On the Role of the Principle of Contextuality of the Whole in Eliminating Set-Theoretical Paradoxes

Classical set theory contains several well-known logical paradoxes, such as Russell’s paradox. These paradoxes arise from the possibility of defining sets independently of the context of the totality to which they belong. In this short conceptual note we argue that these paradoxes can be removed by introducing the principle of contextuality of the whole. According to this principle, every mathematical object must be defined only within the context of a given totality. When this principle is applied to set formation, the classical paradoxes disappear because the construction of sets becomes context-dependent. The idea of the contextuality of the whole was first formulated in our earlier work published on Zenodo.