“Depth” can mean thoroughness. If you discuss or explore a matter “in depth”, you talk about it or look into it, in all its detail, to understand how the details hang together.
“Depth” can also mean foundationality, or (since I have a mild allergy to foundation metaphors) degree of structural dependence. A deep change alters a structure and effects a holistic change, altering the role of many details at once.
Notice that both of these senses of the word “depth” relates to the relationship between the most encompassing, pervasive structures and the most minute details ordered within the structure, and the difference in the sense of the word only pertains to whether the depth is approached bottom-up (detail-first) or top-down (structure-first).
In other words, depth seems to refer to holistic characteristics of a system, the ratio of expansiveness of scope of the whole to the fineness of granularity of parts.
I almost added density to this account of depth, meaning the density of application in relationship between whole and part. Between the encompassing structure and the ordered parts, how thoroughly have these particular relationships have been worked out, understood or established? How many parts are caught up in the structure and ordered and how much is left outside the order? But I had second thoughts, and I am still not sure.
Notice, I left ambiguous whether the system in question is mind or matter or a hybrid of both. It works equally well for both.
In my dual life of philosophy and design, I have in-depth experience with deep changes in philosophical thought and deep changes made to design systems. The similarities in what happens in each case across the two fields is part of what has brought me to think of philosophy as a design discipline, perhaps even the queen of the design disciplines.
Think about it, using this understanding of depth: Instead of thinking of philosophy as a search for a pre-existing truth (or even a fixed plurality of truths) — truth that there to be found or revealed — instead try thinking of philosophy as the instauration (interactive discovering/making, or to keep things simpler, crafting) of conception systems capable of literally making sense of the world. John Dewey called this philosophical approach Instrumentalism.)
Each conception system has its own tradeoffs and gains which make them work wonderfully in some contexts (for some people, in some times, in some places, for some uses), and poorly or disastrously in other contexts). Because of this context-dependence, it makes sense to understand this context deeply, to work within it as sensitively as possible, and to iteratively improve it over time. This is what design does: it creates systems that work well within particular human contexts.
Using these conceptions together — depth, instrumentalism and design — doesn’t this coronation idea (philosophy as queen of the design disciplines) make self-evident sense? But notice, this sense really is made.
In other words, doesn’t this conception-system produce an experience of self-evidence, and at a depth that ripples through just about everything, including your own memories, reordering part and whole…?