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

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 new conceptual panoply and the novel technical machinery of Abstract Differential Geometry (ADG) to various persistently outstanding issues in Quantum Gravity (QG) (Mallios and Raptis Int. J. Theor. Phys. 40, 1885, 2004, Int. J. Theor. Phys. 41, 1857, 2002, Int. J. Theor. Phys. 42, 1479, 2003; Raptis Int. J. Theor. Phys. 39, 1233, 2000, Int. J. Theor. Phys. 39, 1703, 2000, Int. J. Theor. Phys. 45, 79, 2006, Int. J. Theor. Phys. 46, 688, 2007, Int. J. Theor. Phys. 45, 1495, 2006, Int. J. Theor. Phys. 46, 1137, 2007, Int. J. Theor. Phys. 46, 3009, 2007; Raptis and Zapatrin Int. J. Theor. Phys. 39, 1, 2000, Class. Quant. Grav. 20, 4187, 2001). This paper may be regarded as a sequel to the paper (Raptis Int. J. Theor. Phys. 46, 3009, 2007) in the aftermath of the paper (Raptis 2024), which is currently in press. 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 (Raptis 2024a, 2024b, 2024c).