Thought and Being are the Same: Categorial Rendition of the Parmenidian Thesis

Abstract

Classic understanding of logic as an instrument of cognition, which, in effect, pertain rather to human’s mind than to reality itself, gives rise to the fundamental mapping problem of reconciliation of this reality with any possible practices of its representations in thought. In other words, it is essentially not the same thing that can be thought and that can be. However, after unusual and highly abstract (essentially geometric) Grothendieck constructions gave rise to so called categorial analysis of logic, it became possible to show, that (up to categorial equivalence) Parmenides after all was right.

Keywords

• appearing
• categorial equivalence
• grothendieck topos
• ontology
• sheaves
• theory of ω-sets