From Anathem, it seems clear that Stephenson is an idealist, not in the sense of one that puts abstract ideals before personal comfort, but in the sense of one that believes in the influence of ideas on history.
The problem with idealism, from a scientific point of view, is that it's a messy hypothesis. If ideas and beliefs influence history, that means that history is influenced by one of the hardest systems for historians to understand, that is, the human mind. But the reason why idealism is nonetheless alive and well is that the alternative is worse. Materialism, as it is called, holds that history is a consequence purely of material reality and the ideas that people have about that reality are irrelevant to it. Materialism is neat and tidy and easy to understand, but also ostensibly wrong.
Moreover, few of the people that have expounded materialist ideas have taken them seriously. Marx may have claimed that history is a function of the "material forces of production," but he definitely wrote and acted as though communist agitation might do some good for the world. Similarly, the Public Choice school of political economy, in its most extreme forms, models political decision making as a function of voter self-interest narrowly conceived and the structure of the political process. And yet, Public Choice economists have long dispensed liberal helpings of particular policy advice at the slightest provocation, because like virtually all economists, they believe that the advice given by people who actually study policy questions has at least some effect, on the margin, sometimes.
The avout in Anathem made a study of all the different mental models the saeculars have had of them over the ages. They believe, and quite rightly so, that these mental models have real consequences for the way they interact with the saecular world, and they are quite justified in that belief. At the same time, it seems unlikely that these oconographies are the product of environmental factors in any straightforwardly deterministic sense, so they are entirely correct in relying on empirical observation in order to establish which iconography is prevalent at the beginning of a given apert. I apologize for all the in-world jargon, but the bottom line is that the community of people that the book's main character is part of is idealist and not materialist, and rightly so.
