Laurent Dubois

This article-testimony can be seen as an example of a maybe new discipline that could be called "scientific metaphysics" made of thoughts experiments, definitions, some proofs, some explanations, some conjectures. Of course, to be called science, the discipline needs some possibility of "verification" too. We will see if it can be considered. We start from a thought experiment: Can the universe defined as U_Def be aware conscious of itself as whole? This question is a variant of the more familiar: Can the universe be aware conscious? We can distinguish two main approaches in human history in the attempts at answering this second question: 1) the approach by the bottom with a weak version of consciousness: it includes "panpsychic" like theories. 2) the approach by the head with a strong version of consciousness: it includes "holistic" theories. Spinoza's "Pantheism", for example, can be considered as one of them, even if some interpretations of Spinoza's metaphysics are not satisfied with the equation "god = universe". The purpose developed in this article belongs to the second kind of approach. After a definition of the universe \emph{U}$_{\textit{Def}} $ in 7 points and the introduction of 3 premisses, one of them being devoted to our definition of "strong consciousness", we suggest an answer to the initial question and we draw the most important among numerous consequences: - semantical jump by META-abstraction and introduction of the holistic semantics; - extension of the natural language to a supra-natural language; - highlighting of a higher-order solipsism; - etc. We devote some attention to the notion of "model" in its logical and philosophical acceptation and we introduce the notion of evolutional self-modelization.

This article consists in two parts that are complementary and autonomous at the same time. In the first one, we develop some surprising consequences of the introduction of a new constant called Lambda in order to represent the object ``nothing" or ``void" into a standard set theory. On a conceptual level, it allows to see sets in a new light and to give a legitimacy to the empty set. On a technical level, it leads to a relative resolution of the anomaly of the intersection of a family free of sets. In the second part, we show the interest of introducing an operator of potentiality into a standard set theory. Among other results, this operator allows to prove the existence of a hierarchy of empty sets and to propose a solution to the puzzle of "ubiquity" of the empty set. Both theories are presented with equi-consistency results (model and interpretation). Here is a declaration of intent : in each case, the starting point is a conceptual questionning; the technical tools come in a second time\\[0.4cm] \textbf{Keywords:} nothing, void, empty set, null-class, zero-order logic with quantifiers, potential, effective, empty set, ubiquity, hierarchy, equality, equality by the bottom, identity, identification.

The purpose of this article is to present several immediate consequences of the introduction of a new constant called Lambda in order to represent the object ``nothing" or ``void" into a standard set theory. The use of Lambda will appear natural thanks to its role of condition of possibility of sets. On a conceptual level, the use of Lambda leads to a legitimation of the empty set and to a redefinition of the notion of set. It lets also clearly appear the distinction between the empty set, the nothing and the ur-elements. On a technical level, we introduce the notion of pre-element and we suggest a formal definition of the nothing distinct of that of the null-class. Among other results, we get a relative resolution of the anomaly of the intersection of a family free of sets and the possibility of building the empty set from ``nothing". The theory is presented with equi-consistency results . On both conceptual and technical levels, the introduction of Lambda leads to a resolution of the Russell's puzzle of the null-class