A Heuristic Philosophical Discourse on Various Applications of Abstract Differential Geometry in Quantum Gravity Research

TL;DR

This paper explores the philosophical and conceptual foundations of applying Abstract Differential Geometry to unresolved issues in Quantum Gravity, proposing new perspectives and future research directions.

Contribution

It introduces a novel philosophical framework for using Abstract Differential Geometry in Quantum Gravity research and discusses potential future bifurcations in this approach.

Findings

New philosophical premises for ADG in QG

Potential bifurcation routes for future research

Implications for unresolved issues in Quantum Gravity

Abstract

In the present paper, we outline and expound the fundamental and novel qualitative-cum-philosophical premises, principles, ideas, concepts, constructions and results that originate from our ongoing research project of applying the conceptual panoply and the technical machinery of Abstract Differential Geometry (ADG) to various persistently outstanding issues in Quantum Gravity (QG) research. At the end of the paper, we discuss the potential philosophical repercussions of two possible future research routes that the main stream of our applications of ADG to QG may bifurcate towards in view of three independent, but overlapping, research papers that are currently under development.