The Aftermath of Syllogism: Aristotelian Logical Argument from Avicenna to Hegel ed. by Marco Sgarbi and Matteo Cosci (review)

Marco Sgarbi and Matteo Cosci's tightly focused anthology will become an important reference. The volume takes up syllogistic logic after its development through late antiquity. Thus, it deals with technical and sophisticated research in what was already, if not the completed science that Kant imagined, then at least a mature discipline with a defined research program, albeit a research program that extended to epistemology, metaphysics, language, and every other branch of knowledge.

One unifying thread that emerges is the role that the already mature science of syllogistic logic played in the maturation of modern science. Was it heuristic, justificatory, explanatory, or organizational? Logicians, historians, philosophers, and, especially, historians of philosophy and science will all find something of value.

The central essays focus on figures and topics from early modernity, with chapters on Hobbes, Descartes, Port-Royal Logic, Locke, and Leibniz. However, the tone is set by the first two chapters on premodern topics: Allan Black on Avicenna and Alan Perreiah on the history of humanist critiques of Scholasticism. They are very different but effectively complementary. Black provides a detailed, logically technical exposition of Avicenna's work on syllogisms that makes the metaphysical entanglements, epistemological assumptions, and myriad semantic distinctions explicit, while Perreiah paints the history of humanism and Scholasticism with broader strokes, providing both historical and historiographical perspectives. What they have in common is that they debunk entrenched but deeply flawed narratives. Black's presentation of Avicenna's subtle analyses of time and necessity, and trenchant distinctions among various kinds of predication give the lie to idea that the Arab commentators on Aristotle were uninspired technicians; Perreiah carefully marshals publication data to undermine the myth that humanism easily swept aside Scholasticism. He then exposes humanistic attacks on Scholasticism as so much strawman argumentation. History has not always been kind to Aristotle's Arab commentators and Scholastic philosophers. The opening chapters disarm those grotesque caricatures.

The middle four chapters address aspects of the intellectual ferment at the start of the scientific revolution. Although there are no essays specifically on either Bacon or Galileo, Stephen Gaukroger ably addresses the Cartesian assault on Aristotelian science. By highlighting the integral role of syllogistic in Aristotelian science, he shows why Descartes could not ignore logic. In seeking the contributions syllogisms could make to the pursuit not just of knowledge but of self-evidence and certainty, Descartes clarified—that is, limited—the role of logic as a procedure for discovery in science. A more positive role for syllogistic emerges in Russell Wahl's deft and informative presentation of the Port-Royal Logic. Part of the project was to explain how knowledge emerges, and Wahl successfully shows how the key Port-Royal innovations—codifying the rules for evaluating syllogisms without having to reduce them to standard forms and clearly distinguishing the comprehension of a term from its extension—made that possible. If the Port-Royal foray into philosophy of language seems almost contemporary, perhaps Hobbes deserves some credit: Douglas Jesseph's treatment of Hobbes's ambivalence toward logic highlights problems familiar to us now, including the ideas that reasoning is merely computational and such bedrock laws of logic as the principle of noncontradiction are trivial semantic facts rather than profound metaphysical truths. Hobbes's nominalism has echoes in David Poggi's chapter on Locke whose intuitionistic inductivism could serve as a challenge, a supplement, or an alternative to strong deductivist programs.

Wolfgang Lenzen's Leibniz is both a culminating and transitional figure. He advanced syllogistic by fully incorporating the Scholastic introduction of negative terms with the Port-Royal innovations. Thus, he effectively converted Aristotelian categorial logic, by way of an algebra of concepts, into an algebra of propositions. In so doing, he anticipated much of Boolean logic, thereby opening the path to the development of modern predicate logic in the nineteenth century (with some foreshadowing of twentieth-century propositional modal logic).

The final...