Peirce: A Guide for the Perplexed by Cornelis de Waal (review)

Introducing the perplexed reader to a philosophy requires both a comprehensive understanding of the philosophy in question and a rigorous simplifying strategy. But clarity and accessibility come at a price: one has to cut down on complicated and perhaps unresolved lines of thought and arguments, stratifying the development of theoretical positions into a coherent and accessible narrative. This review will address both the success of this book as an introduction and, rather unjustly, those more complex topics that have been left out and might be of interest to readers of this journal.

First of all, let me say that Cornelis de Waal’s Peirce: A Guide for the Pexplexed is a very good introduction to Peirce’s philosophy. The book opens a road to a more comprehensive understanding of Peirce’s philosophy. The nine chapters of the book, following the opening chapter on “Life and Work” and concluding with the ninth chapter on “Mind, God, and Cosmos,” present Peirce’s philosophy by following, more or less, the final version of Peirce’s classification of the sciences of discovery. The path generated in this way connects systematically the theses, principles and arguments in the different fields of Peirce’s philosophical thought, connecting his view of mathematics as a purely hypothetical discipline with his evolutionary metaphysics and philosophy of religion.

In this classification, the place of a science in the sequence depends on its generality, special sciences depending on the more general, comprehensive ones. Or, to put it differently: the more specific the objects of a science, the later it will appear in the systematic sequence. Peirce’s notion of an object plays a special role here. The object is conceived like the causa finalis of a science, functioning as the regulative idea that connects a community of researchers with their field of work. De Waal does not mention this crucial role of the objects of a science and in Chapter 5, which deals with semiotics, he even claims that Peirce’s account of an object and his distinction between an immediate and dynamical object is “fairly traditional.” I will show later on why this claim is misleading and problematic.

But de Waal is right in pointing out that Peirce regards mathematics as a purely hypothetical discipline, because it can be applied to objects of all sorts. In following the descending generality of classification, the second chapter starts with a discussion of “Mathematics and Philosophy.” Here de Waal makes a move that is both fruitful and suggestive. The graphical demonstration (18f) that the sum of the angles of a triangle is equal to the sum of two right angles is used to show that such a proof cannot be a syllogistic one. In this way de Waal achieves several things at the same time. The reader is introduced to Peirce’s visual and mathematical style of thought. The diagrammatic construction of conceptual relations illustrates how Peirce generalizes the Kantian idea that there are necessary conceptual constructions in mathematics that are based on the form of perception. This way of dealing with mathematical principles establishes a crucial difference between Peirce’s and Kant’s thought and exemplifies Peirce’s idea that pure mathematics cannot be a positive science but is a science of hypothetical construction. In this way the ground is prepared for the graphical argument illustrating Peirce’s theorem about the sufficiency of three categories in Chapter 3 on “Phenomenology and the Categories” (41f). Without much ado, de Waal shows in this chapter that Peirce’s phenomenology is a radical undertaking and that the categories are both concrete and general. De Waal models the claim that the three categories are sufficient and irreducible to one another by showing that in a sequence of diagrams, the transformation between three dots and the lines connecting them requires only three categories (42).

What I find at once interesting and problematic in de Waal’s guide is the characterization of Peirce’s general philosophical position. By far the majority of scholars now...