After Husserl, one must study the work of Th. Lessing. Indeed, whereas Husserl’s writings on ethics and formal axiology were neglected (in favour of his books concerning specifically the phenomenology), one of his pupils having attended to some of his seminars, Th. Lessing, took inspiration from his master’s ideas and realized a similar project in a book called Studien zur Wertaxiomatik (without any reference to Husserl, hence a tense exchange of letters with the latter, considering more or less this as a stealing of ideas).
Lessing identifies several axiological axioms, on the model of mathematical axioms.
First, the axioms of constitution:
Identity: “value X” = “value X”
Contradiction: the opposite of “value X” is “not-value X”
Excluded middle: either “X” has a value, or X has not.
Then the axioms of addition:
(value a + value b) > value a
(value a – value b) < value a
And the axioms of commutativity: value a X value b = value b X value a
The axioms of associativity: (value a + value b) + value c = value a + (value b + value c), etc.
Finally, we find the three axioms of dependence proposed by Lessing, including: “If the value of a depends on the value of b, b has a greater value than a”, which is a principle of hierarchy.
Again, we see that these axiological axioms fall under logical or mathematical laws, applied to values. On this basis, a science of values really objective may be founded and developed; its objectivity comes from the fact that no judgment of value is used in these axioms.
These axioms set the formal rules that the judgements of values must observe, to be combined in reasoning, but indicate nothing about the content of the value judgments themselves: from them, we know that “the value of a” multiplied by “the value of b” is equal to the “value of b” multiplied by “the value of a”, but we do not know what can be “a” or “b”, viz. what is likely to have a value.