intellect, the faculty of deduction and that of induction.

Let us begin with deduction. The same movement by which I trace a figure
in space engenders its properties: they are visible and tangible in the
movement itself; I feel, I see in space the relation of the definition
to its consequences, of the premisses to the conclusion. All the other
concepts of which experience suggests the idea to me are only in part
constructible _a priori_; the definition of them is therefore imperfect,
and the deductions into which these concepts enter, however closely the
conclusion is linked to the premisses, participate in this imperfection.
But when I trace roughly in the sand the base of a triangle, as I begin
to form the two angles at the base, I know positively, and understand
absolutely, that if these two angles are equal the sides will be equal
also, the figure being then able to be turned over on itself without
there being any change whatever. I know it before I have learnt
geometry. Thus, prior to the science of geometry, there is a natural
geometry whose clearness and evidence surpass the clearness and evidence
of other deductions. Now, these other deductions bear on qualities, and
not on magnitudes purely. They are, then, likely to have been formed on
the model of the first, and to borrow their force from the fact that,
behind quality, we see magnitude vaguely showing through. We may notice,
as a fact, that questions of situation and of magnitude are the first
that present themselves to our activity, those which intelligence
externalized in action resolves even before reflective intelligence has
appeared. The savage understands better than the civilized man how to
judge distances, to determine a direction, to retrace by memory the
often complicated plan of the road he has traveled, and so to return in
a straight line to his starting-point.[81] If the animal does not deduce
explicitly, if he does not form explicit concepts, neither does he form
the idea of a homogeneous space. You cannot present this space to
yourself without introducing, in the same act, a virtual geometry which
will, of itself, degrade itself into logic. All the repugnance that
philosophers manifest towards this manner of regarding things comes from
this, that the logical work of the intellect represents to their eyes a
positive spiritual effort. But, if we understand by spirituality a
progress to ever new creations, to conclusions incommensurable with the