The goal of this post is to expand on the slides, linked in the previous post, for the talk I gave at the Australasian Association of Logic two weeks ago, on “Why should we care about history of logic?” This isn’t by any means a transcription of my talk, but it is a general summary of the thoughts that I talked about.

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I have been studying, researching, and presenting on topics in medieval logic for more than a decade now. Medieval logic sits in an uncomfortable position at the intersection of mathematical/philosophical logic and medieval studies, and my conference schedule takes me to events from both sides of the spectrum. One thing I have found very interesting is that the logicians are generally much more interested in the medieval stuff than the medievalists are in the logical stuff. I have to spend much more time motivating to the medievalists why this material is interesting to look at, and why I am using modern logical tools to do so, while the logicians generally seem simply curious about the history of their field — and if I throw in a manuscript image or two, it’s a nice break from, say, dualities in Stone algebras. For the first few years, particularly while I was still a PhD student, I was happy to focus on convincing others that what I was doing was interesting and they should accept my abstracts and papers for conferences and journals. But recently I’ve had the desire to move from convincing others that what I am doing is important to convincing others that they should be doing it too.

This is a big step: Many people may be interested in the history of logic as a historical curiosity — happy that someone else is doing it but not interested in doing it themselves. My aim in the talk was to show that logic differs relevantly from other scientific disciplines, and that these differences mean that the study of the history of logic is more than just historical or mere curiosity, but in fact should be seen as the study of logic, no “history of” modifier needed (slide 2).

In order to motivate why contemporary logicians should care about the history of logic, it’s worth first looking at other scientific disciplines where the history of the subject is a mere curiosity. Consider disciplines such as medicine, biology, chemistry, and astronomy. We do not ask medical doctors to read medieval treatises on the four humors, or to integrate medieval cures for headaches (sawing open the skull) or venereal diseases (inject mercury into the offending organ) into their modern arsenal (slides 3-5). No one takes seriously Aristotle’s claim that women have fewer teeth than men (slides 6-7). Chemists need not know about the roles of Mercury and Venus in alchemical processes (slides 8-9). Astronomy students are not taught how to calculate epicycles (slide 10). Certainly if a scientist showed an interest in any of these aspects of the history of their field, this would be encouraged, but not because we think studying the history of these disciplines will provide material relevant to the modern practice of these disciplines — something that I want to argue is different when we consider logic.

What makes logic different from these other disciplines? One answer might be that what we thought we knew then about medicine, biology, chemistry, astronomy was simply false. Now we know better, so now we don’t look to the medieval texts as our guides (slide 11).

But then consider the case of mathematics. Modern mathematicians do not generally study any history of mathematics. Try an experiment: Next time you run into a practicing mathematician, ask them to calculate the subdouble subsesquitertius of 10. Even if you manage to pronounce this correctly, they will almost certainly have no idea what you mean, nor any idea of any of the other complicated names of proportions offered by Roger Bacon in the 13th century (slide 12). And yet, it is nevertheless true that 3 is a subsuperbipartient of 5. Perhaps another alternative is that historical mathematics lacks a necessary clarity (slide 13), a clarity that modern approaches to mathematics have. This explanation seems to have more bite; for it helps us understand why it is that some historical mathematics is still read and used, namely Euclid’s Elements (slides 14-15). In fact, one might argue that it is precisely its clarity that has afforded it its long and fruitful usage.

Still, one shouldn’t draw the conclusion of “medieval = unclear” and “modern = clear”; for even modern logic can lack that necessary clarity (slide 16-17)!

Before I go on to say something about why it is that logic is different from some of these other scientific disciplines, I want to say something about why it matters that we study the history of logic. The most straightforward answer is the oft-repeated adage that “Those who cannot remember the past are condemned to repeat it” (slide 18). I have lost track of the number of times that I’ve been at a talk where someone has said “no one has ever done X before Y”, where Y is maybe Leibniz at the oldest, but is most often someone much more modern, and I have raised my hand during the Q&A to say “Uh, Z did this seven hundred years earlier”. People who do not know the history of their field are far more comfortable making sweeping generalisations about what was done in that history, and in many cases, falsely. Even if one is not interested in learning what was done in logic in the Middle Ages, one should still be sensitive to issues of priority and attribution (a well-known example being the so-called “DeMorgan’s Law”, articulated by a number of 14th C logicians including Jean Buridan and William of Ockham (slide 19)).

So why is logic different from chemistry, medicine, biology, astronomy? The next section of the talk was devoted to going through examples of developments in medieval logic that are of relevance and interest to contemporary logicians, because they provide us with alternative or complementary accounts of some of the same phenomena (slides 20-27). But this way of answer the “why” question still leaves open another “why” question: What is it about logic as a discipline that makes the medieval developments still relevant? Here I do not have a concrete answer to give. One answer that you might wish to offer is that the reason why medieval developments in logic have just as much use and application today as they did centuries ago is that they reflect some timeless truth, some underlying fact about the real nature of logic, that is context and culture independent and necessarily true. I am hesitant to take up such a view, mostly for hubristic reasons: Such a view can have an easy consequence that developments in argumentation and reasoning outside of the Aristotelian-European tradition fall short of reflecting that “real nature” of logic. Another possibility, and one which I think is a more likely explanation, is that what we find important in the use and application of logic changes over time — sometimes being closely linked to linguistic usage and practice, sometimes instead being connected with mathematics — and that what we have seen over the last few decades is a change in emphasis which has lead us back to a point where we have many of the same goals and motivations that the medieval authors did — a focus on dynamic reasoning, multi-agent settings, problems of truth and possibility, questions of how language is actually used, etc. Because our goals align, the developments and insights can still be relevant to our pursuits nowadays (slide 28).

By now I hope I’ve convinced you of the utility of becoming more familiar with the developments in the history of logic, as a practicing modern logician. Now what? (slide 29) Not everyone is going to go out and learn Latin; but that isn’t necessary as in recent years more and more reliable and high-quality translations into English have been published, as well as secondary sources such as the forthcoming Cambridge Companion to Medieval Logic edited by Stephen Read and Catarina Dutilh Novaes. There is also ample resources for support via social media, including this blog and the Medieval Logic FB group