Abstract

Below are reflections on Peirce’s conception of abductive methods and Russell’s conception of regressive methods. Along the way, it will be necessary to examine the marked differences between Russell and Frege on the ins and outs of logicism, from which latter the regressivist ideas first emerged. Russell was aware of Peirce’s contributions to the algebraization of logic and Peirce was aware of Russell’s writings on logicism. However, in framing his thoughts about regressive methods, Russell showed no familiarity with Peirce’s treatment of abductive methods. In 1907, Russell read to the Cambridge Mathematics Club an essay entitled “The regressive method of discovering the premises of mathematics.” Since that paper didn’t see the published light of day until three years after Russell’s death in 1970, Peirce couldn’t have taken notice of it in developing his ideas about abduction. Even so, it has been suggested that there exists a noteworthy similarity between Russell’s regressivism and Peirce’s abductivism. The principal purpose of this essay is to show the resemblance to have been misjudged, in which case, my title would have to be corrected.