Bacon’s Mathematical Epistemology (09_2022)

Roger Bacon’s Mathematical Epistemology: An Interview with Yael Kedar, Giora Hon, and Elena Baltuta

by Mário Correia

September 2022 – What is the role that mathematics and the mathematical method play in Roger Bacon’s philosophy? We discuss about this fascinating topic with three special guests: Yael Kedar, Giora Hon, and Elena Baltuta. They have recently started an ambitious research project in Israel titled “Certainty Without Doubt and Truth Without Error: The Mathematical Epistemology of Roger Bacon” and funded by the Israel Science Foundation. Beside talking about Roger Bacon, Yael, Giora, and Elena also give useful insights on how to structure a successful research proposal and the challenges of working on medieval philosophy and science in the 21st century.

The interview took place in Paris on 24 August 2022.

About Yael Kedar

The Interview

Transcribed by Eduarda Machado and Celeste Pedro

Mário Correia: We are in Paris, in the SIEPM Congress, and we are very happy to introduce Giora Hon, Yael Kedar and Elena Baltuta, that were really kind to give us an interview about what they are doing. The first question I’d like to ask is about your research project on Roger Bacon; could you explain to us how it appeared, what are your goals, what is your methodology, all of that!

Yael Kedar: How did it start? I think it started out of a conversation that Nicola [Polloni] and I had at some point. We were really surprised to find that Bacon is declaring that he wants to use math as method of proof in natural philosophy, but not only in natural philosophy, metaphysics and in theology. We wanted to look a bit into that and then it developed into a full project. In two weeks, we wrote the proposal. The idea was to examine how Bacon thinks math should be applied in studying other areas of knowledge – because Bacon wrote that math is easily known to us. The image that math has is that it is a very difficult subject, and only for very talented people. But Bacon didn’t think that that was the case, he thought that math is natural to us. He thought that by applying methods taken from mathematics to other domains we could be more efficient in achieving goals in studying. So, we called it Bacon’s Mathematical epistemology, because he thought that mathematics is a method of inquiring. As we understand it, that was his stressor and he was unique at that, in his time, and this is what we wanted to explore.

Giora Hon: An important element of mathematics is the concept of quantity, and the question is how Bacon treated the concept of quantity and how he came up with new ideas regarding quantity, to manipulate mathematics vis a vis metaphysics, and to have the authority of mathematics to decide issues in metaphysics, in religion. The focus is mathematics, but it is widespread into other elements/aspects of Bacon’s philosophy.  

Yael Kedar: I will just add that Bacon was not such a great mathematician. His most interesting idea is to use math – but simple math not a complicated one, in other domains. I said before that he thought that math is very natural to us, but he also thought math gives us certainty that cannot be found in other domains, and it is good to let that certainty permeate other disciplines.

Elena Baltuta: One example of that is what we are doing in the session we have on Bacon and error [in the SIEPM congress called Roger Bacon’s Conception of Error]. There, some of us talk about errors in Perspectiva where he uses a lot of mathematics (in the form of geometry) to prove how certain visual error are possible, how they appear to us and how we can explain them away. So that would be one application of how mathematics enters into adjacent fields such as perception, for example, and how it can be applied.

Mário Correia: Yes, I was going to ask you that:  if it is just a proposal or if he is effectively trying to apply it, to really apply it.

Elena Baltuta: If you look at Perspectiva, I think he’s one of the first to have used images and examples from geometry, where he’s proving his theory of vision and errors that can appear in perception. I think he is employing the method of mathematics, at least at that level.

Yael Kedar: I can add that in optics it is not very novel to use diagrams, to use geometry. But he used math also in problems of natural philosophy of motion, and in metaphysics. He is employing it. He’s not just declaring it; he doesn’t remain on the level of declarations. He’s not always successful in doing that, but he tries.

Mário Correia: I don’t know enough about the subject but, is there some relation with the calculatores?

Yael Kedar: That’s a very interesting question.

Mário Correia: Are you trying to address it?

Yael Kedar: No, we didn’t look into it at all, but we found something really interesting. Nicola and I found something in Bacon’s mathematical proofs against the unity of metrics: there, in one of those proofs, he writes about the magnitude of essences, and I was very surprised to find that out. I was thinking we should search if there are any influences of this idea later on. But that’s for the future.

Mário Correia: I want to change a little the focus, it will be a more institutional question. What were your struggles and your challenges to get this project financed?

Yael Kedar: Yes, I can give some advice. We were surprised with how easy it was. But I think one important thing was the Roger Bacon Research Society. We won an ISF grant, which is the Israeli Science Foundation, and what they do is they send your proposal to evaluators, right? and we had to recommend a few evaluators. Because we were part of a lot of events organised by the Roger Bacon Research Society, we knew a lot of people writing in the field, so we knew we had a lot of people who knew us as well. One of the things that the evaluators must evaluate is how fit the researchers are for the project. We had a lot of people who knew what we were doing already and who could recommend positively on this project. I think that is one key advice that I can give. Be part of a community and work together with other people.

Giora Hon: But being part of the community also has to do with publishing and having some material that the community can recognise and acknowledge. This is important to have as a background for the application. First, to have a community that acknowledges your work and then, through their knowledge of your work, they can provide a positive assessment of the application. This is a procedure which I think should work. But, as Yael said, you need to have this circle of people who know your work and are positive about it.

Yael Kedar: And, if I can give another advice for young scholars, is to consult while you write, to show it to other people, to ask them what they think are possible pitfalls, and try to answer them in advance, to know where not to fall, what issues not to address in the proposal. Especially because some issues are very debatable, try to avoid them so otherwise you can really get criticised for this and have lower evaluations and evaluations are not as good as they could have been.

Elena Baltuta: Since we’re on this topic, it’s not related to this project per se, but I think it is very important to take into account that failure will occur, and it’s a normal process, and it doesn’t mean that that is the measure of you as a person. Because I think young researchers – but not only young researchers, take failure very badly, take it very personally and it should not be like that. Everyone has failures, and I think that’s an important part of making it in the field: being able to accept failure and move on.

Yael Kedar: And maybe one last advice. Submit research proposals. If you don’t do that, you’ll never win.

Mário Correia: Great advice. Thank you very much. One last question, more methodological. You’re like in-between disciplines, it touches history of science, a little bit philosophy, a little bit history… how do you manage to navigate in-between these fields?

Giora Hon: I can respond to that: this is why we are working as a group. We acknowledge the contribution of members of the group, the combination of various perspectives, and being productive by putting together all these aspects; and of course, consulting other people when issues require professional attention, then don’t hesitate to inquire, and ask questions about specific technical issues. You have to bring together all these elements in order to combine a coherent picture of that or other aspects of Bacon’s philosophy.

Mário Correia: For instance, do you feel the need to contact mathematicians?

Giora Hon: Maybe, maybe we will!

Yael Kedar: probably! Not mathematicians, but historians of mathematics. I have to say that for me, I don’t see a problem because I think in philosophy, especially medieval, there’s no real gap between philosophy and science. I mean, we do those divisions when looking back at them, but I’m not sure that for them these divisions were so clear. And again, there are all those analytical philosophers who disrespect the history of philosophy. And that was an understatement! Where I work, I have to defend myself. They accused me of not doing philosophy. They said, “what you do is not philosophy”. In my view, what they do is sterilise ideas. They are taking them out of their context and treating them as if they’re out of time, I think it is always a mistake to do that. They talk a lot about intuitions, but intuitions do change over time. My intuitions are not the same as a medieval person, right? For me, what we do is very natural, and I don’t sense any conflict or a problem in this respect. My environment may sense problems, but I don’t.

Elena Baltuta: I have the same idea. I think we are fortunate to work in the field of medieval philosophy because for medieval [thinkers] they didn’t have all these divisions that nowadays we are confronted with. Maybe dialogue is easier among us, unlike someone who’s doing contemporary philosophy, where it would be harder to establish a dialogue, a community to get everyone together. But in our case, I think the material is somehow there, available.

Mário Correia: And finally, one very quick last question. Imagine that a politician comes to you and says, “Why should the State fund this project? Why is it useful for society? What does Roger Bacon have to do with us?” What would you respond to them?

Elena Baltuta: What does history do for us, in general?

Yael Kedar: This is a part of the project of us, human beings, understanding ourselves, understanding our concepts, understanding our ways of thinking, understanding how our understanding of the world develops. Again, you cannot isolate ideas from their context, and all our ideas are grounded in some context. And this is us. This is us exploring ourselves, the way our mind works, the way our concepts develop. So, I think it’s part of us understanding who we are. The first thing that was written above the oracle: “know yourself”.

Giora Hon: This is a question that can be asked about history in general, and of course, the answer is “know yourself”, and we are providing an aspect of that issue. How have we come to be what we are now?

Yael Kedar: Other sciences are doing the same, like archaeology, also psychology. This is self-exploration. So, I mean, if you ask this about history of philosophy, you can ask this about almost any other discipline in social sciences and humanities.

Mário Correia: Thank you very much for this interview. Thank you very much for your advice to our younger listeners. And I hope that this project is successful, I’m sure it will be. It was a pleasure to interview you!

Interviewees: Thank you!