The first and second parts of the Prolegomena have clear ties to the thinking of Kant’s predecessors, and they were central to Kant’s influence in the 20th century. However, the third part represents thinking that is quite new with him, and it is what most captured the imagination of philosophers in the decades following its publication—though often in ways that might not have pleased Kant.
• Just as first part of the Prolegomena focused on sensibility and intuitions and the second on understanding and concepts, the third focuses on “reason” and what Kant calls “ideas.” This is a use of the term ‘idea’ quite different from what we’ve seen so far, and Kant uses the initial sections of the third part, §§40-45 (pp. 64-69), to explain it. (The “syllogisms” Kant mentions in §43 are patterns of argument; they get the same names as the three forms of judgment classified “as to relation” because each of these forms plays a key role in the corresponding sort of syllogism.)
• The rest of the third part is organized around three kinds of “ideas.” This assignment includes the discussion of the first kind, “psychological ideas,” §§46-49 (pp. 69-73). In §46, Kant runs through the key general features of ideas (in his sense) that he mentioned in his initial discussion in part III: ideas are associated with a sort of completion of reasoning (cf. §43); these “concepts of reason” have no application to experience (cf. §44, beginning); they instead function as regulative principles for our thinking (cf. §44, end). Then in §§47-48, Kant points to the inapplicability to the idea of the soul of the principle of permanence that was the synthetic a priori judgment associated with the category of substance (one of the “analogies of experience” discussed in general in §25 but actually stated specifically back in §15).
• In section §49, Kant uses his discussion of the idea of the soul to say more about the distinction between his idealism (which he here calls “formal”) and the idealism he finds in Descartes (which he calls “material”). (Recall that he discusses the same issue also in Remark III at the end of the first part of the Prolegomena.)