Atkins, Richard Kenneth.  “Restructuring the Sciences: Peirce's Categories and His Classifications of the Sciences."  Transactions of the C.S.Pierce Society 42, no. 4 (2006): 483-500.

Abstract

This essay shows that Peirce's (more or less) final classification of the sciences arises from the systematic application of his Categories of Firstness, Secondness and Thirdness to the classification of the sciences themselves and that he does not do so until his 1903's "An Outline Classification of the Sciences." The essay proceeds by: First, making some preliminary comments regarding Peirce's notion of an architectonic, or classification of the sciences; Second, briefly explaining Peirce's Categories of Firstness, Secondness and Thirdness; Third, examining how Peirce classifies the sciences in 1902 and 1903and specifically how the 1903 classification utilizes the Categories; Fourth and finally, showing that he is only led to classify the sciences in this fashion as result of his philosophical inquiries during those intervening months, especially as a result of his Harvard Lectures on Pragmatism.