REVIEWS

GIVE PEIRCE A CHANCE

Sun-Joo Shin, The Iconic Logic of Peirce’s Graphs. Cambridge, Mass:MIT Press, 2002. Pp. x + 208. US$34.95 HB.

By Anne Morgan

Sun-Joo Shin’s book provides both a unique approach to Charles SandersPeirce’s system of Existential Graphs (EG), and a timely contributionto the current research in heterogeneous representation systems. As thisfield of inquiry emerges, researchers will benefit from the richness ofPeirce’s philosophy, including his theory of signs and EG. Shin, whohas made notable contributions to the discussion of logic and graphicalsystems, correctly asserts that Peirce (one of the founders of modern logic)constructed the first thoroughgoing theory of heterogeneous reasoning (histheory of signs), and moreover that EG is a logical outcome of that theory.Shin explains that EG includes three subsystems, the Alpha, Beta, andGamma graphs, which ‘correspond to propositional, predicate, and modallogic, respectively” (p. 37), but her current work deals exclusively withthe first two. Her agenda is to consider several criticisms against EG andanswer each by enhancing and altering existing features within EG, todemonstrate that EG has its origin within Peirce’s theory of signs, and toexplore and defend the role of iconic representation within a formal logicalsystem.

As Shin provides a useful overview of the current debate regardingheterogeneous systems, a reader with limited knowledge in Peirceanphilosophy and logic will find the first three chapters of the book reas-onably accessible. However, in order to satisfy curious cognitive scientistsand logicians, Shin devotes the subsequent chapters to numerous technicalcomparisons between symbolic logic and EG; as such, these chapters willbe accessible mainly to those who have some mastery of formal symbolicsystems.

Shin points out that logicians of the twentieth century were preoccu-pied with symbolic logical systems. Many have criticised EG, saying thatits graphs often yield ‘complicated-looking’ sentences and that the rulesof the system are difficult to employ. Moreover, logicians have worried

Metascience 12: 242–244, 2003.© 2003 Kluwer Academic Publishers. Printed in the Netherlands.

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that the iconic representation used in a graphical system could lead to afallacy in a formal proof (more on this point in a moment). The use ofsuch a system, then, involves too much risk. These criticisms have fed along-standing prejudice against graphical systems – the notion that only asymbolic system can provide the rigour that is necessary in a formal proof– and have also encouraged logicians to ignore the advantages of EG. Shinexplains that logicians have tended to evaluate graphical systems accordingto the criteria developed for symbolic systems, a situation that has createdadditional bias in favour of symbolic systems and has persuaded someto equate the notion of symbolism with formalism. These circumstances,in turn, fostered an even greater bias. Despite the fact that EG is soundand complete, and equipped with all the expressive power of a first-ordersymbolic system, these criticisms have overshadowed any discussion of itsmerits.

Shin’s succeeds in highlighting the strong points of EG, and in dis-arming its critics by presenting new criteria by which one may evaluateEG according to its own positive attributes. Shin believes that Peirce’s‘endoporeutic’ reading method (in which EG’s graphs are consistently readfrom the outer edges inward) is at least partly to blame for the criticisms.Although one could argue that Peirce’s method is simpler and more intu-itive, Shin succeeds in her endeavour to develop an alternative readingalgorithm, the ‘negation normal form’ (NNF). NNF, she argues, gives amore direct reading that prevents one from translating a given graph intoa cumbersome symbolic sentence. Shin also alters and enhances the infer-ence rules of EG, which results in greater flexibility and efficiency for thesystem. Although Shin’s method modifies Peirce’s original formulation, italso accents the visual features that are already present in EG.

Shin locates Peirce’s motivation for the creation of EG in his theory ofsigns, and specifically in his insistence that the three types of signs (icon,index, and symbol) are each indispensable. In contrast to the many logi-cians strongly preferring symbolic notation, Peirce distinguished the threetypes of signs merely by the different functions they perform. Accordingto Peirce, an icon exhibits a likeness or an analogy to its subject; anindex forces one’s attention toward the particular object in question; and asymbol signifies by habitual connection or convention. For Peirce, no onetype of sign is better than another. Shin points out that Peirce’s positionis easily contrasted with the majority of logicians, who have put undueemphasis on symbolic representations. Shin’s treatment of Peirce’s semi-otics is sufficient for her project, but as Shin herself admits, the informationin this book only touches on the richness of Peirce’s theory of signs.

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With Peirce’s semiotics in hand, the author addresses the issue offormalism. Shin argues that while many logicians equate formality withsymbolism, EG is evidence that Peirce did not. EG is a formal graphicalsystem that utilises both symbolic and iconic representation. A symbolrepresents by convention; therefore, the user of a symbolic system isconstrained by its stipulated rules. An icon, however, represents by simil-arity, whether in appearance or in relational aspects. Shin acknowledgesthe danger of using iconic representation; one could inadvertently utilisean aspect of an icon (within a formal proof) that was not intended to berepresenting. In response to this objection, she offers a discussion of themerits and shortcomings of iconic representation that is too complex torecap in this review. Perhaps it will suffice to note that Shin demonstrateshow one can restrict the semantic rules of EG in order to restrict the useof incidental iconic features, thereby restraining the user by the samemethod employed in the symbolic system. In so doing, she establishesthat one can preserve both the rigour of the system and “the visually clearhomomorphism, [that exists] between representing and represented facts”(p. 31); that is, one can preserve the intuitive relations that are depicted bythe iconic representation.

One can only speculate about how Peirce might regard Shin’s modi-fications of his system, but he would likely applaud the contribution tohis work. Peirce held that scientific knowledge will be achieved by acommunity of researchers working in cooperation toward the same end.Scientific truth, he argued, lies in the indefinite future.

In general, Shin’s work explores the similarities and differences thatexist between graphical and symbolic systems of representation, anddiscusses the consequences her findings have in various fields that cur-rently research and utilise heterogeneous systems. With specific referenceto Peirce, she entertains, acknowledges, and answers many complaintsagainst EG. Moreover, she explores both EG’s origin in Peirce’s theoryof signs and the role of iconic representation in formal logical systems.Here her research breaks new ground, as Peirce’s theory of signs has notpreviously been studied in the context of heterogeneous representation.Clearly, this is a very important book for Peirce scholars, logicians, andresearchers in heterogeneous representation systems.

Department of PhilosophyUniversity of KansasLawrence, KS 66045USA