The Ontology of Knowledge, logic, arithmetic, sets theory and geometry

(2019)

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Abstract
At ordinary scales, the ontological model proposed by Ontology of Knowledge (OK) does not call into question the representation of the world elaborated by common sense or science. This is not the world such as it appears to us and as science describes it that is challenged by the OK but the way it appears to the knowing subject and science. In spite of the efforts made to separate scientific reasoning and metaphysical considerations, in spite of the rigorous construction of mathematics, these are not, in their very foundations, independent of modalities, of laws of representation of the world. The OK shows that logical facts Exist neither more nor less than the facts of the World which are Facts of Knowledge. The mathematical facts are facts of representation. Indeed : by the experimental proof, only the laws of the representation are proved persistent/consistent, because what science foresees and verifies with precision, it is not the facts of the world but the facts of the representation of the world. Beyond the laws of representation, nothing proves to us that there are laws of the world. Remember, however, that mathematics « are worth themselves » and can not be called into question « for themselves » by an ontology. The only question is the process of creating meaning that provides mathematics with their intuitions a priori. The first objective of this article will therefore be to identify and clarify what ruptures proposed by the OK could affect intuitions a priori which found mathematics but also could explain the remarkable ability of mathematics to represent the world. For this, three major intuitions of form will be analyzed, namely : the intuition of the One, the intuition of time and the intuition of space. Then considering mathematics in two major classes : {logic, arithmetic, set theory ...} on the one hand and geometry on the other hand, we will ask the questions : - How does the OK affect their premises and rules of inference  ? - In case of incompatibility, under what conditions can such a mathematical theory be made compatible with the OK? - Can we deduce a possible extension of the theory ?
Keywords Ontology  Metaphysics  philosophy of science  mathematics  arithmetics  Whitehead  logic  geometry  Phylosophy of knowledge  Schopenhauer
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