Abstract
Our aim in this paper is to replace the old concept of truth in mathematics, based on the Set Structure provided with idea of true and false characterized by the presence of a characteric function $$\varOmega = \{0, 1\}$$ , by a mathematical structures founded on the idea of Topos, the triple structure $$\{X: (Y, {{\mathcal {T}}}, d_n)\}$$ and the notion of Gradual Truth or Steps from the truth. Our motivations is to understand the mathematical structures underlying the emergence’s mechanism and phenomena. We think that this approach could be useful to better appreciate the subtleties of the notion of truth and gives us a better understanding of the complex and changing phenomena.
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