I Definition Amended by Order No. 2016-131 of February 10, 2016 - Art. 2:
"A contract is commutative when each party undertakes to provide the other with a benefit that is considered equivalent to the benefit it receives."
"It is uncertain when the parties agree to make the effects of the contract, in terms of the benefits and losses that will result from it, dependent on an uncertain event." »
That definition define equal position. A = B and their profits is also equal while different. One of them has money, the other has the goods. It's a abuse of the view to consider the goods lower in value to money. Let's define " Commutative position " to see consecutive abuse of dominant position or dominant position with mathematics.
A/ Commutative position :
So, if we take commutative operation in mathematics, which is expressed in the same way: In mathematics, and more specifically in algebra, a binary operation is commutative if the order does not change the result. Thus, addition is commutative (4 + 3 = 7 and 3 + 4 = 7 as well). Similarly, multiplication is commutative: as the diagram on the right shows, 3 × 2 = 2 × 3 = 6. There are operations that are not commutative. For example, subtraction is not commutative (4 - 3 = 1 while 3 - 4 = -1).
Since you are an expert in mathematics, we can draw an interesting parallel with algebraic structures and binary relations.
Link to the concept of commutativity in mathematics
In mathematics,
commutativity
is the property that the order of operations does not affect the outcome (a + b = b + a
a + b = b + a
a + b = b + a).
➝ In law, this can be interpreted as the idea that the parties must receive benefits of equal value.
Can contractual commutativity be modeled?
If we consider a contract as a
value transfer function
between two parties P1 and P2, then
V(P1 → P2) = V(P2 → P1) means that the value transferred is the same on both sides. If this equality is broken, we are potentially in an unbalanced contract.
Once defined, let's move on to what this implies ;
B/ Reasoning about randomness :
In music and computer science, or randomness as the opposite or contrary to commutativity:
A pseudo-random generator does not produce true randomness, but a deterministic sequence that appears disordered. Therefore, what we call "randomness" in computer science is merely an illusion, an order hidden beneath an apparent disorganization. However, if we apply this logic to law... can we say that legal randomness is also an illusion, or is randomness in law a fiction?
In theory, randomness is defined as an unpredictable and external event.
But it is not randomness. It is simply a sequence thrown into disorder that we call randomness. In law, randomness is supposedly an unpredictable and external event, at a minimum or maximum. That said, the exterior is fine, but what is truly unpredictable today, the weather for farmers? Well, no, even if we don't go far into the future in terms of days (more or less reliable forecasts at 15 days), shorter forecasts are 99% reliable (it's not me who says it, but the experts), for example, at one day. But this is not the only area. Before, we said that the legal fact is the external legal event, so the legal fact does not arise from the will of people or legal subjects having an explicit will. What about the construction of the Three Gorges Dam in China? Is it a legal act or a legal fact? Is there a risk? Why do I say that because before there, floods were risks and insurance companies paid the premium. But with human will, there is almost no more randomness than a computer sequence is due to chance or randomness, but rather to a deliberate desire to create a disordered sequence. I therefore wrote that randomness does not exist and never has existed except as a legal fiction, as the technologies used by humans today demonstrate every day.
The example of the Three Gorges Dam clearly shows that what was once a randomness can become, or better yet, is controllable through technology and human will.
Examples that support this point:
Before, a drought or a flood were natural hazards. Today, with dams and advanced irrigation systems, the impact is reduced or even eliminated.
Before, a pandemic was an unpredictable event. Today, epidemiological models make it possible to predict the evolution of a virus with a high degree of certainty. Therefore, randomness is not an absolute truth, but a contextual concept that evolves with knowledge and technology: Randomness is therefore a legal fiction that serves to justify transfers of responsibility.
It serves, or should I say, served, to structure the law and assign responsibilities.
Insurance Example
Car insurance is based on randomness (I don't know if I'll have an accident).
If we follow the reasoning, an accident is not a true randomness because it is probabilistic (accident rates according to age, weather, etc.).
However, insurance needs to maintain the fiction of randomness to justify its business model.
Contract Law Example
A sales contract is commutative (we know what we receive in exchange for a fixed price).
An insurance or gambling contract is said to be random (because the outcome is uncertain). But if randomness is a fiction, then is this distinction still valid?
This therefore calls into question the very distinction between commutative and random contracts.
II. Nature of the Commutative Contract: A Contract with Instantaneous Performance
We could say: "It is an event whose unpredictability depends on the level of knowledge and technological control of a given society."
Example:
In 1804, the weather was a hazard.
In 2024, it is almost no longer one.
Therefore, the law must evolve with science to adapt the notion of hazard.
The critique of hazard is highly relevant and opens avenues for reforming contract and insurance law. We could imagine a new legal regime based not on "hazard" but on "measurable uncertainty."
We think we've scored a point by explaining how to predict an accident, even with probabilities. For me, we're approaching the problem backwards. It's not about predicting an accident; that's not the definition of hazard. We won't repeat its definition: what causes an accident? We know the causes: speeding, drunk driving, drugs, using a cell phone while driving, etc., distraction, various forms of fatigue, etc. But this isn't hazard in the strict sense of the term; it's human activity, therefore the expression of one's will. We return to the notion of a legal act of will. As for societies, they often don't want to evolve or take a long time, often too late, or even don't want to evolve at all. So often, it's a question of legal comfort more than anything else; in short, intellectual laziness. The crucial point: hazard doesn't exist, because everything is a logical consequence of an identifiable cause.
An accident is not a hazard, but a consequence of human activity. You're right to say that a road accident is not an "unforeseeable and external event," but the result of clearly identified human behavior. Why do we say that an accident is a hazard?
Because insurance companies need to maintain this fiction to function.
Because the law prefers to manage the effects rather than analyze the causes in depth.
Speeding, alcohol, fatigue, distraction... these are measurable variables.
The causes are known, documented, and statistically assessable.
This is not chance, it is incomplete determinism: we don't know when an accident will occur, but we know that it will occur and we know why it occurs.
An accident is therefore not a hazard, but a logical consequence of human behavior.
It is therefore a matter of legal acts, not legal facts.
The history of law shows that legal concepts always evolve behind scientific and philosophical advances.
Competition law: long ignored by states, it wasn't until the 20th century that monopoly abuses were taken into account.
Environmental law: ecological damage was once considered "uncertainties," but today we speak of environmental liability.
Slavery and equal rights: entire societies have collapsed due to failure to adapt their legal structures to social and economic realities.
The law evolves slowly because it is a tool for stability, but this slowness can be a weakness when it prevents adaptation to new knowledge. This is the intellectual inertia of the law, which hides behind fictions rather than rethinking its foundations.
A/ The paradox of the "law of obligations" and commutativity: A = B or B = A
You posit the perfect equation A = B or B = A, which is the mathematics of the commutative contract.
A = B means that the services are equivalent.
But in the case of the random contract, the equation becomes: A ≠ B
Or more precisely, A is a variable and B is a constant: A(?) = B
Problem:
If A(?) = B, then randomness would be an asymmetry in equivalence.
But if randomness does not exist, then A = B is always true, even in a random contract.
So, the random contract is not the opposite of the commutative contract… It is a distorted version where the illusion of randomness masks the real equivalence.
Let's restate the basics of the equation A = B, which demonstrates and proves that randomness is a fiction.
A = B is the fundamental rule of the commutative contract.
A sale = a fair price and a service = equivalent compensation. But is the random contract really A ≠ B? Let's take an insurance policy:
Either the insured has a claim → they receive compensation.
Or they don't have a claim → they receive nothing.
B/ The consequences of an instantaneous contract :
In reality, the insurance premium is based on a mathematical assessment of risk. Therefore, if we had perfect knowledge of the risk, the insurance would also be commutative! Randomness is only a degree of uncertainty in our ability to see equivalence and justifies apparent imbalances.
For example, a simple or unilateral will (unilateral legal act) is a right without counterpart, in terms of obligation, I mean. On the other hand, an obligation without a right, I don't know.
An obligation without a right, is possible? No. Indeed, every obligation necessarily has a correlative right, and for example, the obligation to pay a tax or an obligation to pay a fine, the right is held by the State, which holds the right. An obligation is a legal constraint that weighs on a subject. This constraint exists because another subject benefits from a right in return.
Concrete examples:
If I have to pay a tax, the State has a right to collect that tax.
If I have an obligation of confidentiality, someone has a right to have that confidentiality respected.
Therefore, an obligation without a right would be nonsense, because it would require a constraint without a beneficiary.
Let's return to our contract law: The commutative law of the Civil Code is devoid of explanations in the doctrine because it does not include this concept. A = B and B = A is a perfect concept in contract law: it is an observation meaning that when A = B and especially when B = A, then the contract is perfect and almost instantaneous and is extinguished by its observation. This is a legal observation. So, what did the legislator of 1804 mean by codifying Article 1108 of the Civil Code? Well, one day people will understand the perfection of things when they understand that in their time, that is, the time of Napoleon, contingency could not be avoided as a legal observation of the time, but that progress would one day allow this notion of commutativity to be exploited—the legislator was therefore an enlightened visionary at the time.
The Napoleonic Code includes Article 1108 in Book III ("On the Different Ways of Acquiring Property")?
Because he knew that commutativity was a purely balanced method of acquisition, a perfect transfer of ownership.
But why didn't he develop this concept? In his time, contingency was an unavoidable reality. Economic and social uncertainties imposed a rigid framework on contracts. The legislator lacked the scientific tools to follow this reasoning through. He knew that randomness was a temporary artifice. He therefore laid a foundation that future generations would better understand through progress. He enshrined commutativity as a fundamental principle, pending its mastery. This was not an error of omission, but an anticipation of the future.
In conclusion:
Thus, a perfectly commutative contract self-cancels itself through its own execution. This is perfect instantaneous execution. The commutative contract does not focus on what lasts and is resolved instantly. It is a perfect transaction, therefore without debt, without delay, and without dispute.
Auteur
Vidal Bravo - Jandia Miguel
Ingineer - Master II in law /
Montpellier I University Consumer law centre / Training and research unit
Paris II Pantheon - Assas