[Authors and titles are listed at the end of the review]
Aristotle’s Syllogism and the Creation of Modern Logic is dedicated to the memory of John Concoran and aims to do “for modern logic what Concoran did for the work of George Boole, namely to make sense of and do justice to the idea that Aristotelian syllogistic logic contributed to its creation” (1). Thus, tracing the history of syllogistic from Richard Whately’s syllogistic through the work of Mill, Venn, Bolzano, Brentano, Hilbert, Frege and many other important logicians, up to the 1930s, the authors want to show that modern logic “has reformed and expanded rather than abandoned the Aristotelian heritage” (4). In particular, the aims are:
- to single out the role of Aristotelian syllogistic logic in the creation of modern logic;
- to explain the “different attitudes toward syllogistic” at the basis of the different development of modern logic and syllogistic itself (1);
- to outline the debate on the “proper nature, scope and method of logic” so as to delineate the “cross-pollination” of different traditions (3).
The structure is as follows: after lists of figures and tables used in the book and a list of contributors and the acknowledgements, there is a brief and enlightening introduction, followed by fourteen chapters and, at the end, by a useful index of names and concepts quoted in the several contributions.
In the introduction (“History of Modern Logic in a New Key”) Verburgt and Cosci tackle the so-called “standard narrative on the history of modern logic” as the main target of their enquiry (1). Indeed, it is usually said that the development of modern logic, particularly in the period chosen by the authors, is due entirely to a refutation of Aristotelian logic. According to Verburgt and Cosci, this is clearly expressed by the “Quine-Putnam” explanation of the origin of modern logic. Quine claims that the Aristotelian logic is to modern logic what the ‘arithmetic of primitives tribes’ is to modern mathematics. In other words, ancient logic would be a “prescientific fragment” of the whole logical theory developed in the nineteenth century. Quine also maintains that there is a discrete change between ancient and modern logic, started by Frege’s Begriffschrift, and similarly Putnam thinks that there is a fixed and precise starting point of modern logic, which is not Frege but Boole’s Mathematical Analysis of Logic and Laws of Thought. However, as Verbugt and Consci point out, the so-called “mathematical turn in logic was not a development beginning in the second half of the nineteenth century, let alone an accomplishment of Frege and Boole alone” (3).
The main issue is thus the description of the origin of modern logic, which implies in turn the description of the decline of syllogistic. The question is: given that there is a decline, is it a sudden disappearance or a slow reformulation? It is of course true that in the nineteenth century logic and mathematics had an amazing development, and there was also a revolution based on the rejection of the past. During the 1800s, the domain of the Aristotelian syllogistic was eclipsed. Nevertheless, it must also be said that “the collapse of the Aristotelian empire did not happen overnight” (2). As Rome was not made in a day, it is also true that Rome was not undone in a day. The same holds for the millenarian empire of Aristotelian logic and hence it is not surprising that between the 1820s and the 1930s “there was an explosion of attempts to rethink logic” (2), as in Hilbert’s case – something shown in William Ewald’s chapter, “Hilbert’s Use of the Syllogism”, with the attempt to provide an “internalization” or “nostrification” of the syllogism. So, the “standard narrative” offers discontinuous account of the development of modern logic. In other words, Quine and Putman’s “search for a discrete event (or even an exact year) obscured the fact that the mathematical turn itself was part of a broader process of the lingering demise of the syllogistic, that is, of the gradual downfall of what for over two millennia had been logic’s paradigm” (3). The authors of this book reject this discontinuous account, and trace a continuous line from Aristotle to Gentzen, showing:
- how modern theories are bound to Aristotelian logic or influenced by syllogistic reasoning. For example, Calvin Jongsma in his chapter “Richard Whately’s Revitalization of the Syllogistic Logic” states that “Whately’s logic became the leading traditional text of its time” precisely because it provides a “vigorous defence of syllogistic reasoning” (28). Or, to take another example, Sun-Joo Shin, in Chapter Five, entitled “Logic of Relations by De Morgan and Peirce: A Case Study for the Refinement of Syllogism”, states that a “disconnection” (108) between Aristotelian syllogism and De Morgan and Peirce’s logic cannot be truly sustained without compromising a correct understanding of the logic of relations.
- how syllogistic is influenced by modern theories. For example, the Vorlesungen über die Algebra der Logik by Ernst Schröder, presented by Peckhaus in Chapter Six, “Ernst Schröder’s Algebra of Logic and the ‘Logic of the Ancient’”, provided a fundamental tool for translating the rules of Aristotelian logic into algebraic language. This translation guarantees a reconsideration of syllogistic by which, for example, Schröder can select and rearrange fifteen valid forms of traditional syllogism.
In this way, a “parallel development of modern logicians reshaping the syllogism and reflections on the syllogism shaping modern logic” (1) are perfectly described.
As a collection of different essays by different authors, the work could have become disorganised, as each author has his or her own focus and approaches the chapter differently from the others. However, care was taken to ensure unity and continuity, and to highlight the precedents and legacy of each author. For example, Verbugt’s chapter “Mill and the British Tradition of Inductive Logic: The Role of Syllogism” has a paragraph entirely devoted to the relationship between Mill and Whately, and thus ties in with Calvin Jongsma’s chapter. Matteo Cosci also devotes several paragraphs of his chapter “Brentano and Hillebrand on Syllogism: Development and Reception of the ‘Idiogenetic’ Theory” to the reception of Brentano’s logic and to the influence of Leibniz on Brentano (Cosci shows that, although Brentano does not mention Leibniz in his work, he refers to him in his lectures). Moreover, several parallels between different authors help to give immediate clues to their “different attitudes towards syllogistic” while also giving the impression of a continuous history, instead of an abrupt change from ancient to modern logic. To name a few: the parallelism proposed by Verbugt between Mill and Venn on the petitio principii of syllogisms proper to the empiricist (and the sceptical) rejection of syllogistic logic; the parallelism between Hilbert and Quine on the analysis of syllogism, provided by William Ewald in his “Hilbert’s Use of the Syllogism”; the relationship between Frege’s and Aristotle’s logic proposed by Erich H. Reck in his “Frege’s Relation to Aristotle and the Emergence of Modern Logic”. Finally, the historical background set out in the general overview proves useful to help guide the reader smoothly through the gradual evolution of syllogistic.
Therefore, this work has the unquestionable merit of presenting not only the value of Aristotelian logic in modern logic, but also of emphasising the multitude of interpretations of syllogistic provided by many, sometimes overlooked, authors – such Hugh McColl, presented by Jean-Marie C. Chevalier in “Hugh MacColl: Never Twist the Syllogism Again” – and even the role of syllogistic in the structure of modern logic studies, identifying how syllogistic influenced new theories (as in the case of José Ferreirós’s chapter “The Role of Syllogistic Logic in Early Set Theory” dedicated to an analysis of the cursus studiorum of logic in the syllabus of the German Gymnasium). Moreover, the book reveals the pivotal role of syllogism not only at the formal level, as in the case of the Bolzano’s “objective” logic of “sentences in themselves”, studied by Mark Siebel in “The Aristotelian Roots of Bolzano’s Logic”, or in the case of Boole’s syllogistic as presented by David E. Dunning in Chapter Four (“George Boole and the ‘Pure Analysis’ of the Syllogism”), but also at the epistemological level, as in case of Mill’s discussion of the epistemological status acquired by syllogistic reasoning, presented in Verburgt’s contribution. Finally, in-depth reflection is also successfully conducted on the important topic of how deductive reasoning was progressively distinguished from syllogism and on the role of syllogistic in the development of the notion of deducibility, for example in Paola Cantù’s chapter “Syllogism and Beyond in the Peano School”, and in the last chapter of the book, “The Fate of the Syllogism in the Göttingen School”, by Curtis Franks.
This work fills a gap that has so far existed in the detailed history of modern syllogistic. It also offers suggestions for further research topics, such as the work on philosophical and formal logic by logicians such as E. E. Constance Jones, Sophie Bryant and Augusta Klein.
As a final remark, it can be said that the main thesis of the book seems entirely agreeable and indisputable. One cannot be so naive as to assume that the course of history is discontinuous: even change presupposes that what is negated is considered in the very act of negating it for, trivially, to know whether a negation is true or false one must already know the truth value of the proposition that is negated. To use the words of our authors: “in order to establish a break with tradition, the pioneers of modern logic had to engage with that very tradition” (3).
Surprisingly enough, the authors found themselves forced to repeat what is rather clear for everyone who has done a basic course in history. The fact that historical changes are not abrupt, as thunder at night, is an unquestionable commonplace and, needless to say, this holds not only for historical change in general but also for those particular forms of historical change that are part of larger historical change, e.g. the “mathematical turn” in logic. By this I do not mean to say that the authors have based their book on a triviality so that it appears to be useless. On the contrary, the fact that they felt they had to remind scholars of this elementary principle of all historical research speaks volumes about the state of studies in the history of logic, especially where (and perhaps this is another “standard narrative”) it is believed that the complete understanding of an author’s logical theory can be fully achieved even while ignoring the context and history surrounding it.
Authors and Titles
Introduction, Lukas M. Verburgt (NIAS/Leiden University, Netherlands) & Matteo Cosci
- Richard Whately’s Revitalization of Syllogistic Logic, Calvin Jongsma
- Mill and the British Tradition of Inductive Logic: The Role of Syllogism, Lukas M. Verburgt
- The Aristotelian Roots of Bolzano’s Logic, Mark Siebel
- George Boole and the “Pure Analysis” of the Syllogism, David E. Dunning
- Logic of Relations by De Morgan Peirce: A Case Study for the Refinement of Syllogism, Sun-Joo Shin
- Ernst Schröder’s Algebra of Logic and the “Logic of the Ancient”, Volker Peckhaus
- Brentano and Hillebrand on Syllogism: Development and Reception of the “Idiogenetic” Theory, Matteo Cosci
- Hugh MacColl: Never Twist the Syllogism Again, J.M.C. Chevalier
- Frege’s Relation to Aristotle and the Emergence of Modern Logic, Erich H. Reck
- Christine Ladd-Franklin’s Antilogism, Francine F. Abeles
- Syllogism and Beyond in the Peano School, Paola Cantù
- Hilbert’s Use of the Syllogism, William Ewald
- The Role of Syllogistic Logic in Early Set Theory, José Ferreirós
- The Fate of the Syllogism in the Göttingen School, 1910-1940, Curtis Franks