself into trouble, and if he had left later, he might have been on time. This is not merely a matter of language; the apparent chaos of the world makes such statements commonly true! Contradiction seems, rather than serving as a basis for invalidating the statement and the speaker, to be an opportunity to open the discussion to other, potentially higher, possibilities.

There is a thought experiment in quantum physics that clearly illustrates this point. Schrödinger proposes imagining a cat in a box containing a radioactive particle, along with a radioactivity detector that will release a poison lethal to the cat if it detects that the radioactive particle has decayed. Since the theory of quantum mechanics is probabilistic in nature, at any given moment, there are two possibilities: 1) either the particle has decayed, or 2) it has not. There is no way to know this "without opening the box," or, to put it more technically: without the act of observation that reduces the wave packet of the radioactive particle to a positive or negative value, we must assume that the particle is in both states simultaneously. Without observation, the only possible answer to the question "Is the cat alive or is it dead?" is "It is in a superposition of the two states." Thus, Schrödinger's cat, far from being just a demonstration of the absurdity of applying the precepts of quantum mechanics to real life (as some skeptics claim), is a real warning to wait until opening the box, going to observe in order to obtain, or even generate, the information we lack before throwing the cat with the poison from the box, believing that it is a zombie undead.

Quantum physics has this advantage: it shows us the fundamentally quantized aspect of life on Earth. Despite all the information circulating, we sometimes forget that although the information is there, it only acquires its truth value when we consult it. Will the subway break down? As long as nothing is mentioned on the news, to know, we must take it to observe it. Is the apparent absurdity of a statement nonsense? As long as we haven't observed it, it exists in a state of overlap: if it truly is nonsense, our investigation ends in a dead end, but if a contradiction contains a higher or unsuspected truth, it ends in a mutual understanding between two parties who, while maintaining the status quo to conduct an inquisition into contradiction, they could never have understood each other.

The standard of non-contradiction

Contradiction, defined as a necessarily false statement, is pure conjecture rooted in the nature of legislation in a democracy. It has emerged as a universal, metaphysical, primary cause of a statement's "falsity," a concept accepted by physicists, logicians, politicians, and even the most insignificant individuals alike. Let's examine how Aristotle attempts to refute contradiction:

"If the opinion that supports the contradictory is the opinion contrary to another opinion, it is clearly impossible for the same person to believe at the same time that the same thing is and is not. Indeed, someone who was mistaken on this point would simultaneously hold contradictory opinions."

Ibid. 28-32

Thus, it concerns opinions in terms of whether they are supported or not supported. In this line of thought, it is people who come to support an opinion, or not to support it by holding the opposite opinion: it is clear that Aristotle is not talking here about simple "propositions" such as "it rains" or "Socrates is a man".

It is not even clear that he is referring to a simple opinion in this passage, but rather seems to depict men who are deliberating: they are positions This is the point. This rule of non-contradiction is effective in deliberative assemblies: it is difficult for a single person to hold opposing views. One is either for going to war or against it. One votes for one candidate or another. Since we only have one way to vote, it is impossible to contradict oneself when casting one's vote. Even today, if we vote for more than one candidate at a time, our vote is considered invalid.

A standard of democracy

That said, it's easy to see how non-contradiction can be taken for granted in a democracy. If someone takes all positions at once, we can question their true intentions. For example, when a politician delivers two opposing speeches to two different audiences, our reflex is to doubt their allegiances and assume they are simply seeking electoral gain (seeking only the most votes, not the common good). We may adopt this stance as a form of self-protection, but that doesn't mean the individual is a charlatan. In fact, panelists spend far too much time untangling the apparent contradictions of politicians. Despite being a democratic norm, it primarily serves to discriminate.

Thus, when Aristotle says, "It is impossible to be a man and not be a man at the same time," he does not mean man in the biological sense of the term. For the Athenians, a man is a free man of the City: he speaks Greek and participates in democratic life. He has a place and a voice in the Assembly. Thus, he is neither a woman nor a slave. Either we have a voice in the Assembly, or we do not. This is not proof that the principle of non-contradiction "holds" or "is true," but it indicates that it only applies when it is constructed in this way. The norm of non-contradiction is the product of constructs: it is not a given of nature, it is made of the City.

A standard of discrimination

This standard primarily serves to discriminate against an entity: either by invalidating an individual within the administrative-legal system or a proposition in logic. In "real life," between two job applicants, or between two witnesses before a judge, we disqualify those who appear to have contradicted themselves, thus rendering them unreliable. Therefore, simply contradicting oneself is enough to be discredited and discredited. Even if one hasn't contradicted oneself, if the portion of the story told introduces contradictions into the narrative a judge or investigator is trying to construct, the testimony will be suspect and the witness considered a liar. Thus, the principle of non-contradiction serves to completely contradict oneself to the point of having one's testimony invalidated and one's candidacy rejected. Aristotle's first axiom of knowledge is a criterion of invalidation.

In formal logic, when attempting to solve a statement, we solve it by determining the truth value of each proposition. To do this, we proceed with what is called a proof by contradiction. This involves hypothesizing the opposite of the proposition to see if it would introduce a contradiction. For example, if in the following statement, "A and B implies A or B" is valid, and I question the truth value of A, I could perform a proof by contradiction by hypothesizing "¬A". If I manage to find a contradiction in it—that is, to deduce "A" from "¬A"—then "A" is absurd, and I have proven that "¬A" is true. However, there is one tautology that seems to have been discarded (as tautologies often are in "logic" circles). A(half-tail case), and that it is worth rediscovering, and I hope I have sufficiently shown the ethical reasons for departing from such a norm. Let us see what we can do when we admit that non-contradiction is not a bad thing. It is sometimes necessary for something not to be in order for it to be, and conversely for it to be in order for it not to be.

Filling up on empty truths

The tautology I want to clarify is the following: "A ≡ ¬A → A". This means that for something to exist, its non-existence must imply its existence. Even in cases where it does not exist, its non-existence materially implies its existence. The converse is also true: ¬A ≡ A → ¬A. Another way to formulate it is: "A does not imply (¬ →) ¬A if and only if (≡), non(¬)A implies (→)A." In plain English, this can be expressed as: "the being of a thing excludes the non-being of that same thing (aka the principle of non-contradiction) if, and only if, its non-being implies its being" This stipulates, among other things, that something can be true but false, as long as it is not simultaneously false but true. This can be written using the following tautological formulas:

¬(A→¬A) ≡ (¬A→A)

A proposition can be deduced from its opposite insofar as its opposite cannot be deduced from the proposition, and vice versa.

or :

∀A ∃¬A ⇒ A

For any proposition (∀A), there exists a contradictory proposition (∃¬A) from which it can be deduced (⇒ A).

This kind of tautology is defined in logic and mathematics as a "hollow truth," meaning it is true simply because the antecedent is not satisfied (why did they have the intuition that it was better to say it was "true" rather than indeterminate? I don't even want to ask them (they're the same ones who refuse to divide by zero). I argue here that the "hollowness" of these truths is an artifact of the compression of natural language into the language of formal logic: a compression that one might say lossy.

In truth, in natural language, this "hollow truth" is nevertheless quite easily filled. For the chick not to be a non-chick egg ¬(A→¬A), it had to cease being a non-chick egg in order to become a chick (¬A→A). Without the negation of the egg, the chick would never have become a chick. For everything, it must not be in order for it to be (¬A→A), and the fact that it is not implies that we have a notion of it, but the fact that we can conceive of something does not imply that it is: ¬(A→¬A). The non-chick implies the chick (¬A→A) if and only if the chick does not imply the non-chick ¬(A→¬A), the chick has hatched from the egg, but it does not become an egg again. The being of a thing does not imply the non-being of the same thing ¬(A→¬A) is identical to the fact that the non-being of that thing implies its being (¬A→A).

The non-being of a thing excludes its being is identical to the fact that its being implies its non-being.

Resolution of Russell's "paradox"

Russell's paradox is rather simple: the set of sets that contain themselves would be paradoxical. However, with this tautology, it is no longer so. It's simply that we have dismissed certain truths as empty, and we have ended up with a paradox at the very foundation of all knowledge. If the set of sets that contain themselves contains itself, then it does not contain itself, but if it does not contain itself, then it does contain itself. Russell's error here is having dismissed the empty truths. (A → ¬A) → (¬A → A). Thus, the set contains itself, but this self that contains itself does not contain itself.

Si the set {x|x does not contain x} contains {x} [or A →¬A],
so {x} does not contain {x|x does not contain x} [¬(¬A →HAS)].

What am I doing here? In French, I'm saying that the set contains itself, but this set of itself that it contains does not contain itself. Russell confuses the set {x} with the instructions {x|x does not contain x}. It's like putting a cake recipe inside the cake itself, even though the recipe tells you to print it out and add it to the cake. {x} is not {x|x contains x}. The famous "|x contains x" are the instructions to construct the set, but it's {x} that is the set.

I have no trouble conceiving this set. Let's say that {{a}, {b}, {c}…{w}} is the set {x|x does not contain x and does not contain {x}}. I simply add {x}, in which case it will look like {{a}, {b}, {c}…{w}, {{a}, {b}, {c}…{w}} } and, for short, {{a}, {b}, {c}…{w}, {x}}. Thus, the statement {x|x does not contain x} is satisfied… because x is not {x}. Thus, { {a}, {b}, {c}…{w}, {{a}, {b}, {c}…{w}} } does not contain { {a}, {b}, {c}…{w}, {{a}, {b}, {c}…{w}} } otherwise it would be an infinite regression.

Therefore, the set of sets that do not contain themselves contains itself, but not its definition or the instruction "set of sets that do not contain themselves." The set of sets that do not contain themselves is not itself the set of sets that do not contain themselves. Once constructed, it is merely a set without definition.Upon viewing this set, further deduction would be required to understand that it is the set of sets that do not contain themselves. On our screen, we would only see the following set: {{a}, {b}, {c}…{w}, …, {{a}, {b}, {c}…{w}…} } and we would not see the {x|x does not contain x}. Keep in mind that, although it might appear to be a copy of the set within the set, This copy does not contain itself, therefore it is a set that does not contain itself. and therefore fully satisfies the definition.

Every time someone explains the paradox to me, they repeat the sequence, "But if it doesn't contain itself, then it must contain itself, but if it does contain itself, then it doesn't contain itself..." and so on. As if they were putting the set in and taking it out one after the other, endlessly, like people who never want to stop working. The "Russell paradox" actually points to the set {x|x does not contain x but contains {x|x does not contain x}}. There, yes, there are contradictory instructions, because (¬(A →¬A) →(A →¬A)) is necessarily false. It's an antilogy (the height of irony for a logician!), but it's not a paradox except that we've witnessed a parade of doxa (opinions) on the matter for far too long.

Tautology as a zone of contradictory freedom

The principle of non-contradiction is challenged by a truth that is nevertheless considered hollow. Because I can have A from ¬A, without being able to have ¬A from A, contradiction has a place to occupy. For something to be both able to be and not to be, it must be both not and be at the same time. "Doing philosophy doesn't make you a philosopher" is identical to "not doing philosophy makes you a philosopher." This is a tautology, it is necessarily true: these two sentences say the same thing; they are identical. Together, these two contradictory statements form a tautology. As a tautology, it allows for a wide range of interpretations and uses.

For example, if a pedant belittles you by saying, "Doing philosophy doesn't make you a philosopher," rebuke him by repeating, "So not doing philosophy has made you a true philosopher." But you may have noticed the multiple meanings in these statements. Personally, I would use them more to mock the philosophical discipline than to carve out a place for myself within it. Because I sincerely believe that the more one tries to "be a philosopher" by conforming to the "united-to-Sith-era challenge-low"-sophie", the less one is, because it is not philosophy that is being done there, at best philology, at most the history of philosophy, or for the said ethicists, outright sophistry.

That's one possible interpretation, and that's why I discuss philosophy in terms of prophecy, and religion under the label "philosophy." I believe that a "friend of wisdom" is not a "philosophy expert." For me, being a philosopher is a life one lives, something one embodies in everything one does, like a true friend, and not something one simply knows. If you can summarize Kant's three critiques in an hour, bravo, that's quite an achievement, but is that proof of friendship for wisdom or rather of being a fanboy of books written in obscure German by, incidentally, a philosopher from centuries past?

Thus, this tautology—"doing philosophy doesn't make you a philosopher, therefore not doing philosophy makes you a philosopher"—can be used in many ways, in many contexts, with contradictory meanings, and so can someone else. "I like to speak in tautologies because that way I'm always right, no matter the context" is itself a tautology. As a friend of wisdom, this is precisely how I like to speak. And what others call "empty truths" are, for me, "a crucible of truths."

Conclusion

I therefore arrive here at a dismissal of the axiom of the principle of non-contradiction; it is not a principle, but rather a "code of conduct" that allows for deviations without requiring rejection, all while resolving Russell's paradox. I have shown how this norm of non-contradiction arose from Athenian pseudo-democracy and how Aristotle made it the primary axiom of knowledge of being: thus, from a discriminatory, if not debilitating, norm of nuances in "A-sang-boléss gênèrent-El" to a false principle holding science by the throat for both the physicist and the politician. I have also shown how its relaxation from primary axiom to "crucible of truth" makes possible the reappropriation and thewomen empowerment of people excluded by confused legal norms. I don't see why we should continue to chase contradiction out of our lives. In truth, I believe that people rarely contradict each other. It is far too often on the appearance of contradiction that we fuel demeaning narratives about one another.

Prophecy

When the first axiom of knowledge is primarily used as a weapon to attack each other's dignity, it is time to move from the front lines to the camp of wisdom, where there is space only for friendship, where I will be teaching fragments of Heraclitus: "If you do not expect the unexpected, you will not find it, for it is painful and difficult to find." And when you do find it, it is not what you expected: even when expected, the unexpected does not lose its quality of being unexpected.

Why does this text appear in the prophecies? Because the multiple meanings of a statement have never been the motto of the "scoundrels." It belongs to religions. When Jesus says, "He who does not carry his cross is not worthy of me," some wear a small one around their neck and are dignified by it, others take burdens on their backs and tell themselves that this is what it means to be a good Christian. When the Old Testament communicates the "will of God" through narratives, it is precisely to open up possibilities for interpretation and meaning, not to diminish them as this Immanuel Kant so skillfully does with technical words that he has polished to perfection with his own definitions. As for me, I use words loosely, to make them more poly-fiecious, so that we stop policing these proud de-polite-sharpened.

And if an academic felt offended by this text, I won't apologize. If you find funding to continue the war on contradiction, even less so. A being of contradiction like myself, who embraces it, isn't afraid of making such enemies.

Bonus:

Why is there being and not nothing? Because there is being, this implies, in all hollow truth, that nothingness must have materially implied being. We therefore know that non-being necessarily comes into being.

1. In Aristotle, in addition to having individual oppositions, the entire City is in fact divided into opposing groups: women and men, free men and slaves, Athenians and foreigners… It makes one wonder how Aristotle could have believed that non-contradiction is a metaphysical truth when he himself conceives of society as a totality of contradictions. ↩︎