Earlier this week I was up in St. Andrews for the excellent conference on Medieval Logic and Its Contemporary Relevance, a week after coming back from another very excellent conference, on Feminist Philosophy and Formal Logic. The FP&FL conference sparked a lot of thoughts about Who is our audience? that I wrote up for my other blog, but what I found when preparing for my talk in St. Andrews is that a lot of the things that came out in discussion between feminist philosophers and formal logicians are relevant to the study of medieval logic, and why we do it.

Above is a photo of the notes I wrote up for my talk, and I want to use this blog post to recount what I asked my audience: Why do we study medieval logic?

There’s a number of possible answers, of course, and people can have multiple reasons (sometimes all at the same time!). But the answers are all going to fall on a spectrum that has:

**On the one end**, Pure research/edification: The study of medieval logic is an end in its own right. I feel quite strongly that this is a *very good reason* to study medieval logic, and it’s one that motivates me quite a bit. There is value in participating in a society where learning for learning’s sake is rewarded, and I think that we should be fighting to maintain such a society: There is no inherent need to justify our study of medieval logic beyond “it is there to be studied”. We study it simply to __learn more about it__, and that is sufficient. There is no further requirement that we __learn from it__ or that we can apply it or use it or that it has impact in other fields.

Nevertheless, **on the other end**, Solve all modern problems: We want to cure cancer, identify and block fake news, solve world hunger, etc. Of course, no one thinks that medieval logic can do all this. But we *do* think that it can do *something*, that we can do *more* than just learn __about__ it, we can learn __from__ it, too. But what?

Now some personal confessions: Every paper on medieval logic that I’ve written has contained a paragraphing either (1) explaining why medievalists should care about reading something written in symbols or (2) why modern logicians should care about reading something written in Latin. Every single one. My experience, both in publishing and at conferences, is that (1) is harder than (2), and that this tends to be because medievalists tend to reject formalisms because they are more interested in learning __about__ medieval logic than learning __from__ it, and given that, since they are not versed in modern logical symbolism, having a paper that uses it can prevent them from learning __about__ medieval logic. Broadly speaking, their emphasis is on the “historical” part of historical logic, not the “logic” part of it.

There are a lot of facile answers that can be given for why (2) is easier. One was given in the description of the St Andrews conference itself: Those who do not know their history are doomed to repeat it. This is expressing __pragmatic__ concerns:

- Reinventing the wheel is a waste of time: We have a finite about of research energy, we should spend it wisely, doing
*new*things not things others have already done. - Priority: Standards of academic conduct (w.r.t. to plagiarism and attribution, but also with a growing recognition that canon tends to erase certain parts of history, which may result in disproportionately harsh consequences on certain groups of people modernly) require us to attribute results to those who first proved them, and in order to do that we need to know the history of our subject.

But none of this says much about what we can learn __from__ medieval logic — we don’t just study medieval logic so that we can write a proper history of logic. If that were our motivation for studying medieval logic, then we would *also* be spending more of our time studying non-western logical developments, women logicians, etc. So we still have the question of what we can learn from medieval texts.

More autobiography: I have a relatively stable method for writing papers on medieval logic: I pick an interesting text, summarise its contents, build a formal model, compare it to some modern formalism, and then say something about the result of having done so. What I have to say in what follows is predicated on my own experiences (but people in the audience at the workshop told me afterwards that even if they weren’t in the business of making formal models, what I had to say was relevant for them).

What we (=me) often say in these papers is that we build logical models to offer solutions to modern __logical__ problems (so, not __all__ problems, no cancer-cures, but at least some modern problems), for example:

- The Liar Paradox
- Dynamic reasoning
- Epistemic reasoning
- Temporal reasoning
- The nature of logical consequence
- etc.

But what we can learn from the models depends on who our audience is:

- Medieval philosophers/medievalists
- Modern logicians
- Ourselves

(During the Q&A, someone suggested that I add another category “historians of philosophy”.)

If (1) is our audience, then we have to motivate how modern logic can tell us something more __about__ medieval logic, something we didn’t know before. If (2) is our audience, then we need to be clear regarding how accurate we are being; if our goal is to learn __from__ medieval logic, then this sometimes happens at the expense of the medieval system itself. In these cases we need to be clear when something is, e.g. “Buridan’s logic” or merely “Buridanian logic”. We needn’t be slavish to the medieval texts, if our goal is to take them and learn from them, but when we are not, we must be precise about our deviations.

But if our audience is (3), ourselves, then what do we learn from constructing formal models of medieval texts? For me, the answer is that it teaches me the sorts of questions that I should be asking. The process of constructing a formal model identifies areas where the content needs to be clarified, and where gaps can be found. It’s not so much that the end model gives us an answer to a question but that the process of beuilding the model gives us new questions to ask — both __about__ medieval logic and __for__ modern logic.

A bit more autobiography: At the end of every paper, once I’ve produced my formal model, there’s always a paragraph or two that says “and now given this new temporal operator which the medievals already knew about, I can go forth and __SOLVE ALL THE PROBLEMS__“. But this is really a bit of a lie: In many cases, I don’t intend to write that “further work” or “future research” paper wherein in I apply the tool I’ve created to some modern logic problem; and I also don’t even worry too much about whether someone else will do it instead of me. For me, the process of modeling is more important than the resulting model itself because of the ways in which it teaches me things, about both modern and medieval logic.

In conclusion, I think that all three of these audiences (four if you add in general historians of logic) should merit our attention, but what kinds of papers we write, and hence what sorts of things we can learn from medieval logic, and what sorts of answers we can give to the question “why do we do medieval logic” are going to depend on which of the audiences is the primary one for any given project. As I argued in the post linked above, I think we don’t always pay as much attention to questions of audience as we should, and that doing so can help us refine and clarify what it is we are doing when we study medieval logic.

I have a question for you. What do you mean by constructing formal modelling? Do you have an article where you undertake this formal model construction? Are there books that you can suggest to those who want to start adopting this philosophical methodology? A recommended reading list would be great. I would be very grateful if you could enlighten me with your feedback. Thanks in advance

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That would be a good topic for a blog post in itself! But for a few quick links, my PhD dissertation (http://www.illc.uva.nl/cms/Research/Publications/Dissertations/DS-2009-04.text.pdf) and Catarina Dutilh Novaes’s PhD dissertation (turned into a book: https://www.amazon.co.uk/Formalizing-Medieval-Logical-Theories-Consequentiae/dp/9048174589/al) both discuss formal modeling of medieval logic and give examples.

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