2/ The idea of a formal axiology
With the projects of formal axiology appeared in the late 19th century, axiology has probably found its ultimate expression.
Such a project has been initiated by Brentano, Husserl, and Th. Lessing.
The idea is to draw a parallel with the formal logic, by the discovery of formal axiological laws, viz. laws making abstraction of the question as to what has a value, but aiming at identifying the necessary relations between the axiological concepts.
As we know, logic exposes a priori relations, characterized by their necessity and universality, like “if A is B, and that B is C, A is C”, notwithstanding the nature of A, B and C. By analogy, the formal axiology should propose laws based on the same model, like “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”, notwithstanding the nature of A, B and C, viz. dismissing the question “what has a value?”.
So formal axiology is based on the principle of epistemological prudence, and on an époché of values, conceding that we do not know whether this or that thing has a value, but holding that if A or B have a value, then, there are such and such necessary laws which apply to these values.
The point is to dismiss the “philosophies of value” being so far presented, in order to develop a scientific discipline whose specific object of studies is value, as universally valid as logic, and proceeding a priori.
In this case, we reject the intuitionist idea of an immediate knowledge of values, to affirm the necessity of the constitution of a discipline, proceeding through mediation of arguments and reasonings. However the evidence retains its role in this process of mediation. Indeed, the chain of arguments must be based on axioms, obvious in themselves, a tradition inherited from geometry.
For example, let us consider the famous axioms of Brentano. This philosopher presents in the Origin of our knowledge of right and wrong these four propositions about values, considered as obvious, and therefore as axioms. For example:
The existence of a positive value is itself a positive value
The nonexistence of a positive value is itself a negative value
The existence of a negative value is itself a negative value
The nonexistence of a negative value is itself a positive value
We see that these propositions leave undetermined the question “what has a value?”, but stick to the formal laws concerning the concept of value. As such, they are deprived from all consideration of values, and so from all biases as to values. Consequently, they could enable us to develop an objective formal axiology, discovering certain truths, at the price of abandoning the axiological question of what has a value.