This will be a relatively long response to Ian Durham's thoughtful critique. First though a comment on Eddington's Fundamental Theory, I did try it many years ago and found it very tough. In the end I concluded he was incapable of saying anything that made sense, though he seemed to be groping towards a Machian standpoint. One of my lecturers at Cambridge referred to the book as "that graveyard of so many promising theoreticians."
Now to reductionism:
First, I spent some time looking for what seems to me to be the best definition of reductionism and found something that basically matches the opening of my abstract:
"According to reductionism, every complex phenomenon can and should be explained in terms of the simplest possible entities and mechanisms. The parts determine the whole." You say:
"Nevertheless, I have to say I was a bit surprised by some of your assertions regarding reductionism. I think there is a subtle but important distinction that appears to have been muddled in several of the essays that have been critical of reductionism and that is the difference between reductionism as a method for investigating science and reductionism (or "constructionism" as P.W. Andersen called it) as an actual causal "structure" to the universe."
I'm afraid the latter meaning is too subtle for me too. What is a 'causal "structure" to [sic] the universe? You also say:
"By dint of the fact that something possesses non-uniformity, which it must if it is to be understood as *having* parts to begin with, requires some recognition of those parts as individual features. Thus it would seem reductionism is *required* to some extent for an understanding of anything other than an utterly featureless structure."
I completely agree that a prerequisite for science is nonuniformity. That was the whole point of Leibniz's objection to Newton's absolute space. However, I am not sure that this establishes parts as primary. A part of a landscape is of necessity extended and thereby a whole, since you need attributes to identify it. It has long been recognized that a thing is defined by a collection of attributes. Leibniz liked to say that a thing is defined by a true principle of unity, not by mere aggregation like a heap of stones.So I think a thing is a holistic concept; a triangle in Euclidean space certainly is.
You also say:
"So, for instance, in your example of the triangle from shape dynamics, the concept of "shape" still requires knowledge of the concept of angles. To a large extent, this is still reductionism. Thus, while the universe itself may not be reductionist in its structure, I fail to see how we can make sense of it outside of a reductionist framework which is much broader than you make it out to be."
Here you do make a point that I find persuasive (though mathematically one needs the concept of a scalar product to make sense of angles in a vector space, which seems to me holistic). I didn't mean to claim one can utterly banish all part-like concepts (or, at least, I am not yet in a position to do so). The point that I was trying to make is that the universe may be far more holistic than is usually believed. I only claimed that shape dynamics changes our notion of the parts, winnowing away as much reductionist chaff as possible.
"Honestly, I really don't see how any of the shape dynamics arguments point to any serious flaws in reductionism itself unless one takes a seriously narrow definition of it that is completely inconsistent with the way it has been used over the years." I am not a philosopher of science, but have read generally on the topic and checked a few definitions before writing my essay. What you suggest does not match my reading and understanding. At the least, I am sure that there is a huge conceptual difference between the structure of Newtonian dynamics and shape dynamics. I would say it is the difference between a basically reductionist and a basically holistic conception. That was the message I was trying to get across.
"incidentally, with regard to shape dynamics, I fail to see how it is all that different from a block universe" In a (classical) block universe, many different histories coexist and there is no criterion that allows one to choose in a non-arbitrary way a special distinguished one among them. In shape dynamics there is.
"not to mention the fact that it seems as if the changes still need to be relative to *something* though heaven knows what that is." Shape dynamics is better described as being about differences rather than changes. Its key mechanism, best matching, enables one to quantify the difference between two nearly identical wholes without using any structure extraneous to each of them. That is where it differs radically from Newton's scheme, in which the external structure of absolute space has causal effect.
You also say
"Regarding the history of reductionism, I also don't see how Newton's notion of absolute space "introduced" reductionism. That seems like a bit of "backward causation" from the shape dynamics argument about triangles. The truth of the matter is that reductionism as a method for carrying out the scientific method was developed by a number of people over a span over nearly 200 years."
Of course, methods develop over a long time and qualitative reductionist notions, above all in atomism and in Descartes's mechanical philosophy, predated Newton. However, I would still argue that reductionism got into its stride with Newton. His scheme was above all suitable for my purposes because shape dynamics is, I would still maintain, far more holistic.