Kant- The Pure Intuitions of Space and Time Pt. II

Given the considerations in my last post, we can begin to understand why Kant believes that we can have a priori synthetic knowledge (that is, a priori knowledge that adds to our knowledge, ie. certainty of the necessary connections of cause and effect, etc.). Kant says that "Geometry is based upon the pure intuition of space. Arithmetic attains its concepts of numbers by the successive addition of units in time". (Prolegomena Part I) Kant says further that "Sensibility, the form of which is the basis of geometry, is that upon which the possibility of external appearance depends." There are grand implications which follow from this statement in Kant's metaphysics. The implications are basically that our experience of space must conform to the same rules of sensibility that geometry conforms to.

Lets take an example: Kant says that the reason that there are only three spatial dimensions is geometrically based. Kant says that this is because not more than three lines can intersect to form right angles at any one point. This can be illustrated( or maybe intuited) by using the Cartesian coordinate system. Imagine an x and y axis, one for length and one for width. They intersect to form right angles. Now you can probably imagine a third axis, the z axis, which would represent depth. This line also forms right angles with the first two (you can visualize this by drawing a cube). Now if you try to figure out how to add another line which forms right angles through the same point, you will see that you cannot. It is a geometrical rule that no more than three lines can intersect to form right angles at any one point, and it is this rule to which our experience conforms. In fact, the possibility of our experience rests on its conformity to the pure intuitions of sensibility.