Comments on Richard K. Atkins’ Peirce on Inference

Abstract: This article offers a critical examination of some central components of Richard Atkins’ Peirce on Inference. First, I discuss Atkins’ reading of Peirce’s notion of a “leading principle” as a conditional whose antecedent is simply the conjunction of an argument’s premises (LPP). Drawing on Peirce’s Baldwin Dictionary entry, I suggest instead that a leading principle is a general description of possible premises and conclusions (LLP), and that the alleged Peircean “confusion” between LPP and LLP is unsubstantiated. I then emphasize Peirce’s distinction between logical and material principles and show how his account of the redundancy of logical leading principles both blocks Carroll’s regress and supports his claim that every mental action is, in form, a valid inference. In the second part, I endorse Atkins’ arguments against identifying Peirce’s late abduction with his early hypothesis, but propose an alternative clarification of the distinction based on the different roles of explanandum and predictions. Finally, I question Atkins’ typology of deduction and his identification of deduction with logical calculus, arguing instead that Peirce takes deductive logic to analyze mathematical reasoning and that deduction proceeds in stages—logical analysis being followed by demonstration, which may be corollarial or theorematic.