Pluralist-Monism. Derived Category Theory as the Grammar of n-Awareness

TL;DR

This paper introduces a novel mathematical framework for modeling awareness and reality through higher category theory, emphasizing pluralism and offering new insights into time, change, and personal identity.

Contribution

It develops a pluralist model of awareness using derived categories and $( abla, 1)$-topoi, creating a new meta-language and temporal ontology for philosophical analysis.

Findings

A categorical model of awareness based on higher category theory.

A new temporal ontology ('n-time') for understanding change and simultaneity.

A novel approach to personal identity over time in a pluralist context.

Abstract

In this paper, we develop a mathematical model of awareness based on the idea of plurality. Instead of positing a singular principle, telos, or essence as noumenon, we model it as plurality accessible through multiple forms of awareness ("n-awareness"). In contrast to many other approaches, our model is committed to pluralist thinking. The noumenon is plural, and reality is neither reducible nor irreducible. Nothing dies out in meaning making. We begin by mathematizing the concept of awareness by appealing to the mathematical formalism of higher category theory. The beauty of higher category theory lies in its universality. Pluralism is categorical. In particular, we model awareness using the theories of derived categories and $(\infty, 1)$-topoi which will give rise to our meta-language. We then posit a "grammar" ("n-declension") which could express n-awareness, accompanied by a new temporal ontology ("n-time"). Our framework allows us to revisit old problems in the philosophy of time: how is change possible and what do we mean by simultaneity and coincidence? Another question which could be re-conceptualized in our model is one of soteriology related to this pluralism: what is a self in this context? A new model of "personal identity over time" is thus introduced.