What is a pure concept, according to Kant?

In a sense, there aren’t any. In a sense, that is, all our actual concepts are empirical concepts.

A concept is a kind of representation. Specifically, it is an intellectual representation of a discursive intellect. But what Kant calls a “representation” is what Descartes calls an “idea”: an act of a psychic faculty which not only, like every being in general, has formal or actual reality, but which also has objective reality — that is, reference (Beziehung) to a possible object. Hence for an act of our soul to be, strictly speaking, a concept, it must fulfill both formal conditions — that is, conditions which arise from the fact that it is supposed to be a mode of the thinking subject — and material conditions — that is, conditions which arise from the fact that it is supposed to have an object, and in that sense a “matter” (a materia circa quam: see the explanations in Thomas, Wolff, and Baumgarten). Because an intellect which represents via concepts (conceptus communes) is discursive, i.e. relies on a non-intellectual faculty (sensible intuition) for immediate relation to an object, these material conditions concern the fitness of the concept to be applied, via the imagination, to intuitions — that is, its schematizability.

General logic is formal logic. In general logic, that is, we abstract from all the material conditions and consider intellectual representations insofar as they fall under the formal conditions only. In transcendental logic, on the other hand, we abstract from some, but not all, of the material conditions. The dividing line is this: of the conditions which allow an object to be given via an image of the concept, some are conditions on the object given, whereas others must already be in place for there to be an object given. The latter are, for us, conditions on objects qua beings which are prior to being in order of predication: that is, transcendental conditions. In transcendental logic, we abstract from the former, but not from the latter.

However, to abstract from a condition is not to make it go away.¹ There are always also a posteriori conditions for the objective reality of a discursive intellectual representation. In fact, the last transcendental condition, expressed in the category of modality, is just this: that any concept must represent its object as possible (due to some satisfiable empirical conditions), hence as actual (under those conditions), and as necessary (relative to the fulfillment of those conditions).² The first and most general such empirical condition is that the object must be a real movable in space which exerts a force on our sensorium. This is therefore the definition of “matter” (again: materia circa quam) for the purposes of pure natural science, as opposed to the definition of matter in transcendental philosophy, as the object of our outer intuition überhaupt.³

It follows that a “pure concept” is always either an empirical concept considered in abstraction from its empirical content, or, if the phrase is supposed to name a fully concrete act of our intellectual faculty, then it names one which is not, strictly speaking, a representation: it fulfills the formal conditions and some, but not all, of the material ones. In particular, to speak of the pure understanding thinking the pure manifold of sense through pure concepts (as schematized by the pure imagination), is only a metaphorical way to describe the process of actual, empirical thought in abstraction from its a posteriori content.

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Footnotes

¹Cf. KdrV A281/B387-8: “so wird, durch eine sonderbare Übereilung, das, wovon abstrahiert wird, dafür genommen, daß es überall nicht anzutreffen sei.”

²Modality is last before being in order of predication. It is first in order of definition, however (A289/B346).

³“Wenn ich den Begriff der Materie nicht durch ein Prädicat, was ihr selbst als Object zukommt, sondern nur durch das Verhältniß zum Erkenntnißvermögen, in welchem mir die Vorstellung allererst gegeben werden kann, erklären soll, so ist Materie ein jeder Gegenstand äußerer Sinne, und dieses wäre die blos metaphysische Erklärung derselben” (MAdN, Ak. 5:481).