2/ The Idea of a Formal Axiology

The formal axiology projects that emerged in the late 19th century likely represent axiology's most refined expression to date.
Historically, figures like Brentano, Husserl, and Th. Lessing pioneered this approach.

The central idea is to draw an analogy with formal logic, suggesting that we could discover axiological formal laws—laws that set aside the question of what specifically holds value and instead focus on identifying the necessary relationships between axiological concepts.

Logic, as we know, reveals the necessity and universality of a priori relations, such as 'If A is B, and B is C, then A is C', without regard to the specific nature of A, B, and C. Similarly, formal axiology would propose laws such as 'The value of A depends on the value of B, the value of B depends on the value of C, so the value of A depends on the value of C', without needing to specify the nature of A, B, and C—that is, without addressing the question of what actually possesses value.
Formal axiology thus relies on epistemological prudence and a suspension (epoché) of value judgments; it acknowledges that we may not yet know whether values exist or what holds value, but it asserts that if A or B have value, the necessary laws governing these values would be as follows.

The aim, therefore, is to move beyond the 'philosophies of values' we have explored so far and to establish a scientific discipline focused specifically on values, with universality and a priori validity similar to that of logic.

In doing so, we depart from the intuitionist notion of immediate knowledge of values, instead asserting the need to constitute a discipline that advances through structured argumentation and reasoning. However, self-evidence retains a role within this mediated process. Following a perspective rooted in the geometric tradition, the chain of arguments should be anchored in axioms deemed self-evident.

Brentano’s axioms provide a compelling illustration. In The Origin of Our Knowledge of Right and Wrong, Brentano presents four propositions concerning values, which he considers self-evident and, therefore, foundational axioms. For example:
The existence of a positive value is itself a positive value.
The non-existence of a positive value is a negative value.
The existence of a negative value is a negative value.
The non-existence of a negative value is a positive value.

These propositions clearly leave the question of what specifically holds value undetermined, focusing instead on the formal laws governing the concept of value itself. As such, they avoid any particular value biases, allowing for the possibility of constituting an objective and certain formal axiology—albeit at the cost of abandoning the axiological inquiry into what possesses value.