Multidimensional Logic on the Generalized Consequences. In: 2000 European Summer Meeting of the Association for Symbolic Logic Logic Colloquium 2000, Paris, France, July 23-31, 2000

N. Vasiliev’s early 20th-century concept of multidimensional logic, developed alongside L. Brouwer and J. Lukasiewicz, proposes a non-Aristotelian framework. It distinguishes logical laws into external (gussiological) and internal levels. The external level follows multidimensional principles and the law of the excluded middle, while the internal level depends on endalogous assumptions about the cognizable world. In a one-dimensional world, only positive statements are atomic, with negative statements arising from inference, underscoring the constraints of directly expressing negation.