It is astonishing that the principle of non-contradiction has survived empirical observation. Although the criterion of scientificity is falsifiability, it would seem that the principle of non-contradiction is exempt from it. Many imagine that the world, natural or otherwise, is devoid of contradictions, and that if any are found, it is merely an illusion: either because a statement is poorly formulated, or because one fails to distinguish between the essential characteristics of a thing and its incidental characteristics.

This reformulation in case of contradiction, so that the statement does not contain any contradiction within itself, is the reason why the principle of non-contradiction is unfalsifiable. Language allows us to (re)formulate everything, through the use of synonyms, or even the creation of new words, in order to satisfy the principle of non-contradiction. An apple would not be spherical in shape, but it is spherical, you see…

Furthermore, the artificial distinction between the essential characteristics of a thing and its incidental characteristics creates a theoretical but effective sub-world in the practice of academics, in which those who imagine that non-contradiction is a characteristic of the cosmos take refuge, in a state of collective psychosis. In truth, the fact that our language allows us to formulate the characteristics of a thing, or a state of affairs, in both contradictory and non-contradictory ways is a good sign that, if not the cosmos, at least our language allows for contradiction.

There are good reasons to believe that paraconsistency is one of the properties of the universe, that it admits contradiction. Therefore, classical logic would be disconnected from reality, and it would be paraconsistent logic that conforms to metaphysical laws, if they truly exist.

Genesis of non-contradiction

The principle of non-contradiction was first formulated by Aristotle in his books of MetaphysicalHe presents this principle as the most certain and beyond doubt, but at the same time admits that it is unprovable. When he offers its justification, he reveals that it is rather incongruous in a democracy to hold two contradictory positions when we have only one vote. It is impossible for a citizen to vote for one proposal and against another: this is therefore not a metaphysical rule per se, but a political principle of democratic life.

Let's keep in mind that it wasn't Aristotle who classified this text as metaphysics, but rather Andronicus of Rhodes, who is responsible for the label associated with Aristotelian texts. However, this classification seems to have had an impact on the tradition. We far too often consider non-contradiction to be a metaphysical law or a law of nature, so much so that so-called classical logic falls apart as soon as it accepts a contradiction.

This is what we call the explosion principle. (If we have a lesser contradiction that is admitted as true, either in our premises or in the propositions that follow from them, we can prove anything, because we only need to hypothesize a proposition, recall our contradiction to demonstrate that the hypothesis is absurd, and thus admit the contrary proposition, whatever it may be, and repeat the same process for its opposite.) The idea is that if we have a contradiction, there is necessarily an absurdity: therefore, admitting an absurdity amounts, in classical logic, to admitting everything and its opposite. This is the slippery slope fallacy embedded within the system of classical logic, which the system of paraconsistent logic avoids by not allowing us to deduce just anything from a lesser contradiction.

On the tautological contradiction

The world contains a great deal of absurdity: the existentialists aren't entirely wrong that our existences are absurd. We live without knowing why we live. One of the myths that resonates most with us is the myth of Sisyphus, because we are all condemned to work, simply to have to repeat the task the next day. Why on earth is there always dishwashing to do? Who is responsible for such a state of affairs? I've washed all the dishes, and yet a few minutes later there are still dishes to wash. Let's look at two real examples of absurdity:

Example 1: The status of the embryo. It is both human and not human. It is a human in the making, certainly, but this "in the making" is precisely why there is so much debate surrounding the rights of the embryo: does it have human rights or not yet? The debate is not entirely settled because the embryo possesses these two contradictory characteristics, being human and not being human, regardless of the acceptable definition one gives to "human." We will return to these irresolvable debates later.

Example 2: It is raining and it is not raining.Have you ever seen the rain coming down on a sunny day?It is possible that it will rain and that it will not rain if we are talking about a territory, even if it is less than 100km²For example, if it's raining in the Plateau Mont-Royal neighborhood, but not in Côte-des-Neiges, we can say that the statement "it's raining and it's not raining in Montreal" is true. If we extend this logic to the entire Universe, the statement "it's raining and it's not raining" is always true, because there will always be, at any given moment, a place where it's raining and a place where it's not in this vast Universe. Thus, a contradiction has become a tautology.

Starting with example 2, it's helpful to open a discussion on tautological contradictions: this term, which is itself a tautological contradiction, allows us to see a certain aspect of reality. We often describe reality as chaotic, full of contradictions: sometimes it rains, sometimes it doesn't; here we bask in a ray of sunshine, and a few meters away, a cloud casts a shadow for others; for it to be daytime in America, it must be nighttime in Asia, and vice versa… it's clear that the Universe is the realm of all contradictions. Without specifying a point of view, the proposition (A & ¬A) would be more of a tautology than an absurdity.

The Socratic source of non-contradiction

At what precise moment did the principle of non-contradiction become a law of the cosmos? It is difficult to say. One might attribute this to the reception of Andronicus of Rhodes' classification of Aristotle's writings: in a text considered metaphysical, it is easy to assume that it is a metaphysical principle, whereas when Aristotle says of this principle that it is the most certain and beyond doubt, perhaps he is saying that it must be adopted with assurance and that no doubt should remain about it, as a political strategy to confront the Sophists. After all, when one criticizes the Sophists for being able to prove a thing and its opposite, it is easy to forge a logical weapon that defeats them for sure: forbidding the proving of a thing and its opposite.

This principle was supposedly used throughout the scholastic tradition when the texts received from Aristotle were held in undisputed authority. But perhaps we should blame the Enlightenment and its successors, who, in initiating critical thinking, failed to challenge the notion of non-contradiction, so self-evident did it seem. Logic became formalized when it became a fully-fledged academic discipline, and contradiction found its place in a system of logic that has been called para-consistent, forever barring it from the label of classical.

After all, ever since Socrates, it has had a bad reputation. It was by making the city's leaders contradict each other that Socrates ridiculed them and drew their wrath, leading to his unjust execution. The event of his death sealed the truth of his strategy of ridicule and elevated it to a metaphysical law. But in truth, it is merely a social rule: anyone who maintains a thing and its opposite is ridiculed; no one wants to be ridiculed, and it is therefore better to satisfy the conditions of what we call "consistency." Nowadays, a witness's credibility in court is destroyed the moment they contradict themselves… yet language and the world allow for contradiction.

On the unfalsifiability of the principle of non-contradiction

Karl Popper identified the criterion of falsifiability as the attestation of a statement's scientific nature. If we can falsify a statement, then it belongs to the domain of science. For example, "All swans are white," although false, is a scientific statement because it is possible to falsify it, and indeed it has been. For although it was long believed that all swans were white, the empirical observation of a black swan led to a revision of the statement's truth value, and it turns out that some swans are black. Although the criterion of falsifiability is itself unfalsifiable, it has established itself within the discipline of epistemology as a reliable sign of a statement's scientific nature.

However, the principle of non-contradiction does not address this. It is indeed impossible for any observation to falsify the statement: "The cosmos admits no contradictions." This is due to the nature of language. Language is riddled with synonyms and allows for neologisms; in other words, it is always possible to nuance, even to the point of inventing new words, in order to reformulate a contradictory statement and give it the appearance of non-contradiction.

Let's take the example of the weather in Montreal. Since "It is raining and it is not raining in Montreal" is unacceptable in classical logic, because one cannot conceive that the universe admits contradiction, the logician will accept the statement "It is raining in the Plateau Mont-Royal and it is not raining in Côte-des-Neiges" even if the two neighborhoods are in Montreal and therefore it would follow that it is raining and not raining in Montreal.

Since it will always be possible to rephrase a statement in such a way as to erase the contradiction, even its mere appearance, it is therefore impossible to falsify the statement "The cosmos admits no contradictions," even if empirical observation seems to support the contrary. Non-contradiction thus appears to stem from a belief akin to religion rather than a principle of scientific rigor. After all, if contradiction were not inherent in the cosmos, how is it that we contradict ourselves so often and that cognitive dissonance is such a widespread phenomenon?

Anti-contradiction: psychosis or delusion?

The religious nature of non-contradiction leads those opposed to it to imagine artificial constructs as real, such as essential characteristics of things, even of theories. If, for example, a sound theory exhibits characteristics of both relativism and non-relativism, instead of admitting that a good theory can have contradictory characteristics, one will decide in favor of one or the other by declaring, for example, that "non-relativism" is an essential characteristic of the theory, while everything relativistic is merely incidental, and if the theory must be definitively classified, it would be among the non-relativistic theories, or vice versa.

Things in the world have characteristics. It would be ludicrous to claim otherwise. But things in the world don't come with some characteristics that are essential and others that are incidental. They come with both essential and incidental ones. This is true for theories as well. This indiscriminate nature of characteristics, however, seems to fall by the wayside with the practice of classifying or labeling things. It seems that consistent categorization is imperative.

Even if, for example, democracy is characterized by both relativism and non-relativism, since every citizen has the right to vote, it is relativistic and absolute, therefore non-relativistic. It is absolute that the right to vote is inalienable, and it is possible to vote for anything, therefore it is relativistic. Democracy has these two characteristics, and thus the debate about how to classify it is destined to be irresolvable and reveal the positions of those involved rather than revealing the subject of the debate. Critics of democracy will cite relativism as an essential characteristic, because relativism is currently unpopular and democracy seems ill-suited to being defined as relativism. Defenders of democracy will posit absolutism as essential because non-relativism seems to be a minimum for any decent political system.

It is important to note here that social desirability is the deciding factor for each position. Just as Socrates ridiculed those who contradicted themselves, it is equally possible to ridicule a position or a thing by attributing to it characteristics that are unpopular, or even have a bad reputation.

Yet this categorization of characteristics, like the classification of Andronicus of Rhodes, is entirely artificial. It is not an intentional classification that Aristotle attributes to his writings, just as it is not an intentional categorization of the cosmos, either by its engineer, if such a thing exists, or by the chance of events that led to what we observe today. It is a sub-world that is thus created, a sub-world where essentially contested concepts take root and where it is possible to discourse endlessly.

However, this subculture in which academics live is disconnected from reality. At best, it's a world of illusion, but in any case, it takes on the appearance of a collective psychosis in which these so-called experts are steeped—experts who are the authorities in public debates and whom it is socially unacceptable to ignore. These days, anyone who speaks against (contradicts) the experts is ridiculed. I don't mean to say they're always wrong! Because the psychosis is collective, even architectonic, their opinions often turn out to be the "correct" ones. They will be confirmed when adopted, since the actions they prescribe take place within the very collective psychosis in question.

Conclusion

It would therefore be wise to undertake a complete reassessment of science by applying a so-called paraconsistent logic, admitting contradictory statements, provided they are acceptable. For example, it is entirely possible that the scientific paradigm in physics is not destined to be replaced. It is entirely possible that gravity is a law of the universe that simply does not apply at the quantum scale, and that a quantum theory of gravity is simply not a possibility. It is also entirely possible that a theory of everything that exists is not feasible, at least as long as we reject any contradiction whatsoever. It is entirely possible that the universe operates according to different laws at different scales. So many possibilities are not accepted as such, as long as non-contradiction holds the status it is most often accorded in academic circles.

In academia, contradicting oneself is even considered professional suicide. There is a certain intransigence mentality in debates that are nevertheless irresolvable, as we have seen, with the sub-world created by non-contradiction, creating artificial categorizations, such as essential and incidental characteristics, as well as through the reformulation of statements that are both acceptable and proven.

If we are to move forward together in this millennium, we must begin by abolishing a weapon we have forged to invalidate one another. A criterion that serves only to discredit and undermine is not a step in the right direction for what we might call living together. This issue deserves further research, both on the effects of the belief in non-contradiction and on redefining the limits of the scientific acceptability of statements, whether they contain contradictions or not.