Below are working definitions of the more nuanced concepts used across this site. I will add to this list as I am able. Each are works in progress, subject to revision and debate (as all ideas should be).
To say that something is complex does not mean that it is complicated. A complicated system has many different interacting parts that behave in unique ways. A complex system, by comparison, is one comprised of many interacting parts that follow a relatively small set of simple rules which create, cumulatively, outcomes that cannot be predicted by an analysis of the rules themselves. Arisotl's addage "the whole is greater than the sum of its parts" is an effective summary of the notion of complexity.
The concept of culture was created by anthropologists as what Gregory Bateson calls an "explaining principle"--a proxy explanation for when no actual explanation is known. It is a container concept in that it usually is taken to include such phenomena as traditions, languages, mores, kinship conventions, and livelihood practices. Few people agree on a single definition of culture, or for that matter whether it really exists (or is a handy heuristic like ecosystem). I prefer Daniel Quinn's definition of culture: a people who share a world view and enact a common story (see below).
The marginalization-degradation thesis is from the field of Political Ecology. It suggests that unsustainable behaviors are driven not by basic failings of human nature but by failings of social institutions to protect people's rights. When people are marginalized by society, struggling to make ends meet, they resort to unsanctioned / unsustainable practices. The thesis also posits a feedback loop, wherein marginalization drives environmental degradation, and increased environmental degradation further marginalizes the people relying on those ecosystems.
I'm not entirely certain that I have come to terms with the relationship between the concept of a culture's story and its world view. Daniel Quinn describes story as an interrelation between the gods, man, and the Earth, with a beginning, middle, and end. A culture's story is no-doubt imbibed with world view: concepts such as progress derive from our received understanding of the nature of the world and our place and role in it. I think the important nuance is that world view provides the logic, whereas story provides the narrative.
Resilience describes the ability of some system to maintain its fundamental structure and function (identity?) when impacted by some stressor. It is a measure of system performance, with stability being the ideal behavior: does the system return to its previous state, and if so how fast?
Sustainability is a difficult concept to define, though it is so central to the ideas presented here that some discussion of how I understand it is essential. My "meta" definition of sustainability is that it is a property of behavior. A behavior is sustainable or it is not. Now, the criteria by which that sustainability is measured is a subjective matter, beyond at least the issue of biophysical limits. Some definitions for sustainability attend only to the biophysical aspects, whereas others argue that sustainability also requires certain social outcomes, specifically just outcomes.
A second area of subjectivity with respect to a behavior's sustainability relates to the level or scale atv which sustainability is evaluated. A particular behavior may be sustainable if one person adopts it, or a community adopts it, but not if an entire nation adopts it. Some call this the "collective action" problem, referring to unsustainability as a sort of tragic, emergent phenomenon of well-meaning people. I argue that the issue of scale highlights the importance of understanding all behaviors and technologies as situated in place and in culture.
As used here, this is simply shorthand for a system of making a living – hunting and gathering is a way of life; slash and burn agriculture is a way of life. "A people" is often used as a shorthand for a group of people who share a way of life.
A perennial philosophical question is "how ought one to live?" The answer to that question, or at least what people believe to be the answer, is the fabric of world view. World view subsumes such matters as the basic nature of man, man's relationship with the natural world, and the criteria by which we will be judged as good or evil. Angayuqaq Kawagley describes world view as "the principles and beliefs - including the epistemological and ontological underpinnings of those beliefs - which people have acquired to make sense of the world around them." Most important, in my opinion, is the relationship between worldview and the 'rightness' of a thing. It is worldview, not evil, that allows for the Holocaust, or the decimation of traditional cultures in the name of civilization.