A good many concepts have grabbed me over time. Guess I'll start with two:
reification:
this is an originally Marxist concept whereby people find themselves compelled to view ever dynamic social processes, their participants, and according consequences as stable things, not just representative of the processes they reflect but obfuscating their origins. A key instantiation thereof is commodity fetishism, whereby items we purchase are viewed as things with inherent, objective qualities, to be traded among atomized individuals (rather than as mere aspects of a particular moment within given practices of production, distribution, and the social context that conditions such practices).
I guess what intrigues me about reification is that society as a system in motion produces an illusory view of both the whole and its constituents as it functions, but it is through action via this illusory lens that this social system is reproduced.
strange-loop:
God, this is challenging for me to conceptualize, let alone describe.* The strange loop is a type of conceptual relation that is Douglas Hofstadter's near singular fascination, and one he considers to undergird consciousness. Basically, the idea is that with a given system (physical or conceptual...this whole idea undermines the very distinction, as we'll see) existent in terms of multiple 'levels of analysis' and capable of self-representation, attempts by the system to describe itself at any given level of representation will lead unexpectedly to an account at another level of representation (and in turn paradox via self-reference).
To start, look at the Russel Paradox: take the set of all sets that are not members of themselves. Is it a member of itself? If we assume it is, it's entailed by its very definition that it is NOT a member of itself. If we assume it is not a member of itself, it's entailed by its definition that it IS a member of itself.
Another good example is the first Godel incompleteness theorem**, which demonstrates that no symbolic framework complex enough to allow derivation of arithmetic can be both consistent (disallowing the derivation of contradictory statements using the system's rules validly. . .put otherwise, entailing that validly applying derivational rules to true premises will yield true conclusions) and complete (allowing for proof of all true true theorems expressible by that system within that system). To do this, Godel used integers to represent statements about the symbolic underpinnings of arithmetic (let's call the latter symbolic system "Theory T"...there are many such possible Ts). Godel's key move was to express a self-referential statement, "This statement is unprovable within theory T," using an integer, let's say "G". This is problematic: assume that G is true. This entails that T contains theorems that are true but cannot be proven by valid use of its rules, so T is incomplete. So instead, let's assume that G is false. This means that T can prove G, a false statement, and T is thus inconsistent.
I find this intriguing, as it suggests that no complete and rigorous description of a given system can be made within that system.
Hofstadter thinks that the emergent self, a mind trying to describe itself to itself, provides another such example of a strange loop. Neural activity in producing the experience of dynamically linked symbols produces a conception of a coherent self that exercises 'free will' (let's define the latter autonomous causal influence over what this self does), understands motivations in terms of its desires, feelings, etc., provides an account of itself in terms of strings of memories, and so forth. If this description were true and exhaustive, then the neurology of the brain couldn't have produced it. Yet it is through the symbolic systems of the mind that we fashion an intelligible description of this neurology itself (for only conscious investigators come to know about neurology).
*like, really, someone else should chime in with elaborations and/or corrections
**again, I'm not too happy with how this took shape despite additional consultation, including a wikipedia-based refresher
ebola