BODY AND PRACTICE IN KANT

SPATIAL SCHEMATISM 193
account the spatial form of this object, i.e. its shape, and this is done, by
means of an act similar to an act of construction. Now, how does this
help us towards a better understanding of the relation between
subsumption and construction in Kant’s theory of schematism? As the
theory needed to answer this question is only hinted at in the schematism
chapter, we have to try to deduce it from the little that is said. Let us try
to do so, however, and in order not to stray too far, let us concentrate on
the triangle example.
Following the example of the triangle, Kant tells us that his theory of
schematism may be used to solve the old problem of the generality of
concepts, namely how can a concept be general and still apply to
particulars which, moreover, are not congruent? If we think of the
concept as an image, or something like an image, the required generality
would never be attained, he argues.
No image of a triangle would ever be adequate to the concept of it.
For it would not attain the generality of the concept, which makes
this valid for all triangles, right or acute, etc., but would always be
limited to one part of this sphere. (A 141/B 180)
If we instead think of the concept of a triangle as a rule-governing
practice through which all existing triangles may be produced, the
problem of generality is solved. Let us represent the rule of this practice
linguistically like this: ‘Draw three straight lines in a plane. Each line
must intersect the other two. The triangle is the figure constituted by the
lines connecting the intersections.’ By means of this practice, an infinite
set of triangles may be produced. Further, since the rule is unspecific
regarding angles and distances, each new triangle produced is potentially
different from the others. However, as long as they are produced
according to the rule, they are all triangles. The problem of generality is
solved because the generality is guaranteed by the procedure. In a sense,
the generality is found in the procedure rather than in each individual
triangle.
Kant has now demonstrated that the procedure for producing a
triangle may be conceived of as general in the same sense that a concept
is usually considered to be general. However, the main question is still
left unanswered, which is how does this help us understand what
subsumption has to do with construction? Let us assume that we have a
triangle before us, a triangle empirically given, for example one drawn on
a piece of paper or made of wood. How do we recognize this triangle as a
triangle? And how does this recognition involve an act of construction?
What does Kant mean when he suggests that the capacity to recognize it