Andrey Rodin. Endurance, perdurance, and category theory
In this paper I argue that the concepts of «temporal parts», «temporal extension» and «thing which perdures over time» are special cases of «spatial parts», «spatial extension» and «spatially extended thing» correspondingly while there is a sense in which the concept of endurance and that of time are identical. Using the formal apparatus of the category theory I provide an ontology which allows an enduring object and the perduring «history» of this object to be different descriptions of the same thing – very like the intension and the extension of a predicate. As far as both of the descriptions are obtained simultaneously within the same formal construction there is no reason to believe that one of them is ontologically prior. Besides I show that an enduring object may have an additional «relational» extension which in certain cases is interpreted as a minimal time interval through which the object can endure. Categorial definitions of the concepts of «temporal part», «spatial part», «point» and «moment» are provided.
A. Rodin. Endurance, perdurance, and category theory// Transcendental Anthropology and Logic. Proceedings of the International Workshop “Anthropology from the Modern Standpoint” and the VIIIth Kant Coference. P. 98 – 132.
