BODY AND PRACTICE IN KANT

SPATIAL SCHEMATISM 187
Philosophical cognition [Erkenntnis] is rational cognition from
concepts, mathematical cognition that from the construction of
concepts. But to construct a concept means to exhibit a priori the
intuition corresponding to it. For the construction of a concept,
therefore, a non-empirical intuition is required, which consequently,
as intuition, is an individual object, but that must nevertheless, as the
construction of a concept (of a general representation), express in the
representation universal validity for all possible intuitions that belong
under the same concept. Thus I construct a triangle by exhibiting an
object corresponding to this concept, either through mere
imagination, in pure intuition, or on paper, in empirical intuition, but
in both cases completely a priori, without having had to borrow the
pattern for it from any experience. The individual drawn figure is
empirical, and nevertheless serves to express the concept without
damage to its universality, for in the case of this empirical intuition
we have taken account only of the action of constructing the concept,
to which many determinations, e.g., those of the magnitude of the
sides and the angles, are entirely indifferent, and thus we have
abstracted from these differences, which do not alter the concept of
the triangle. (A 713f./B741f.)
The example of the passage is a triangle. To construct the concept of a
triangle, so we learn from the text, means to produce [darstellen] a priori
an intuition corresponding to the concept. Kant then says that this
requires an intuition that is not empirical, but that still qua intuition is
both an individual object, and at the same time, exhibits the general
features of all objects falling under the concept, that is, all triangles. Let
us stop here to reflect on what Kant is saying.
First, Kant seems to say that the general features of the triangle are
not found in the triangle as such, but in the procedure by which the
triangle is constructed, a procedure, moreover, that is common to all
triangles. I will return to discuss this point below. Further, we are told
that the product of the construction just referred to is an intuition that is
not empirical. This may seem to suggest that the construction in question
does not include empirical elements such as our hands, a pencil or a
piece of paper, but is performed in some other way, outside the empirical
or even the spatio-temporal domain, and Kant’s remark that the
construction is a priori may seem to support this interpretation. The
notion of the a priori is typically seen as opposed to the notion of the
empirical.
I think we would be wise, however, to refrain from reaching such a
conclusion just yet. Kant continues by distinguishing between two ways
of constructing a triangle: it may be constructed either through the pure
imagination, or on a piece of paper. In the second case the construction