Note: this transcription was produced by automatic voice recognition software. It has been corrected by hand, but may still contain errors. We are very grateful to Tim Wittenborg for his production of the automated transcripts and for the efforts of a team of volunteer listeners who corrected the texts.
Peter Adamson: As a preliminary question, I've just said we're going to be talking about medieval logic, and I'm wondering whether that really makes sense. Do medieval philosophers even have a defined notion of logic as a discipline? And if they do, how would they explain the difference between logic and other areas of philosophy?
Catarina Dutilh Novaes: Okay, well, let me start by saying that everything I will say during this interview pertains to the Latin authors, the authors who are writing in Latin. So I will not say every time the Latin medieval authors, but it should be clear that it’s not that I’m disregarding all the other traditions which were active at the same time and which were not writing in Latin. But so about the Latin medieval authors, they in fact didn't care much about the issue of the scope of logic as much as modern contemporary philosophers of logic and logicians do. So there's this big ongoing debate in philosophy of logic on criteria of demarcation for logical constants, and that's because many people now seem to think that this is the best, perhaps even the only way to demarcate logic as a discipline, to demarcate the class of logical constants. And they also feel that it's impossible to understand logic as such unless we have a clear criterion, a clear demarcation of logic from the other disciplines. And my feeling is that this is a bit of a Kantian influence, this obsession with demarcations and borders, etc. But so the medieval philosophers were not engaging in this project, they were not actively looking for sharp ways to demarcate logic from other disciplines, that's not something they were concerned about. But this being said, they do offer considerations on what counts as logic, and one place where this typically happens is that the prefaces of their big sums of logic works, right? So they have these big textbooks in logic, and very often the very first one or two pages they're saying what logic is all about and why logic is important, and that's why the student will do well to go on and study all of it through their textbooks. And so two people who do this, for example, are two of the main 14th-century logicians, William of Ockham and John Buridan. And then they say, for example, that logic concerns reasoning, that it concerns the principles to establish the truth and falsity of propositions, it concerns producing new knowledge, so they say many things along these lines. And also some authors, many authors say that one of the main purposes of logic is to teach people how to engage in disputations and debates. So that's also thought to be an important function for logic, which of course ties up with Aristotle and say the Topics and the Sophistical Refutations, which are also about debates. But so despite the fact that, despite their lack of interest in the question of a sharp demarcation for logic as a discipline, logic as such was a fairly well-defined discipline. And there are two main reasons for that, well, two main ways to think about the unity of logic at the time. One is purely institutional, you might say, you might call it purely institutional, which is that logic was one of the topics taught to students very early on in the standard curriculum. It was part of the trivium together with grammar and rhetoric. And so that's really pretty much the first thing that students would learn, even as they were very, very young when they learned that, so even like 14 years old, they were already learning logic. And this for many reasons, and one of them is that also there was the thought that knowledge of logic was thought to play a fundamental role for other so-called higher disciplines like law, theology, and medicine. So logic was supposed to provide the foundations for any intellectual inquiry. So it was very important.
Peter Adamson: And actually, that's something that's common between late antique philosophy and medieval philosophy.
Catarina Dutilh Novaes: Absolutely.
Peter Adamson: So this idea that logic is the first thing you study and then you go on to the higher sciences.
Catarina Dutilh Novaes: Yeah, so that is absolutely there. And so that's why logic had a very important role to play. On the one hand, there's also sometimes the thought that logic was for schoolboys, right? So many of the Latin authors, what they did is they wrote on logic at the early stages of their career, and then the serious ones then moved on to one of the other disciplines and in particular theology, which was supposed to be the most noble one of them. And one exception to this is, for example, John Buridan, who I just mentioned, he's one of the few people who have stayed at the arts faculty throughout his career. So he did not move on to become a doctor in theology. He did not move on to write on theological matters. And by contrast, William of Ockham, who I also just mentioned, did exactly the opposite, did what most other important authors did, which was to first write on logic as a young man, as a masters of art, and then move on to write on theology and other so-called more important topics. But anyway, that's one observation. And the other thing is that besides this institutional factor that made logic a coherent whole, there's also the influence of the logical writings of Aristotle, which really provided the main background for the development of medieval logic, especially starting at the 13th century. So that's what I'm saying here now, that the role of Aristotle is not to be found, certainly not to the same extent in the 12th century and before, but from the 13th century onward when the logical writings of Aristotle became widely read again in the Latin world. And so that, just to be clear, the categories and on interpretation were read throughout and people had knowledge of syllogistic through Boethius, but they didn't read the Prior Analytics, the Posterior Analytics, the Topics, the Sophistical Refutations, they didn't read that. And this picked up again in the 13th century. And from there on, Aristotle really was the main kind of figure that gave unity to the discipline too. And again, Buridan and Ockham, who I've been mentioning quite a few times already, both explicitly mention Aristotle in their prefaces to their big logic compendia.
Peter Adamson: So basically the conception of what logic is, is one of the many things that changed because of the reintroduction of the complete works of Aristotle into the Latin tradition.
Catarina Dutilh Novaes: Absolutely. And in fact, there are even names for that in the Latin tradition. So already back in the medieval times, there was a well-known distinction between logica vetus, which means old logic, logica nova, which means new logic, and logica modernorum, which means modern logic. A logica vetus category was used to describe the material pertaining to the texts by Aristotle that had been known throughout, as I said, the Categories and the Interpretation. And this tradition continued. So of course, in the 12th century, that's pretty much all there is. And sometimes people think that in the 13th, 14th century, these discussions were abandoned, but that's not true. They continued to talk about and saw these discussions on universals and on categories pertained to logica vetus. Logica nova is the category where you find works that deal explicitly with the new, so-called new texts by Aristotle, new in the sense that they became available again. And this is the Sophistical Refutations, the Topics, and the two Analytics. And so logica nova is when people are commenting on these particular texts and writing questions on these texts, so really engaging with these texts. So it's still Aristotle, but it's the so-called new Aristotle. And then logica modernorum were the developments, which were in numerous ways related to Aristotle's logical writings, but were medieval innovations. So for example, the theory of obligationes, which is a particular kind of debating technique, which was very influential in the 14th century, that doesn't connect in any direct way to the work of Aristotle. And so that's why it's called logica modernorum. Another concept is the concept of supposition, which is the main notion in the medieval theories of semantics, right, in the medieval theories of what propositions, sentences mean. And that's also part of the logica modernorum.
Peter Adamson: Okay. So obviously, from what you've just said, there's lots and lots of things we could talk about here.
Catarina Dutilh Novaes: Yes, absolutely.
Peter Adamson: Lots of topics that get covered within actually all three of those branches of medieval logic. And from all these things, I thought we could focus on just one because you've published about it. And this is the question of whether medieval logic is formal, and what it would even mean for logic to be formal. So before we get into the formality of medieval logic, let's just talk about this phrase formal logic. So this is a word you sometimes see thrown around. For example, it's used in the name of courses you can take at universities. I'm studying formal logic. Presumably this doesn't mean logic while wearing evening wear. It must have some other meaning. So what do we nowadays mean when we say that logic is formal?
Catarina Dutilh Novaes: Yes. Well, this is actually a very difficult question. A very interesting, very important question, but also very difficult. So in fact, the main problem is that, as you say, it's a set phrase in a sense, formal logic. And people use it very, very liberally and very often. And yet, often people are talking past each other because there are different meanings of formal, of the adjective formal as applied to formal logic. And these meanings are all kind of floating around. And so the set phrase is being used in equivocal ways, and often people are not aware of that. And so because I was worried about this situation of people talking past each other, I once wrote a paper called “The Different Ways in Which Logic is (Said to be) Formal,” where I wanted precisely to do a taxonomy of these different ways in which people talk about logic as being formal nowadays, but also actually going back in history. And there I distinguished eight senses, eight – so that's quite a lot – different senses of formal relevant for logic. And so I tried to organize a bit these debates. And I just want to mention that I was not the first one to do this. John MacFarlane had already done work in this direction. For me, it was very influential, but there were things that I thought could be done even better than he had done. And that's why I thought, okay, I'm going to write this paper.
Peter Adamson: That's how research works.
Catarina Dutilh Novaes: Exactly, right? Yeah. Yeah, but I mean, I don't want people to think that I'm saying I'm the first one who worried about this. No, MacFarlane, at least MacFarlane had done serious work on this.
Peter Adamson: You are the first person to discuss it on this podcast.
Catarina Dutilh Novaes: Okay, good.
Peter Adamson: You get primacy there.
Catarina Dutilh Novaes: Okay. So just of the eight senses that I distinguished in this paper, I'll just briefly mention three, which may come across as familiar to some of the listeners. So one is the formal schematic, which is the sense of formality that one typically encounters in the first pages of logic textbooks. When people explain what is logical about, they say, well, logic deals with arguments and we're interested in the schemes that underlie arguments. And so we are not interested in the non-logical words that are occurring in the argument where only we take them out and we just focus on the scheme and we study these schemes.
Peter Adamson: So it's like using variables.
Catarina Dutilh Novaes: Yes. Well, yeah, or schematic letters. I mean, so there's this important distinction between schematic letters and variables, but that's exactly the idea, right? So you have all A is B, all B is C, therefore all A is C. That's a schema, right? And the letters are taking the place of terms that you can fill in and produce real arguments. So that's a very, still very pervasive sense of formal. But then there's also the formal as total abstraction from meaning, which became in the 20th century a rather influential notion of the formal. And I call this notion of the formal formal as de-semantification. And here you can think of people like Hilbert and Bernays who have written on this notion. And then another important sense for modern logicians is the form was computable and that is understood as formal as pertaining to operations that can be carried out mechanically, which don't require insight or ingenuity. And so just to go back to our medieval authors, I want to say that the formal schematic has its roots in Latin medieval logic. So it's very important. And that's one of the things I did. So I have this entry in the Stanford Encyclopedia of Philosophy on medieval theories of consequence. One of the things I wanted to do there was to trace the history of the notion of the formal schematic, going back to the Latin medieval authors. But these other senses that I was talking about are for the most part later additions. So they're not as relevant for us when we're talking about medieval authors.
Peter Adamson: Actually when we talk about formal logic, since as you were saying before, the context for medieval logic is so deeply Aristotelian, even for the old logic, it was Aristotelian. It calls to mind immediately the Aristotelian distinction between form and matter. So to what extent does that distinction play a role in the ancient and medieval conception of logic? Do they think of logic as being formal in the sense that it has to do with form rather than matter?
Catarina Dutilh Novaes: Yeah. So this is really also one of the things that got me going on this research. All right. I thought like, you know, the notion of form and formal is so important in current debates and philosophy of logic. But I mean, ultimately it should go back to Aristotle, I thought. Right? So how does this goes back to Aristotle?
Peter Adamson: Everything goes back to Aristotle.
Catarina Dutilh Novaes: That's true in any case. But I think in this case in particular, I thought people were not sufficiently aware of the metaphysical Aristotelian roots of this. Sometimes I call it this ideology, the logical form ideology and the negative connotation is intended. So I thought that you really needed to go back and try to understand the presuppositions that are being taken for granted when people are thinking about these matters. And I thought one way to do this is to go all the way back to Aristotle and understand to which extent the Aristotelian distinction between form and matter was really the starting point for this tradition. So and then what happened was that I quickly discovered – and this is something that has been acknowledged by other people before me – that Aristotle himself does not apply the metaphysical form-matter distinction to arguments, to logical or linguistic objects, with two exceptions, one passage in the Physics and one in the Metaphysics. And they're virtually identical, these two passages, by the way. That's the only two places where he does that. And then I was quite struck by this. I thought, well, funny. And that's something that John MacFarlane also says. Aristotle is the father of hylomorphism, Aristotle is the father of logic, but he's not the father of logical hylomorphism. But he doesn't mix the two things. And so that's an interesting observation. And so I thought, what happened in between? Why do we now apply form and matter so extensively to logic? And the first step in this development after Aristotle was with the ancient commentators, which I know have been extensively covered by the series of podcasts and rightly so because they're wonderful. And the first person that we know of having applied the form-matter distinction specifically to arguments is Alexander of Aphrodisias. And so we don't know for sure whether he was picking up from a source that we now no longer have or if it really was an innovation by him. We don't know that for sure. But he really starts talking about the form and matter of syllogisms and applying these two concepts to syllogisms. And so that's a big transformation. So you may ask yourself, is it that Aristotle thought that arguments were not the kinds of entities which would have form and matter as constituent elements? Right. So, I mean, that goes back to the discussion of Aristotle's Metaphysics, of Aristotle's hylomorphism, what kinds of entities actually do have form and matter. And that's a big debate in Aristotle's scholarship, which I'm going to leave aside. But so apparently Aristotle didn't think that arguments had form and matter properly speaking. But then some centuries later, we have somebody like Alexander clearly thinking that it made good sense, that it was appropriate to apply this distinction to arguments.
Peter Adamson: So what would that mean? What would it mean to say that a syllogism has a form and then matter? What’s the difference between the form and the matter of a syllogism?
Catarina Dutilh Novaes: Yeah. So this is also something that underwent a transformation over time. At first, people like Alexander and other ancient commentators, they usually reserve the term form to talk about the figure of a syllogism. So the figure of a syllogism has to do with the disposition of the terms. And so there's first figure, second figure, third figure. And so this does not have to do with the so-called logical terms. It does not have to do with terms like all or no, right, which are now thought to be the logical terms. The logical terms, so to say, they define the mood of a syllogism, right. And the moods are BARBARA, CELARENT, etc. And the mood is really, with the logical terminology in it. So it's very important to realize that at first, people were using the concept of form to talk not about the so-called logical terminology in syllogistic arguments, but to talk about the relative disposition of the non-logical terms in the argument.
Peter Adamson: And just to make sure that that's clear, so the figure would be, for example, AB, BC, therefore AC. And then an example of a mood would be BARBARA, which is all A are B, all B are C, therefore all A are C.
Catarina Dutilh Novaes: Exactly.
Peter Adamson: So you add the all to get the mood.
Catarina Dutilh Novaes: Yeah. So for example, BARBARA and CELARENT are both first figure syllogisms, but BARBARA is all A is B, all B is C, therefore all A is C and CELARENT is all A is B, no B is C, therefore no A is C.
Peter Adamson: Right. The listener can check the validity of that at home.
Catarina Dutilh Novaes: Yes. Homework.
Peter Adamson: Right. Okay. So what did the medievals then do with this idea?
Catarina Dutilh Novaes: Yeah. So a lot of things happen, right. So one of the main steps in this important transformation – because as I was saying, the schematic notion of the formal would then apply to syllogisms, would then say that the form of a syllogism is the mood of the syllogism. And that's very different from what the ancient commentators were doing. And this transformation went stepwise. So at some point already in the 12th century and early 13th century, you see some authors saying that the form of a syllogism can now be understood in two ways, either as pertaining to the figure or as pertaining to the mood. And then by analogy, they would also say that the matter of a syllogism could also be understood in two ways, either as pertaining to the propositions or as pertaining to the terms. And so, there's this 12th century anonymous commentary on the Prior Analytics, the only that we know of, this commentary already talks about these two senses, but it doesn't say that one has priority over the other. And then already in the 13th century, you see texts talking about these two senses of form and matter as pertaining to syllogisms, and then they talk about one being the proximate cause and the other being the remote cause. So there's already an important distinction there. But at that time, so there was still these two senses, right, of the form and matter of syllogisms. When you get to the 14th century, the sense of form as pertaining to the figure of syllogisms is nowhere to be seen anymore. And then we really moved to what I call the schematic notion of the formal. And the other notion of the formal, which pertained to the disposition of the terms and not to the logical terminology, is no longer to be seen.
Peter Adamson: And so on the schematic understanding, the idea is that when you actually substitute words like giraffe or animal into the argument form, giraffe and animal would play the role of matter and the scheme is the form.
Catarina Dutilh Novaes: Exactly. So if you take BARBARA again, right, the schematic version of BARBARA is all A is B, all B is C, therefore all A is C. I can replace whatever terms for A, B and C in a systematic way, and I would produce an argument that has the property of necessary truth preservation, which means that if the premises are true, then the conclusion will necessarily be true as well. So if I say to you, all cows are blue, all blue things are made of stone, the conclusion is all cows are made of stone, and this is a valid argument even though the premises are false.
Peter Adamson: Right. Okay. Well, if we take this seriously, this idea that arguments have matter and form, then it seems that we have a kind of metaphysical understanding of what an argument is, just as in the case of say a giraffe, my favorite example, instead of cow, you have the soul playing the role of form, you have the body playing the role of matter, but then there's this very powerful unity between the two, so that's why you get one animal or one giraffe. Can we conceive of syllogisms or arguments in general having this kind of unity, this very strong unity that comes from somehow inserting matter into form? Because actually it seems sort of like, well I could kind of chuck any terms into that scheme and so it's quite accidental, the relationship between a particular scheme and a particular set of terms that are supposedly playing the role of matter.
Catarina Dutilh Novaes: Yeah, so the first question, if you're serious about thinking about the metaphysics of arguments, the first question you need to ask yourself is whether arguments are the kinds of entities to which one can attribute form or matter. As I was saying, it looked like Aristotle thought that they were not and then later the ancient commentators thought that they were, and one hypothesis that somebody put forward to me once, but I haven't investigated and to my knowledge nobody has investigated yet, is that the Stoic idea of lekta, of arguments as being viewed as more reified entities, that might have played a role in these developments. Then you think, okay, they're really entities in a robust sense and therefore you can apply the metaphysical notions of form and matter to them. But as a matter of fact, both in the medieval times and in current discussions, a lot of people I think don't take the metaphysical perspective sufficiently seriously. So on the one hand they import many of the presuppositions, for example the idea of uniqueness of form, right, so an argument can have only one logical form. This is a metaphysical presupposition that makes sense in the context of say, Aristotelian hylomorphism, but does it make sense when you're talking about arguments? And so one of my worries is that a lot of people import these metaphysical presuppositions without having thought hard enough about them, right, so in an uncritical way. In the medieval times what you see is that a lot of authors take the connection when they're talking about form and matter with respect to logic, they take the connection to metaphysical hylomorphisms quite lightly. So for them it's just a convenient way to refer to certain logical properties of arguments, use the terms matter and form without making stronger metaphysical claims. So you see that a lot. But there are authors who take the metaphysical perspective on arguments very seriously, and the main example of that will be Robert Kilwardby who's a 13th-century author and in many senses one of the most sophisticated 13th-century philosophers working in the Aristotelian tradition. So what he did, I always say he wanted to be more Aristotelian than Aristotle himself, what he wanted to do was to unify the different doctrines that Aristotle had in different fields and put them all together. So Kilwardby is very serious about thinking about arguments as having form and matter from a metaphysical perspective, and it's very, very interesting what he does and very sophisticated. So there was some of that too and all these difficult questions, these difficult metaphysical questions that you were raising with respect to unity or form, he deals with all of them. He's very, very committed to thinking hard about these matters.
Peter Adamson: It seems to me like an obvious objection against that sort of view that these arguments are actually metaphysical entities that have a form and a matter is that there's just various ways that you can formalize a given argument. And so something like Kilwardby’s position sounds to me like it implies that there's just one right way to formalize a given argument. And I'm wondering why anyone would say that, is the idea that there can only be one reason why a given argument is valid and that the form tells you why the argument is valid? Because it seems to me that if you took a certain argument and you could say, well, I can formalize it in three different ways and all the formalizations are valid, then what's the problem?
Catarina Dutilh Novaes: Yeah. So as I said, if you take seriously the idea of form and matter as applied to arguments and in a metaphysical sense, then you might start thinking that form is something truly inherent in the argument as such on a deep ontological level. And then the question arises whether plurality of forms is possible at all. And this is actually an interesting debate in 13th-century metaphysics, where people like Rufus and some other authors were saying that it made perfect sense to talk about plurality even of substantial forms in one and the same substance. I think this is crazy. I mean, me being the Aristotelian that I am, I think that form and matter are the parts that the principle of unity ties together. So there cannot be a multiplicity of forms. But some of these authors thought that it made sense. So in that sense, if you think that there can be only one form in one entity and you're serious about the idea of arguments having form and matter, then the conclusion will be that there can only be one correct form for an argument because this is an inherent metaphysical property of the argument itself. And you, as a logician, you're in the business of discovering this pre-existing entity in the argument itself. But if you take a lighter perspective on all these things and you think, well, it's not really something that's really there, right, in an independent way, but it's something that you can attribute to an argument because then it makes it convenient to study this particular argument from a particular perspective. And so what I want to say is that a lot of the people who discuss these matters in contemporary philosophy of logic, import some of these assumptions like the assumption of uniqueness and the assumption of a pre-existing entity, but in an uncritical way without being aware of the metaphysical presuppositions that are grounding these assumptions. And so that's one of the things I did with my work was try to be critical of that.
Peter Adamson: It sounds like there's quite a lot of variety then in the way that medieval philosophers think about even this one issue, the question of whether syllogisms have form and matter, and if so, what would be the form, what would be the matter? And I was going to finish the whole discussion by asking you whether it makes sense to talk about medieval logic as being formal and what that would mean for medieval logic. But now I'm wondering whether the answer is just, well, it depends because it depends what formal means and the medieval philosophers themselves had different views about what formal means. And so Kilwardby’s logic would be formal in maybe a different sense than say Ockham's because I presume Ockham wouldn't have these kind of very robust metaphysical assumptions about what a syllogism is.
Catarina Dutilh Novaes: Well, so the thing is that in any case you need to understand, and that's very important, that medieval logicians, nobody thought, nobody, that logic deals only with the formal. This is a very important difference between current thinking about logic and medieval thinking about logic. So, for example, there is the distinction that you find in the 14th century, for example, with Buridan, between formal consequence and material consequence. And so modern logicians would say that only formal consequences fall under the scope of logic these days and material consequences are not logic. So they would say that an argument like Socrates is a man, therefore Socrates is mortal, falls out of the scope of logic because it's merely materially valid. The medieval authors would never think of restricting the scope of logic only to what even they would call formal. So that's a very important thing to keep in mind. But this being said, what you can do is look at medieval logic either looking for their own conceptions of formality or using our modern conceptions of formality and trying to see whether what we call formal, if these properties are also to be seen in medieval logic. So these are two different things. So I would say that certainly with respect for the formal as schematic, that's already there. But then again, that doesn't exhaust the scope of logic for the medieval logicians, whereas some modern people might think it does. But even if you think about the formal as computable, which is not a notion that they had in any way, some of the theories, for example, Ockham's supposition theory, and I've written on that too, in a sense what he's after is principles of interpretation of propositions that can be applied in a more or less mechanical way. And there is a sense in which that theory is formal in the sense of computable, which is a modern notion of formality, just because it's about not involving the ingenuity or insight of the interpreter. So one of the terms that I use to describe Ockham's theory of supposition is as formal hermeneutics. So there are all kinds of ways in which you can ask this question. And yeah, I guess we probably don't have the time to talk about all of them, but just to give a glimpse of the complexity, but also of the relevance of the question.