The Historian (of Logic)’s Craft – A conversation with Calvin Normore

Today, rummaging through my files, I stumbled upon the transcript of a very informal interview I had several months ago with Calvin Normore, for an issue of The Reasoner that I guest edited.

Since it might be of interests for the readers of our blog, I am sharing it here too.


Graziana Ciola:           Did you begin as a medievalist?

Calvin Normore:         In a way, I did. As an undergraduate – I think I was in the beginning  of my senior year –, at McGill we had a new professor, John Trentman, who had come from the University of Minnesota, where he had been a track star, actually. John gave a seminar on Buridan’s Sophismata, which had just come out in the T.K. Scott’s translation – there was no text –, and I got very interested in this. I had gone up to university wanting to be Bertrand Russell, so I wanted to do both math and philosophy. I was not as good at Math as I guess I was at Philosophy. In Math, I like more to have done it than – I discovered – to actually doing it. So, I was switching over into Philosophy and John’s seminar was really interesting. He got me interested. It was just at the moment when Arthur Prior was still at Oxford – I think he died the next year – and so there was question of what to do. I thought we were going to study with him. He had suggested that if one were interested in modal and tense logic, then there was lots to be learned from the medievals. And I was very interested in modal and tense logic. In the event, I went to Toronto, because that was the place to do medieval things in those days, and certainly if you were an Anglophone and a Canadian – but I think in general. So I went there but, frankly, I found the medieval atmosphere somewhat boring, so I fell in with people in the Philosophy Department who were more interested in contemporary things. Hans Herzberger, who was working on truth, became my supervisor; Bas van Fraassen had just come to Toronto as well, so I took courses from him; David Gauthier was there, and John Woods, who was a good logician. I worked really more with them at the beginning, but I did the things one did at the Institute. When I had been thinking of going up to Toronto, I had gone to the city and I talked with Father Ed Synon, because the question was: “should I apply to come to the Pontifical Institute or should I go to the Philosophy Department?”. And Father Synon said: “Oh, you should go to the Philosophy Department, because you can do everything you like at the Institute if you are in the Philosophy Department. And what’s more you’ll get a job, which you wouldn’t do if you came to the Institute”. So I got into the Philosophy Department, but I continued to do all these things at the Institute: I took their first year programme, the palaeography courses and so on. But I was working mostly with Hans, actually. I got interested in Ockham because… one could. This was 1968, when I went up. It was just at the moment when Saul Kripke and Charles Chastain were working on the causal theory of names. It was actually Chastain whose work I encountered first; and he came to Toronto and gave a talk. I had been reading Ockham at the same time when I realised “ah! this is a very similar view! let me explore it further…”. And that’s really what got me into Ockham.

GC:                             So, when you started working on these topics in Ockham’s philosophy, were you already more focused on the history of logic rather than philosophy?

CN:                             I didn’t see a distinction. Remember: Prior had claimed – quite correctly, I thought – that if you wanted to do modal and tense logic you could learn a lot from the medievals. And he was right! So I thought of working on these 14th century people as very much a contemporary project. I did never see it as a different issue at all. Later on, partly under the influence of Michael Frede, I came to think that there might be a subject – the History of Philosophy as a subject. But I am sure that when I was a graduate student I didn’t think of them as distinct subjects at all.

GC:                             There are some strong reasons for a philosopher to be interested in the History of Philosophy – same for a logician to be interested in the History of Logic. Your thoughts? How did your outlook evolve? How did it change over time?

CN:                             There is this famous quote of Quine that “logic is an old subject and since 1879 it has been a great one”, referring to Frege’s Begriffsschrift. This, I think, is just a mistake. What Frege was trying to do was to develop an adequate foundation for mathematics and to show that you could develop an adequate foundation for mathematics that relied only on concepts that would be uncontroversially thought of as logical. But, of course, that presupposes already that one had a conception of what was logical, right? Otherwise it would make no sense – and you might ask “well, where did that conception of logical come from?”. I think that is a part historical project. If you go back to Aristotle, something that, for example, Chris Martin has emphasised (and it’s true), is that Aristotle doesn’t have a propositional logic at all: he’s got a logic of terms, that explores relations among certain expressions we would call quantifiers. The Stoics developed a theory, which explores the relations among certain words – let’s suppose – or concepts that we would regard as propositional connectives. And medieval theorists inherited both: more obviously, Aristotle; but they inherited a good deal of Stoic material as well. What you find throughout the Middle Ages is an exploration of a number of these items (quantifiers, connectives, and so on) under the general heading of “syncategorematic expressions” – and also some “partially” syncategorematic expressions, as they thought, that is: expressions that when you analyse them turn out to have a syncategorematic component. The medievals were working to explore the structure of these syncategorematic terms. About the time you get to Frege a lot of that could simply be taken for granted. The logic that has been developed since 1879 is just, as I see it, a continuation. If you teach Introductory Logic these days, you teach your students, typically, a propositional logic – and what do you do? You explore the structure of conjunction, negation, disjunction, sometimes a conditional; you go on to explore the structure of some quantifiers; you worry, at some point, about how to give a translation of this into a mathematical framework –that is new: that wasn’t done much, before Frege. But the idea that you are going to explore the core of some syncategorematic terms, that has been the core of the subject. I don’t see it as a different subject now.

GC:                             I agree with you. However in many Departments, both in Europe and in the US, it is still common to find a split between historians of Philosophy and philosophers “in a proper sense”, as if the former were not as much philosophers as the the latter. And that seems very wrong to me.

CN:                             I think it’s wrong. When I went to Princeton, in the late ’70s, that split was very much there. Gil Harman is a wonderful philosopher but really did not think that the History of Philosophy belonged in a Philosophy Department. Now, interestingly, I don’t think that Michael Frede would have agreed exactly that it didn’t belong in a Philosophy Department, but Michael thought of it as a distinct subject. And the reason he thought of it as a distinct subject was that he thought that, unlike Philosophy, the History of Philosophy, as he saw it, was also a branch of History – and he thought of Philosophy and History as two distinct disciplines. So the History of Philosophy had two masters; because it had two masters, it had a master that wasn’t just Philosophy. How you lodge these people institutionally, that’s just an institutional accident. But the thought that a historian of philosophy had to be a good historian, as well as a good philosopher, meant that it was an open question whether the History of Philosophy would be best done in a Philosophy Department. Now, my own view is that Michael is right: there is a way in which a historian of Philosophy has answerable to the discipline of History, but also to the discipline of Philosophy. You have to be doing Philosophy: you can’t even understand the history, typically, unless you do the philosophy well. There’s something quite exciting about encountering ideas that are not part of the current philosophical landscape but you realise could be, as well as what got me into it – encountering ideas that were part of the contemporary philosophical landscape, but really hadn’t been explored yet very much. I don’t see any particular problem in housing a historian of Philosophy in a History Department, but I don’t see any reason to think that a historian of Philosophy couldn’t just as well be in a Philosophy Department. Nor do I see any problem in thinking that contemporary Philosophy can be informed by ideas that come from doing the History of Philosophy.

GC:                             Many historians have chosen to formalise medieval logical theories to make them intelligible and interesting for contemporary readers. What do you think about formalisation in approaching the History of Logic?

CN:                             Formal tools are very old: Aristotle used schematic letters to represent things in the syllogistics; the Stoics used analogous things – they had “the first”, “the second” and various kinds of expressions like that. I don’t think of formalisation as distinct in kind from regimentation. What does happen more recently is the development of a formal semantics. You have a formal semantics when you take a symbol that doesn’t have any natural language meaning – if you like, just a letter of the alphabet or something – and you assign it something in your semantics. And of course if the formal semantics itself is something presented in set theory, then it’s going to look rather different from if your formal semantics is a fragment of natural language. But when you teach Introductory Logic, typically, before you dwell upon any formal semantics, what you do is you present an interpretation of the symbols you use, in ordinary natural language: it’s just a schematic way of presenting a fragment of the natural language. I think the big shift is not with introducing symbols and letters: the big shift is presenting something like a set-theoretic semantics. That’s of course new, because Set Theory is new, but the idea of schematic representation is not new – in Leibniz, Aristotle, etc.

CG:                             Where do you think the discipline is going?

CN:                             Here’s something that’s important, I think: what’s important is that Logic itself is becoming an orphan. My mathematician friends who do Logic say it’s less and less a standard part of Mathematics; philosophers think of it as less and less a standard part of Philosophy. It’s becoming an orphan. I don’t think this is anything special about the History of Logic, here: it’s that Logic itself is loosing the central place that it has had both in Philosophy and in Math. Now, you might ask why. This is an interesting question. In the first half of the 20th century, there were some extraordinarily exciting results in Logic, which gave us reason to think that the whole project of presenting a theoretical picture of the world was different from the way we had previously thought it was. The limitative results that Gödel and Turing and others showed were just mind-blowing or earth-shaking. Now there has been nothing like that since. And what’s more, the techniques that have been developed for exploring parts of Set Theory, in particular, have become very recondite: ever since Cohen’s works on forcing, and the beginnings of the development of large cardinal axioms and things like that, the technical side of contemporary Logic had less to do with anything other than itself than it ever had before. In Mathematics there’s a project, which Harvey Friedman and others have, of what they call “reverse Mathematics”, which is to take Mathematics as it currently stands and try to see what sort of logical foundation you need for it; it turns out that you don’t need most of the stuff that has been developed since 1964, for example. In Philosophy we teach our students how to read the symbolism; on a good day, we teach them something about Gödel’s results, for example. But we don’t take it very seriously and people don’t think hard about it anymore; that has just made Logic itself less and less central in the field – and, of course, the History of Logic follows. But some of that is just a plain mistake, because people haven’t appreciated the significance of the results that were developed throughout the 20th century. There’s also this other thing, which is reasoning. Logic is not a theory of reasoning, because what Logic can tell you is what follows from what, but it doesn’t tell you what to do once you discovered that. There’s much more to Reasoning than Logic. And so Reasoning, the theory of reasoning, is a lively part of the contemporary scene; it just presupposes a lot of the logic that people have taken for granted. What’s interesting is that, if you look at the History of Logic, the History of Logic is often in part a History of Reasoning, so it’s a wider subject than Logic once Frege, and eventually Russell and Whitehead, tried to use it as a basis for Mathematics. Because of that, in some sense, there’s perhaps more to be learned from earlier logical developments about what’s currently relevant than from the Frege or Russell project.

CG:                             I completely agree. So, what would you tell a student who’s becoming interested in the History of Logic?

CN:                             I would recommend to remember that the History of Philosophy has two masters – and so they have to be good at Philosophy and they have to be a good historian. I would urge not to forget that: you won’t understand what you are doing, if you haven’t thought hard about what philosophical issues are involved; and you won’t know what to do, if you haven’t thought about the historical context. I think that’s all true. From a purely sociological point of view, there’s no good reason not to get into this stuff. I point out to my students that a couple of years ago in North America there was one dedicated job in the Philosophy of Language and four in Medieval Philosophy. So if you are thinking just of an academic career, there’s no particular reason to prefer doing the Philosophy of Language to Medieval Philosophy. But if you are thinking of the subject, the key thing is to not be too narrow.

GC:                             Thank you, Calvin.

CN:                             My pleasure.


About grazianaciola

Bene nati, bene vestiti, et mediocriter docti. Medievalist, logician, philosopher (?), incorrigible procrastinator, tea drinker, and fond supporter of the Oxford Comma. If it is in Latin, I probably like it; if it is wrong, I almost certainly like it too.
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