2/ The Idea of a Formal Axiology

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

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

Logic, as we know, discloses 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 proceeds with epistemological prudence and a suspension (epoché) of value judgements; it acknowledges that we may not yet know whether values exist or what holds value, but maintains that if A or B have value, the necessary laws governing those values would be as follows.

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

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

Brentano's axioms offer a compelling illustration. In The Origin of Our Knowledge of Right and Wrong, Brentano sets out four propositions concerning values, which he regards as 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 leave the question of what specifically holds value entirely open, focusing instead on the formal laws governing the concept of value itself. As such, they avoid any particular value bias, which opens the possibility of constituting an objective and rigorous formal axiology—albeit at the cost of abandoning the axiological inquiry into what possesses value.