A book on ethics and philosophy of values

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After Husserl, we finally reach Th. Lessing. Indeed, while Husserl's writings on ethics and formal axiology were somewhat neglected (in favour of his writings on phenomenology more specifically), one of the auditors who had attended Husserl's seminars, Th. Lessing, inspired by Husserl's ideas, carried out a similar project in a work entitled Studien zur Wertaxiomatik (without any reference to Husserl, which led to a somewhat tense correspondence with the latter, who felt he had been robbed of his thoughts).

Lessing identifies several axiological axioms, on the model of mathematical axioms.
First, we distinguish between the axioms of constitution:
Identity: "X value" = "X value",
Contradiction: "value X" has the opposite "non-value of X".
Excluded middle: either 'X' has a value, or X does not.

We will then identify the addition axioms:
(value a + value b) > value a
(value a - value b) < value a

To which we can add:
Commutativity axioms: value a X value b =value b X value a,
Associativity axioms: (value a +value b) + value c = value a+ (value b + value c), etc...

This leads to the three "axioms of dependence" proposed by Lessing, including: "If the value of a depends on the value of b, then b is of greater value than a", which establishes a principle of hierarchy.

Here again, these axiological axioms are logical or mathematical laws applied to values. A truly objective science of values can therefore be built on them, objectivity guaranteed by the fact that it will not be established on the basis of any unfounded value judgement.
These axioms lay down the formal rules that value judgements must respect if they are to be articulated in reasoning, but they say nothing about the content of the value judgements themselves: we know from them 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 "a" or "b" can be, in other words, what can have a value.