I was asked to write a review of Terry Parsons' Articulating Medieval Logic for the Australasian Journal of Philosophy. This is what I've come up with so far. Comments welcome!
Scholars working on (Latin) medieval logic can be viewed as populating a spectrum. At one extremity are those who adopt a purely historical and textual approach to the material: they are the ones who produce the invaluable modern editions of important texts, without which the field would to a great extent simply not exist; they also typically seek to place the doctrines presented in the texts in a broader historical context. At the other extremity are those who study the medieval theories first and foremost from the point of view of modern philosophical and logical concerns; various techniques of formalization are then employed to ‘translate’ the medieval theories into something more intelligible to the modern non-historian philosopher. Between the two extremes one encounters a variety of positions. (Notice that one and the same scholar can at times wear the historian’s hat, and at other times the systematic philosopher’s hat.) For those adopting one of the many intermediary positions, life can be hard at times: when trying to combine the two paradigms, these scholars sometimes end up displeasing everyone (speaking from personal experience).
Terence Parsons’ Articulating Medieval Logic occupies one of these intermediate positions, but very close to the second extremity; indeed, it represents the daring attempt to combine the author’s expertise in natural language semantics, linguistics, and modern philosophy with his interest in medieval logical theories (which arose in particular from his decade-long collaboration with Calvin Normore, to whom the book is dedicated). For scholars of Latin medieval logic, the fact that such a distinguished expert in contemporary philosophy and linguistics became interested in these medieval theories only confirms what we’ve known all along: medieval logical theories have intrinsic systematic interest; they are not only curious museum pieces.
Despite not being the first to employ modern logical techniques to analyze medieval theories, Parsons' approach is quite unique (one might even say idiosyncratic). It seems fair to say that nobody has ever before attempted to achieve what he wants to achieve with this book. A passage from the book’s Introduction is quite revealing with respect to its goals:
It has been suggested that I am trying to impersonate a 15th-century logician who happens to have the skills and habits of a 21st-century graduate student. I discuss known medieval views with some care, and show how far one can go without introducing any logical principles beyond the medieval ones. (p. 4)
Prima facie, this seems like an accurate description of the whole project. However, the first sentence is not quite true, and in fact there is something of a tension between the two sentences in this passage. The main goal of the book is indeed to ‘show how far one can go’ with only medieval logical principles; the conclusion of the book is that one can go very far, in fact pretty much as far as modern logical theories, as argued in chap. 9 (medieval logic also encompasses fragments of modal logic, a topic treated in chap. 10). But what does it mean to ‘go far’ here? What Parsons seems to mean is something quite modern, and indeed rather un-medieval: what is the deductive power of the system? What is its expressive power? How many non-trivial theorems can one prove with just a few basic principles?
Now, the idea of designing logical systems containing just a few basic rules and principles and yet being able to prove a lot with it – which could be described as a principle of logical economy – is simply not a significant concern for medieval logicians. True enough, insofar as they inherited the ideals of the Aristotelian axiomatic model of science, in particular the desideratum of parsimony with respect to the establishment of first principles, this principle of economy is not entirely alien to medieval logicians. However, it can be plausibly argued that, in practice, this was simply not something medieval logicians cared much about (Parsons of course knows this: ‘there were only a few attempts to carry out the project of deriving most principles from a basic few’ (p. 1)). Medieval treatises often contain extensive lists of basic principles and definitions, and while the authors were familiar with the idea of deriving conclusions and new principles from the more primitive ones (see e.g. Burley’s On the Purity of the Art of Logic, or as noted by Parsons, Buridan’s Treatise on Consequences), the idea of seeing ‘how far one can go’ with just a few principles – which is a distinctively meta-theoretical question – is not a goal that most medieval logicians would have readily recognized as worth pursuing.
And so, it seems somewhat inaccurate to describe the book’s project as that of impersonating ‘a 15th-century logician who happens to have the skills and habits of a 21st-century graduate student’; what we encounter is not only 21st-century skills and habits, but also 21st-century goals. What remains purely medieval are the basic principles and rules of the system, and the project of investigating the deductive and expressive power of this collection of principles and rules is philosophically a very interesting one. Indeed, as Parsons notes on p. 259, his results put pressure on the Fregean claim that a thoroughly artificial language is required for scientific purposes, given the hopeless inadequacy of the ‘languages of life’. Parsons’ results show that the Fregean indispensability claim is not nearly as obviously true as is usually thought, given that medieval logic is by and large based on regimented versions of medieval Latin.
But what are these famous basic principles? Parsons isolates three principles as fundamental: (in modern terms) indirect derivation (or reductio), existential instantiation, and existential generalization. The last two correspond to the technique of ekthesis, already known to Aristotle and passed on to the medievals in various forms (e.g. the notion of expository syllogism). (Indirect proof, or proof through the impossible, was also well known to Aristotle and adopted by the medievals.) Parsons shows that these three basic principles together are sufficient for the derivation of the whole classical syllogistic system, but in fact they allow us to go much further. Medieval logicians extended the classical system of syllogistic in a variety of interesting ways, so as to include quantification in predicate position, singular term predicates, negative terms, anaphoric terms, genitives, demonstratives, sentences with verbs other than the copula etc. Parsons shows that, on the basis of the three primitive principles, and adding a minimum of inference rules so as to cover the new cases in the expanded language, again one obtains a coherent, elegant unique system. (The concern with systematicity also seems to be one of the main driving forces of the project.) The goal is thus that of developing a system that corresponds quite closely to what medieval authors recognized as valid logical principles, at least within the scope of the phenomena that the book addresses, on the basis of the three basic principles. (Parsons readily recognizes that there is much more to medieval logical theories than what the book covers – p. 5.) In the opinion of this reviewer, Parsons fully achieves this goal.
The book also has a few peculiar features; for example, the grey boxes entitled ‘Applications’ scattered along the different chapters, containing what can be described as ‘exercises for the reader’ (the solutions are however not to be found in the book). As a matter of fact, this reviewer happens to know that, initially, Parsons conceived this book as something like a textbook on medieval logic; but the project then changed in nature along the way. However, besides the ‘Applications’ boxes, there are still other traces of the book’s previous incarnation as a textbook, in particular chapters in which there are very few references to secondary literature – a sensible choice for a textbook, but perhaps less sensible for a book that intends to be ‘scholarly’ at least to some extent. (Especially chapters 1 and 2, on Aristotelian syllogistic, do not refer much to the vast and interesting secondary literature on the topic.)
Indeed, scholars closer to the historical end of the spectrum alluded to above might object to the absence of extensive discussions on the existing secondary literature, or else to the somewhat restricted collection of texts examined (though Parsons does provide quite extensive textual corroboration for the principles that he attributes to medieval logicians), or even to the lack of a more general historical embedding of the discussions.
More generally, I suspect that a number of historically-minded medievalists will not recognize Parsons’ project with this book as a legitimate one. In particular, he does not pay much attention to what medieval logicians themselves did with their logical systems; instead, he adopts a meta-level perspective to investigate properties of the systems as such. (What medieval logicians were first and foremost interested in was arguably the application of logical theories and principles, given that logic (broadly understood) provided the methodology for investigations in all fields of inquiry.) But others, including logicians, linguists, non-historian philosophers, and those scholars of medieval logic sympathetic to the systematic end of the spectrum, will likely view Parsons’ project with this book as one very much worth pursuing, and will be impressed by the mastery with which it is carried out.
In the limited confines of this review, I’ve chosen to focus on explaining the nature of the project, in the hope that this will allow the reader to determine whether she belongs to the target audience of the book or not. In effect, this is a book likely to provoke extreme reactions. Some will dislike it, and will worry in particular about the somewhat anachronistic picture of medieval logic painted in the book. Others will love it for its skilled application of modern logical and linguistic techniques to the medieval material, presenting it with a systematicity not to be found elsewhere (neither in the medieval authors themselves nor in the recent secondary literature). Some others might be of two minds, feeling the pull in both directions. But without a doubt, the book is a milestone in medieval logic scholarship.