• The ideas of the second sort, discussed in §§50-54 (pp. 73-82), are themselves treated unequally: the third of the four “antinomies” Kant associates with them gets most of the attention. Although this discussion, in §53 (pp. 78-81), will also receive most of our attention, the general idea of the antinomies of which it is an example is probably best understood by thinking of the first, which Kant discusses in §52c (p. 77).

• Kant’s single paragraph on the third sort of ideas (§55, pp. 82f) is a place where he omitted much material that appears in the Critique. The corresponding part of the longer work is an extended discussion of proofs of God’s existence, and the only hint here of that discussion is the next-to-last sentence.

• The final “general remark” (§56, pp. 83-84) is very important, especially the distinction between “regulative” and “constitutive” principles. The corresonding discussion in the Critique is the place where Kant moves from a discussion of “pure” natural science to say some things about the actual content of natural science. For example, the regulative principle associated with ideas of the third sort says that the world should be regarded as if it was designed to exhibit something like the features—the greatest variety with the simplest means—that Leibniz held we that could know it was designed to exhibit. Kant associated this regulative principle with efforts directed at scientific classification and the confidence that such classification is possible. (Kant offers an example from chemistry, the classifications acid and alkali, which had been introduced by Lavoisier only a few years before.)