Peirce’s Speculative Grammar: Logic as Semiotics by Francesco Bellucci (review)

Peirce’s Speculative Grammar is a masterful chronological reconstruction of Peirce’s work on logic as semiotics, or the study of signs and the purposes to which we put them. Peirce’s writings on these topics span more than fifty years. Moreover, his manuscripts number well over 100,000 pages, many of which have yet to be published. Patently, gaining a comprehensive overview of Peirce’s writings on logic is no small feat, and Bellucci is to be celebrated for his efforts. (Full disclosure: I had read a draft of the book and offered Bellucci comments on it.)

Peirce wanted to be known foremost as a logician. He did not, however, want to be known primarily as a formal logician. In a drafted lecture from 1905, he tells the audience that his reputation as a formal logician is unfortunate, for he is only in and not of its world. The mature Peirce distinguishes between formal logic as a part of mathematics and logic as semiotics, which he regards as a normative science. The latter divides into three sub-disciplines: speculative grammar (which studies the classification of signs); logical critics (which studies the conditions of the validity or strength of arguments); and methodeutic (which studies the methods of scientific inquiry).

Bellucci’s book is the first in a planned three-volume opus corresponding to those sub-disciplines of logic as semiotics. The book is excellent, but not for the fainthearted. Peirce’s complex theory of signs, his love for threes, and his growing number of classes of signs—from three to ten to sixty-six—sometimes make for opaque claims and idle distinctions. Many readers are familiar with Peirce’s icon/index/and symbol distinction. Some may know that the type/token distinction is Peirce’s, too. But tell most philosophers that Peirce also distinguishes among descriptive potisigns, designative actisigns, and copulative famisigns, and they will politely excuse themselves from the conversation. Because of its mind-numbing complexity, I have sometimes thought of the study of Peirce’s semiotics as travelling down a rabbit hole—a dark and deep hole where rabbits slowly suffocate and die.

Fortunately, Bellucci shows judicious restraint in declining to exposit Peirce’s classification of sixty-six signs and largely focuses on Peirce’s growing understanding of how this classification is supposed to inform the analysis of arguments in the context of scientific inquiry. The book concludes by summarizing five reasons why logicians and philosophers generally should be interested in the theory of signs: (1) “illation can be reduced to sign relation” since the premises are signs of the conclusion (355); (2) an anti-psychologist approach to logic should be grounded not on an analysis of thought but of sign relations; (3) arguments are composed of propositions and propositions of terms, all of which are signs; (4) although not all signs play a role in reasoning, their study nevertheless sheds light on signs that do play such roles; and, (5) Peirce thought it should fall to logicians to investigate signs since there was then no separate science of semiotics.

Chapter 1 is an examination of Peirce’s lectures of 1865 and 1866, in which he treats of logic as objective symbolistic, or “the study of the validity of certain substitutions of symbols with other symbols that have the same object” (22). The chapter provides a nice overview of Peirce’s early distinctions among deduction, induction, and hypothesis, as well as among what we would today call extension and intension, and what Peirce calls information. It also contains interesting claims on the relation of Peirce’s early semiotics to truth. Chapter 2 is a study of Peirce’s logic of ca. 1873, out of which the more famous Illustrations of the Logic of Science grows. This chapter is brief and light on Peirce’s theory of induction, but the Illustrations series may be more fully addressed in Bellucci’s forthcoming second volume. Chapter 3 examines Peirce’s logic in the years 1879–1884. This...