TL;DR: Is it possible to define hierarchy, as a useful term for communication and association between anarchists? If so, what are some of those definitions?
There are many different strains of anarchism, and specially since anarchists mostly believe in decentralization, I feel like many of our efforts go diluted for lack of collective organization. Sure, there are big anarchist collectives doing work out there, but I have the sensation that most youth or influential people who identify themselves with anarchist causes get lost in the plot simply for lack of a bigger movement. For most of the modes of anarchism there is one big bad evil guy, commonly named “hierarchy”; although writers and academics define those terms in their publications, I can’t help but notice, at least in the forums I’ve been around, your average anarchists could be talking about two completely different concepts of hierarchy or oppression. Maybe if we had agreed upon definitions to those hot topics it would be easier to associate. Is that even possible? That we all agree on the same meaning for a word? Do we call Chomsky to solve this linguistical issue?
Or am I completely wrong in my questionings?
It is tricky to do this in a way that allows for complex coordination at scale while avoiding the oppressive properties of systems which we would all recognize as undesirable. The concept that is required in order to properly navigate this is ‘coercive control’.
Hierarchy happens when some people are ‘above’ others, or, in other words, can make decisions for other people and enforce them without their consent. This is coercive control. This is the situation that we want to avoid.
At the same time, the collective does have to be able to enforce rules, so some degree of coercion must be allowed in order to avoid a sort of paradox-of-tolerance situation. To resolve this apparent contradiction, we introduce the notion of a ‘social contract’. To be a part of an anarchist organization would require that a person agree to a social contract. As long as the person upholds the social contract, they cannot otherwise be coerced, as that would be a violation of anarchist principles, and could result in oppressive behavior. (Note: For this to be self-consistent, coercion has to be outlawed as part of said social contract.) If a person breaks the social contract, then they are also no longer protected by it, and can be coerced by the group to leave or such.
The social contract bit is sort of an aside to the original question, but I think people get confused by what is and isn’t hierarchy because they understand the first part in some way, even if they don’t have the words for it, but then they don’t know how to solve the obvious problem of enforcing rules so that people’s freedoms can actually be protected in practice.
Centralization doesn’t necessarily imply hierarchy, as, given an undirected acyclic graph, you can pick any node to be the ‘root’ and end up with a valid ‘tree’ - the structure that most people would visualize when they hear the word ‘hierarchy’. Of course, we would prefer to not pick any node as the root, as the hierarchical structure implied by such a distinction shouldn’t be necessary for the collective to reap the benefits of such centralization. There is a whole discussion that could be had about how to actually implement centralization without falling into various traps, but that isn’t really what the question in the OP is about. I simply bring it up because some people confuse centralization for hierarchy, and end up shooting themselves in the foot for doing so.