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  • C.S. Peirce's System of Science
  • Rosa Mayorga
Frances Williams Scott. C.S. Peirce's System of Science. Elsah, Illinois: The Press of Arisbe Associates, 2006 160 pp.

This is the seventh volume of the Peirce Studies series, whose editorial aim, we are told, is to "encourage a wider understanding" of Peirce's writings as well as "the further development of his ideas."1 Overall, [End Page 181] Scott's work makes a contribution to this general aim, especially as regards the "wider understanding" part.

Scott states her particular aim in the introduction: subscribing to the now uncontroversial view that Peirce's writings "were neither fragmentary nor unsystematic," but instead comprised a "developed and highly organized system" (p.4), she proposes to explore in her study the following hypothesis regarding the nature of Peirce's system:

Peirce . . . conceived of his work in terms of a comprehensive and unified System of Science which he had developed; a familiarity with his system is essential for understanding the interdependent relationships between his contributions to mathematics, certain special sciences (particularly physics and chemistry), logic, and philosophy.


This "System of Science" is a theory that describes science as "a living activity of scientific methods" (p.5). Scott considers that Peirce's "one animating purpose" was to explain "the derivations and nature of methods of scientific thought" (p.5), and Peirce bases this scientific method, she will claim, on the model of mathematics. Although she considers herself a "non-mathematician" (p.52), Scott proceeds to show in the rest of the book why the diagrammatic characteristic of mathematical reasoning, is, for Peirce, "the basis for examining the structure of all scientific intellectual activity" (p.36). She tries to achieve this by analyzing the interrelations between Peirce's conception of philosophy, logic, semiotics, and science in general.

Part one is devoted to a basic explanation of the broad sense in which Peirce used the term "science" and of his scientific method as the preferred way of the four methods of fixing beliefs. Noting that Peirce claimed that the classification of the sciences was the key "to approaching the overall pattern of his thought" (p.5), she then lays the groundwork in the second chapter for the claim that the science of mathematics is to be considered the most basic science in terms of methods of reasoning. Claiming that Peirce's classificatory model of the sciences is itself a schema that displays in "skeletonized form" (p.34) both Peirce's primary concern and his proposed solution regarding methods, she argues that since mathematics (in both versions of the model which she discusses) is listed first under "Theoretical Science" (Science of Discovery), this shows that mathematics is identified as the fundamental science in terms of methods of reasoning. Since in this model the sciences are classified "in descending order of methodological dependency" (p.7), and since Philosophy (Coenoscopy) including Phenomenology, Normative Science (Logic, Esthetics, Ethics) and Metaphysics, as well as the Special Sciences (Physical, Psychical), all are positioned after Mathematics, this is seen as an indication that "the methods of objective inquiry used by all the other sciences beneath it are derived in part from the methods of mathematics" (p.7). [End Page 182]

All science involves observation, (including philosophy, which is concerned with analyzing the common experiences of life), but different sciences are observational in radically different ways. Although defined by Peirce as "the science which draws necessary conclusions" (p.103), Scott will argue that Peirce considers mathematics to rely on observation, as well as on hypothesis and experimentation (p.9). These requirements for all objective inquiry are met through diagrammatic reasoning in mathematics, since such diagrams not only offer "an efficient economical research tool for experimentation and observation by the individual inquirer, but they also afford opportunities for public accessibility and replication of these processes" (p.11). The role of diagrams, then, is essential in mathematics for they are the key as to why it is presupposed by other sciences. Since Peirce subscribed to the dictum that all knowledge begins with perception, to develop mathematical concepts, a perceivable means of experience is needed. Mathematical diagrams are visual, making it possible to isolate...