From Catalaxia: Against Intellectual Property (Formal Proof) catalaxia Substack, (nov 12, 2025)

Purpose of the Formal Argument

I propose to question the justification of intellectual property based on a formal reasoning that establishes concepts of “good”, “use”, “authority”, “property” and “abundance”, among others. The formal system is structured by means of definitions and axioms that, together and with some premises, attempt to demonstrate solidly (solid deductive argument) that the assignment of exclusive property rights (especially in the context of abstracted ideas or properties) leads to contradictions when considering goods that are abundant (i.e., susceptible of being used simultaneously by different agents).

The strategy of the argument is to carry out a reduction to the absurd. It starts from an assumption, called the “statist assumption”, in which it is stated that there is at least one good (for example, an ideal or idea) that is abundant and, at the same time, exclusive property is assigned to some subject. It is then shown that, by assuming an abundant good, it follows that it is impossible -in modal terms- for exclusive ownership to exist, since exclusivity requires conditions (such as rivalry of use and normative authority) that cannot be met in shared goods. By generating this contradiction, the possibility of justifying intellectual property in such cases is formally rejected.

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Conclusion of the Analysis

To summarize rigorously:

1. Introduction and Objective:

The argument aims to demonstrate that in a normative system where good, use, authority, exclusive control, and property are defined, the assignment of exclusive property is incompatible with the abundance of a good (that is, the possibility that two or more agents may make use of it).

2. Definitions and Axioms:

Each of the axioms and definitions is used to construct the theoretical framework linking the possibility of use with the exclusivity required for having property. In particular, property is equated with exclusive control, which requires that the good be rival (that it prevents simultaneous uses) and that normative authority be exercised.

3. Development of the Argument:

– The argument begins with the statist assumption asserting the existence of an abundant good over which some subject is the owner (Property(x, y)).

– It is assumed that there exists at least one simultaneous use by two agents (which defines the capacity of being an abundant good).

– Through the relationship established in the ethical theory (especially through the equivalence between normative authority and rivalry), it is deduced that if a good is simultaneously used by different agents, it cannot satisfy the condition of rivalry required for authority and therefore for exclusive property.

– The modal impossibility of property (¬◊(Property(x, y)) ) is obtained, which contrasts with the initial hypothesis, and through reductio ad absurdum, the statist assumption is rejected.

4. Clarified Inference Rules:

– Existential introduction and conjunction are used to formulate the use hypotheses.

– Modus ponens is employed in various steps to apply implications derived from the axioms (for example, the equivalence between normative authority and rivalry).

– Finally, reductio ad absurdum is used to conclude that the assumption leads to a contradiction.

The final conclusion is that, within this formal framework, it is not possible to justify exclusive property over a good that is inherently abundant, which challenges the formal justification of intellectual property when applied to goods that can be used by multiple agents.

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