• The key ideas in §§6-12 are attached to the related terms forms of sensibility and pure intuition. Kant’s use of the term “intuition” is special and can be puzzling. One way to understand it is to regard ‘intuitive’ in his sense as a kind of opposite to ‘discursive’ or ‘conceptual’, and this difference is related to the old saw that a picture is worth a thousand words—that is, that there is a form of thought that is not verbal.

• The argument in §13 concerns what have come to be called “incongruent counterparts.” It continues to attract the attention of philosophers, and people don’t agree about either what Kant is arguing or whether his argument is a good one. Very roughly, he points to the difference between reflection and rotation of 3-dimensional objects are argues that the difference between objects that are mirror images but cannot be rotated to coincide cannot be explained as a difference between the objects themselves (since reflection also preserves all the distances between their parts) and thus requires some reference to space itself.

• In the three remarks, Kant begins to present his version of idealism. In the first, he notes its importance for his account of mathematics; in the second, he spells out its content; and, in the third, he distinguishes it from the idealism he finds in Descartes and Berkeley. This is only his first discussion of a side of his views that he will have much more to say about later, and you can expect it to take a while to feel you have a hold on what he wants to say.