Bonjour,

j'ai rédigé un article étudiant les conséquences de l'introduction d'une pseudo-constante pour le vide dans un langage du 1er ordre dédié à une théorie axiomatique des ensembles;

le sujet est à la frontière des mathématiques, de la linguistique et de la philosophie; je reproduis ci-dessous le chapitre introductif, en format tex et en anglais (désolé mais je l'ai écrit directement en anglais car destiné à une revue internationale)

"The purpose of this article is to elaborate an axiomatic set theory expressed in a first order language in which the pseudo-constant Lambda, $\Lambda$, denoting the void has been introduced. ~The introduction of $\Lambda$ into the first order language of set theory allows to build the empty set from the void by means of the axiom of the parts. ~On a conceptual level, taking into account $\Lambda$ makes it possible to redefine the concept of set and to give the empty set a positive definition and a status of emblematic set.
On the other hand, the introduction of $\Lambda$ into the language of a set theory with an empty universe makes it possible to highlight a zero-order logic different and probably more legitimate than the propositional logic, which classicaly deserves the title of zero-order logic because of the absence of quantification on propositional variables. The presence of $\Lambda$ within a formal language for a theory without elements of type 1 or higher highlights a zero-order logic where quantification is possible on type-0 element. The semantics of such a language will appear empty, but will be the opportunity to introduce the pre-truth value $\emph{Empty}$.\\
In a first order theory with a non-empty universe, the interpretation of Lambda as a pseudo-constant and of $\textit{Empty}$ as a pre-truth value, i.e. as different from the "neither... nor" would let the possibility to work with a standard logic rather than with a paracomplete one.\\

First Lambda will be defined conceptually.
After that will be described a zero-order logic based on Lambda for a theory with an empty universe.
Then the highlighting of the pre-truth value "Empty" will follow.
The second section will be about the description of first-order language and theory taking into account the pseudo-constant $\Lambda$, about the axiom of the void, and about the construction of the empty set and that of a hierarchical universe from $\Lambda$.
Finally, we will pay attention to the conceptual importance and consequences of Lambda.\\

\emph{Keywords}: cut, void, potential, pre-element, pseudo-constant, zero-order logic, Empty, pre-truth value, empty set, relative nothing."

L'article fait une vingtaine de pages; quelqu'un aurait-il le courage de le lire et la gentillesse de m'exprimer ses remarques et critiques?

vous pouvez m'écrire à:

** pas de mail, merci **

merci d'avance,
Laurent