May 22, 2018:
"Problematic" is a noun, not a description. The concept was produced by Althusser's friend Jacques Martin. A Problematic is a system of interrelated concepts existing in a hierarchical relationship revolving around a dominant concept that assigns the others their specific meaning and effectivity within the system. Think of Freud's conceptual universe: Displacement, Condensation, Repression, Transference: these concepts are made possible and are assigned their effectivity by the central concept of The Unconscious, without which they couldn't exist. Althusser suggests that all systematic bodies of thought conform to this pattern. He calls the determining concept "the theoretical object", or just "the object&qut;, and demonstrates the systematicity of the theoretical "space" thus defined, where "space" is a metaphor intended to make it easier to "see" these relationships.
If you're familiar with Thomas Kuhn's term "Paradigm" this may seem familiar to you. The difference is that Kuhn's Paradigm exists inside the heads of individual subjects: it's a description of the way they think about things. Althusser's Problematic exists nowhere: it's visible only in its effects, which are the logical relationships between the concepts it necessitates and makes possible, and also those it necessarily excludes. It's the system of logical implications of the concepts themselves, in their interrelationships. It doesn't matter whether individuals are aware of thinking within Problematics: they'll be forced to think within them whether they recognize that or not. You can word this in a very radical way by saying that the Problematic will produce the individuals who think it: if Niels Bohr had never existed someone else would have produced the principle of complementarity, because it's implied by and necessary to the problematic of quantum physics. Paradigm is subjective; Problematic is objective. Paradigm is immediately visible, and so available, inside the heads of the people who think it; like the Unconscious, the Problematic exists only in its effects, requiring a symptomatic analysis to make it visible. Paradigm is a description; Problematic is a concept.
Problematic is an abstract concept — an isolation of logical phenomena found concretely only in complex articulations. In the thought of real individuals, multiple problematics coexist, interrelate, overlap, interpenetrate, and there's a specific articulation between these elements which can be teased out and made visible through a process of theoretical labor — a "symptomatic reading". In Capital, Marx thinks primarily within the Marxist problematic, but there are inescapable presences of the Hegelian and Feurbachian problematics: there's an inevitable tension between them. Disentangling the problematics within which people think is part of the job of readers who read as Althusserians.
Here's what's so useful about this concept. It enables objective, robustly analyzable distinctions between bodies of ideas. It makes these distinctions visible, along with their sometimes surprising relationships. Where most of Althusser's examples are from the history of science or philosophy, here's one from life. AA conceptualizes alcoholism as spiritual dysfunction, a moral issue, in which the alcoholic is not in a right relationship with her higher power. Addiction science conceptualizes it as a medical issue, a type of physical brain damage causing communication between neurons to fail in specific centers of the brain. AA's is an idealist problematic about God; science's is a materialist problematic about brain chemistry. They're incompatible conceptualizations, which strict AA members acknowledge when they insist that medication is not allowed in the program. The Problematic enables you to draw clear, logically rigorous lines of demarcation like that one between and within bodies of thought. Here's an example which might be a surprise to Marxists. Marx held two incompatible theories of history simultaneously, showing no awareness of that fact. Sometimes he described history as the teleological self-development of the productive forces; other times as class struggle. These incompatible theories have incompatible implications. One of them implies a fatalism, the other can be a basis for activist political strategy. This tension is unresolved through the history of Marxism.