Jeff> I tend to think the later writings often build on the earlier. As such, I wonder what the later proof borrows by way of premisses from the arguments developed in the 1903 Harvard Lectures on Pragmatism. Once that is clearer, we can then ask what might have been added to the later argument by way of additional premisses.

Peirce's ideas were constantly evolving up to the very end.  He frequently went back to earlier ideas, but always with some new insights or directions from his later developments.  For pragmaticism,  his 1903 Harvard and Lowell lectures were an important starting point.  And the word 'prolegomena' in 1906 is an important clue.

An interesting occurrence in December 1902:  Carus published a new English translation of Kant's "Prolegomena to any future metaphysics" and Peirce published a notice of it in the Nation in June 1903. -- he must have been reading (or rereading) it around the same time as he was preparing those Lectures.

Peirce must have read it (in German) during the time that he and his father were studying Kant.  After Kant finished the first edition of KdrV (or CdrV as Peirce preferred to refer to it), he wrote the short Prolegomena as an intro and overview of the questions that he tried to answer in the first edition of the K(C)drV.  Those questions were the prelude to his second edition, which he finished a few years later. Although Peirce had criticized some of Kant's fundamental assumptions, he always had a high regard for Kant, and he cited him frequently throughout CP.    And he had a very high regard for Kant's questions, which are the main topic of his own Prolegomena. If you (a) read Kant's questions and (b) read Peirce's writings from 1903 onwards, you can see a strong influence of Kant's questions on Peirce.  In fact, Peirce's 1903 classification of the sciences seems to be part of Peirce's answers to K's three transcendental questions.

Even stronger evidence for Kant's influence is Peirce's 1906 Apology for Pragmaticism, which is written as a prelude to a series of articles he planned for the Monist.   Unfortunately, he ran into difficulties around 1909, which led him to the series of ten MSS on "Assurance" (R661 to R670) from 1910 to 1911.

There's much more to be said about all these issues.  I recommend an article about Peirce's Apology by Max Fisch (1982) and reprinted in a book by Fisch in 1986.  In that article, Max F. wrote that methodeutic is a key topic that Peirce was addressing in his planned proof.  I agree. 

And I also believe that there were two reasons why Peirce stopped in 1909:  (1) problems with phaneroscopy as a science egg (R645) and (2) problems with logic, which were the reason for his ten studies (R661 to R670) from 1910 to 1911.  These are the reasons for major revisions that Peirce made in 1911 and 1912.  It's sad that he was converging on important new ideas just when he had that accident in 1911 followed by the cancer.

There is, of course, much more to say about all these issues.  And as Max Fisch also said, that's why we need all of Peirce's late MSS available in suitable formats.  As Peirce's late letters show -- he was thinking very hard about all these issues.  And he didn't hesitate to make major revisions when necessary.

John