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- [00:00]
Unidentified Host
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Dr. Guillermo Badia
Nice.
- [01:18]
Unidentified Host
Nearly every single print, ebook and audiobook from Princeton University Press. Just go to press Princeton Edu to get 50% off. Incredible Books like Disneyland and the Rise of Automation and Beyond Belief How Evidence Shows what really Works. There are so many fantastic books that you can get an incredible deal on. Go to press Princeton Edu and use the code spring50. That's S P R I N G50 press Princeton Edu the sale only lasts for a month, so go and get some books. Hey NBN listeners. We're running our 2026 New Books Network Audience Survey and we'd love just a few minutes of your time. NBN has been bringing you in depth conversations with authors and scholars for over 15 years. We haven't done a comprehensive audience survey, so since 2022, and a lot has changed since then, it's time to hear from you again. Here's why we're asking. We want to understand who's listening, what subjects and podcasts you love most, and where you'd like to see us grow. Your responses help us tell NBN's story to the publishers, libraries, and institutions we partner with. When we can show that our Listeners are serious readers, lifelong learners, and heavy library users. It opens doors to new partnerships, better resources, and ultimately a stronger NBN for everyone. And one more thing, if you leave your email address at the end of the survey, you'll be entered to win a $100 gift card to bookshop.org, a chance to stock up on books while supporting independent bookstores at the same time. The survey takes just five minutes. Your answers are confidential and your email will never be shared. Head to newbooksnetwork.com to take the survey today. We really appreciate your support. Now go take the survey.
- [03:11]
Dr. Guillermo Badia
Welcome to the New Books Network.
- [03:16]
Pat McConville
How does art shape ideas? Join me as I explore this question through conversations with philosophers and thinkers about the influence of art on their scholarly work. I'm Pat McConville and this is Concept Art. In this episode I speak with Dr. Guillermo Bardia. We discuss logic, murder mysteries and the counter revolutionary search for truth. Dr. Guillermo Badia is a philosopher working in logic. His research interests are logic and computer science, semi ring based logics and models of computation, and modal, intuitionistic and other non classical logics. Dr. Guillermo Bardia, thank you for joining Concept Art.
- [04:02]
Dr. Guillermo Badia
Thank you, path. It's a pleasure to be here.
- [04:05]
Pat McConville
Can you begin by telling us a little about yourself and how you came to be doing your academic work?
- [04:10]
Dr. Guillermo Badia
Sure. I mean, this is a little bit of a long story. I was born in Cuba, which for those of you that don't know, this is a communist dictatorship in the middle of the Caribbean. It's a pretty terrible place to be born in. However, now, since I was a little kid, I suppose I was interested in science, literature, general culture and so on. And one of the things I was interested in was a writer by the name of Umberto Eco. There was this novel, the first one I read, which was called the Name of the Rose, which is a story about monks and a detective story in a monastery, well, in an abbey to be more precise. And there was another book that was influential to me, Foucault Pendulum. This was my favorite book by Umberto Eco. And I was fascinated by it. And then I decided I wanted to be a writer. But of course you don't live in a writer, right? So you have to have a job to become a writer. So I looked up what Umberto Eco was doing, you know, as a profession and he was a philosopher. So I decided, well, why don't I become a professor of philosophy? This is going to help me to. To write wonderful novels, you know, very deep novels that people are going to love Because I never wrote any novel. But I did end up going to study philosophy at university. Unfortunately, that was a big disappointment as well, because in Cuba, being a communist dictatorship, the only kind of philosophy you could study was nothing like what I was expecting to study. It was just Marxist, Leninist philosophy. Okay, so it was quite limited in scope. Well, I wanted to do medieval philosophy, but that was not possible. But I remember it was perhaps in first year or something like this, we had a class which was on dialectical materialism. And one of the things that they would mention in this class is that of course they would mention these figures from Anglo Saxon philosophy, in particular, Bertrand Rasse. And they would tell you, oh, why these people are radical right wing bourgeois ideologues, right? And they are the scum of the earth. But I was very curious about these people. I tried to find out a little bit more about veteran Russell. So I learned about, you know, that he was doing something called logic. I mean, I knew, roughly speaking, what logic was in the sense that, you know, see logistics, Aristotle, whatever. So I went to the library of my university and it turns out that there was only one book there on this topic of, of mathematical logic. And this was a wonderful book, but extremely old and quite difficult to learn logic from. But for me, this was like a drop of water in the middle of the desert, right? So this book was by Steve Clooney and it's called Introduction to Metamathematics. It's an old book from the 60s. And that was kind of my introduction to Logic. But then I also found the Stanford Encyclopedia of Philosophy. This was basically another wonderful research. I should clarify. In Cuba, we didn't have Internet, but my mother, she was a medical doctor. And if you were a medical doctor in Cuba, they would give you an email. It was not, you know, Internet, but they would give you an email. And you had some kind of intranet within the country where you had access to some websites of certain universities elsewhere. There I found the Stanford Encyclopedia of Philosophy. And then, you know, I read a couple of articles about various topics, you know, like modal logic, this and that, and I got in touch with a couple of people that were quite helpful to me, honestly, because when you are an undergraduate student there in the middle of nowhere, in a place where, in fact, when you have this kind of interest, this is frowned upon, right? In fact, remember that they used to tell us that this sort of mathematical logic thing, this was a bourgeois again sort of way of thinking that was not to be cultivated because of course, I mean, things like the principle of non contradiction or whatnot. This is in contradiction per se, right? With some precepts of Marxism, right. In particular with dialectical materialism, right? So they couldn't put those things together, so they preferred to reject it. They didn't want logic to have any part within philosophy, at least not logic in any traditional sense of the word. So what happened is that then I got in touch with Ed Salta, right? So the editor of the Stanford Encyclopedia and another friend, Chris Mensell, who was the author of a, you know, a couple of entries on modal logic and philosophy of modal logic and stuff like this. And they helped me a lot because then I had back and forth with them where I would ask questions and they spent awful amounts of time replying to my stupid undergraduate questions in Cuba. Now in retrospect, I realize how crazy this was that these people would take the time to reply to me anyhow, but that was really, yeah, a game changer for me. And then eventually I realized that this might be a way out of Cuba because then I thought, okay, so maybe I can apply for a scholarship to do a PhD somewhere, right? Like that they might take me and maybe I can do mathematical logic there. And then it turned out that there was an opportunity in New Zealand. So I applied for this thing and I got it. And they were extremely kind, Otago with me because I didn't even have transcripts. My university in Cuba, they didn't want to give me my transcripts. They told me that I had to pay US$6,000 for my transcripts. And you have to imagine my mother as a medical doctor in Cuba was making 25amonth. So you can imagine that when they tell you, oh, if you want your transcripts you have to pay US$6,000, they're basically telling you, hey, you're never going to get those transcripts, right? But Otago, they were kind enough to accept my application with sort of transcripts where I basically wrote up the courses I had taken, the marks I had gotten in those courses, and I had a professor from my undergraduate university basically sign that and say, oh yeah, yeah, I can vouch that he has gotten these marks. I mean, this is not official, this is nothing, it's just a piece of paper. But they were kind enough to accept me because also Ed, he, he wrote me, Ed Salta, he wrote me a letter of recommendation and Chris Mensella as well. And I was told in no uncertain terms that these letters had made all the difference for me. So that's basically how I ended up going to logic. Then I got out of Cuba in 2013, which was the one year when the dictatorship allowed people to leave the country without any kind of permission or anything. You could just leave, no matter what your profession was. No matter what, you know, your political ideology was, right? You could leave. That lasted one year. Then they changed that back because they realized that too many people were leaving. So they got nervous. So they say, okay, no, no, no, wait, wait, wait. So if you have any kind of useful profession, we are not going to let you out, right? If you're a medical doctor, you know, engineer, whatever, you have to ask for permission. And we will see. We will see what we do with you. Okay? But I guess I was fortunate because I had decided to study this completely useless degree. I mean, at least in the. It was completely useless. And for them it was, okay, fantastic. I mean, you are going to be better use abroad than here. You can go, right? It was a lucky stroke for me.
- [11:44]
Pat McConville
And did you ever think that you would jump on the Stanford Encyclopedia of Philosophy and look up some medieval philosophy?
- [11:54]
Dr. Guillermo Badia
That's a good question. I already decided that I wanted to be a logician. By the point, I ended up in the Stanford Encyclopedia. I didn't know what that entailed because I had only read that one book, which was great. It's a fantastic book. But it also means that when I talk to colleagues in my area in terms of my education, the people I have something in common with are in their 80s. That was the time when that book was actually standard.
- [12:22]
Pat McConville
Did you go straight to your. To your PhD studies in Otago first?
- [12:26]
Dr. Guillermo Badia
Originally, I went there for a Master's. Okay. But then that Master's ended up being updated to a PhD because, yeah, they counted my first year, so year of the Master as the first year of a PhD, essentially. Right. So I applied for that change and it worked out because, I mean, I was very stressed out. I could not. I didn't want to have to go back to Cuba once I was out. And if I had waited for the Masters and all of this, there was a possibility that then my visa would run out and then, you know, or expire and then I would have to return. And then if I return, I didn't know if I was going to be able to get out again.
- [13:01]
Pat McConville
And how did you find Dunedin?
- [13:03]
Dr. Guillermo Badia
I was amazed, I can tell you. The most amazing thing for me was that when I arrived, my landlord gave me a little radio, okay. So I could practice my English. So I would turn it on and I would listen to random radio programs. And I remember the first thing I heard was a show where they were criticizing the Prime Minister. I could not believe this. This was unthinkable to me, right, that you would be in a place where you could actually openly criticize the leader of the country in the radio, I mean, on the radio. And, you know, not hiding. It was not a secret thing. No one was so watching over you and say, oh, you cannot do this, or the police was not going to come in and take you somewhere. This was really an amazing experience. I cannot even describe it because now I have forgotten what it felt. I mean, I remember, but it's very hard for me to replicate that feeling again because of course has been many years. But at the time I could not believe it. I thought that this was a fictional place that I was living in land of dreams. How was it possible that people could speak out about politicians? I mean, this was unthinkable. And also, going to the supermarket, this is a ridiculous thing as well to hear from many people. But you know, New World, this was a supermarket, you know, in New Zealand. It's a famous brand of supermarkets. I remember going to New World was for me, literally a new world. And I saw that it was more than one kind of bread. That was also crazy. More than one kind of bread.
- [14:35]
Pat McConville
So the regime in Cuba felt that logic was counter revolutionary. Do you feel like you're doing counter revolutionary work or is it just doing work and being free to put your energy where you want to? Is that in itself counter revolutionary?
- [14:49]
Dr. Guillermo Badia
Well, I mean, that is counter revolutionary. Because when you say counter revolutionary, you mean not kind of revolutionary. You mean counter revolutionary. Yeah, exactly. So, yes, I would say that if I would have to place myself somewhere, yes, I am definitely a counter revolutionary from this point of view. And I am happy to do things like that that I was told I was not meant to do. At the end of the day, I spent 23 years of my life there living under those kinds of conditions. Yeah, definitely. I would most certainly say that what I do is counter revolutionary.
- [15:27]
Pat McConville
Has art influenced your academic work?
- [15:30]
Dr. Guillermo Badia
Yes, my interest in art in the form of literature to be precise, is certainly what led me to academia at all. I had a job, part time job when I was doing my degree as a TV editor. So this was my alternative career pathway. So if I could not manage to get out of Cuba to study somewhere or whatever. Right. I would just have continued that pathway. Right. And I would become an editor and hopefully maybe one day I would have been able to cut a movie or something like this. And it would have been interesting, but I quit that job actually, because I was told by some person that, oh, well, but, you know, you are editing for tv, but that's not actual art. You are just a technician. You're not an artist. And then I started thinking about that and I thought, okay, yeah, maybe she's right. I mean, maybe I'm not an artist. And I kind of gave up on that sort of idea. So I decided, okay, so where else can I be a good technician? Okay? And it felt to me like academia was a little bit like that. But it turns out like logic in particular, mathematics in general, but also philosophy. Like it requires something certain level of creativity that, yeah, it is very analogous to artistic activity, I would say. But also there is another, perhaps more abstract way in which this has influenced me, which is, as I mentioned, I mean, these books, this Umberto Eco novels, they had one thing in common, that they were these sort of detective stories. Right. But not just any detective story. Right. It's a detective story with a whole of, you know, little puzzles and clues and, you know, pieces of history here and there. Right. So ensembling a story, a story from things that, you know, you come across facts or data that you come across and you don't know how to put them together and you put them together in some kind of coherent manner. There's sort of Sherlock Holmes kind of character. You know, there is also this other character by Edgar Allan Poe. Was it Lupin? Right. I think it's the name of the original detective on which Sherlock Holmes is based on. I think that this completely analogous to the activity of a logician or a general mathematician or anyone working in theoretical computer science or even the activity of an abstract philosopher. So you have a problem or even more general, the activity of someone that is pursuing a PhD. So you have a problem and you really have to solve that model. So you see something, you want to explain it, and you are really coming up with an explanation. I think that there is a lot of analogies there. So the people that are typically curious or interested or motivated by these kind of puzzles, I think that they have a strong inclination to end up in some kind of academic activity or other, because it's really about learning the truth in a way, or the truth as best as you can. Because obviously you might not be able to get the whole truth, but at least the truth that you can put together the best, the best explanation, if you will. Right. I definitely believe that having a taste of an interest in these kind of detective stories is a trait of personality. That helps with this other kind of inquiry also. You have to be relentless. You have to not give up. And you really want to know the answer to this parcel? Sum up? Yeah, of course you need many more skills. Obviously you need organization. You need a little bit of ingenuity as well. But at least that initial step of being curious about detective stories, I think that that's a good starting point, I would say.
- [18:59]
Pat McConville
Do you still read those sort of novels?
- [19:01]
Dr. Guillermo Badia
I do when I have the opportunity. I mean, there are other writers I enjoy along this kind of line, right. Like there is also Italo Calvino, right? Like he has an excellent novel. I mean, maybe not a detective story, but there is a mystery and the mystery gets. They try to solve. Right. If on a winter's night a traveler. Right. This is the name of the. Of the book that's quite enjoyable. There is a guy, my namesake, I suppose, an Argentinian guy, Guillermo Martinez. He has a couple of very lovely novels. Guillermo Martinez is somehow in between. Okay, so he's not as deep as Humberto Echobad. He's not as stupid as Dan Brown, right? So that's quite amusing. And he has his series of novels which, as you can imagine for me personally, are great because the main character is a logician, right? An Argentinian logician by the name of Guillermo that moves to Oxford to study logic. And this sort of semi autobiographical because the author, Guillermo Martinez, he indeed did one year at Oxford as a visiting PhD student. Right. And he has this novel, the most famous one is called the Oxford Murders. All right, which in fact has a movie. Okay, Is there one movie where you can see a whole scene about Wittgenstein? It begins, it starts with Wittgenstein in the trenches, right? In the. During the first world War. And he's writing the Tractatus, okay. At the very beginning of the movie. It's an Elijah Wood movie. You should look it up if you don't know. I love it. I mean, he's a wonderful, wonderful movie.
- [20:31]
Pat McConville
The enigma that he tried to decipher was the following.
- [20:35]
Dr. Guillermo Badia
Can we know the truth? Truth.
- [20:40]
Pat McConville
Ruby Student. What are you doing here? I live here.
- [20:45]
Dr. Guillermo Badia
What's your excuse?
- [20:46]
Pat McConville
Visit?
- [20:46]
Dr. Guillermo Badia
No, friend. I received a note during the conference. What did it say? The first of the series, Logical series with serial murders. I don't even know if the movie is even better than the P. I. I should say perhaps.
- [21:04]
Pat McConville
Well, those are great book and movie recommendations. Gimme. Thank you. So you work on, among other things, non classical logics and sometimes on puzzles and paradoxes solved or generated by different ways of looking at things. And I wonder if you could tell us a bit about the 1988 novel Foucault's Pendulum, written by the Italian intellectual and novelist Buro Eco.
- [21:24]
Dr. Guillermo Badia
So this is a story about a group of intellectuals. The main character is a student that has just graduated from university. At some points, it's kind of unclear in this novel itself if this is a philology or a philosophy student, but somewhere in between, and he has graduated and he doesn't know what to do with his life. He's trying to get a job and he meets this other sort of senior guy, maybe 15 years old, who works at publishing house. All right? But the funny part about this publishing house is that they, during the day, they are a serious kind of university press. However, during the night, they have a second phase to the same publishing house. They get these authors, they entice them to come to the publishing house and spend awful amounts of money in, you know, producing their own work. So it would get out there. Let it be poetry, let it be novels, but also esoteric works. Right? Like, it works this kind of New Age literature. Conspiracy theories. Oh, what happened with the Templar Knights? Oh, what is the mystery behind the Grail? Oh, what happened with, you know, the history of alchemy? So this guy, he gets wrapped up and this thing leads to another in the sense that they start meeting weirder and weirder characters.
- [22:50]
Pat McConville
Yeah.
- [22:51]
Dr. Guillermo Badia
So Foucault's pendulum sort of brings all of these, in theory, crazy ideas together. I mean, I guess the final message of the book is sort of be careful with what you believe. All right? So don't take things. If you end up staring at the abyss for long enough, the abyss is not only going to step back at you, but it's going to draw you in. Right. Like something like that. They were so embroiled with these conspiracy theories, with these esoteric people, that they end up falling victim of the same kind of affections. So for me, it's a very nice book. They also mentioned Goethe theorem at some point of the book. Right. But it's just only mentioned in passing. Umberto Eco's forte was definitely not logical or mathematics, but it's still a very pleasant book to read. Yeah, for me, it was a very fascinating note because I'm interested in this kind of history of the occult. Right. Like, I mean, it's a very curious topic to me because things like alchemy, they do have an interest. I mean, there was a point as to why humanity had to develop this kind of knowledge. I mean, it's not knowledge in the traditional sense, but let's call it these kinds of systems of thinking, right? Because if we hadn't had alchemy in this state of precise, we wouldn't have had chemistry, right? Even Newton was an alchemist, right? He in the old days and he was very interested in these kind of esoteric readings because it was just what people used to do, right? So you had to go through all of these stages to create the kind of science that we know today. So maybe in 1,000 years from now, what we are doing today sounds like magic to them and it's completely ridiculous. I mean, maybe quantum mechanics will be seen as magic in the future, right? And they will say, oh, these nonsense people. What are they doing? Right? This is not even. Maybe science will have a completely different method, right, in the future. Who knows what's going to happen? Maybe we are going to look like fools.
- [24:46]
Pat McConville
I wonder if you could tell us a bit about the work that you do, what the logic that you do. And maybe this is a bit of an ask, but it's sort of situated in the kind of stuff that you were just talking about there. Are you after truth in your work? Are you after new ways of looking at things and thinking about things?
- [25:06]
Dr. Guillermo Badia
I was having this conversation one time with a colleague of mine. He also likes Humberto. He has read the books and I was telling him when I was a kid and I read this book when I was 13 or so, I could not believe that this was what people actually were. That was so foreign to me. The characters were so foreign to me. I loved it because it was a completely new world that was disconnected from my own reality. That was utter poverty. But then today I feel like I'm living in that novel, which is a very interesting situation to being not because of the topics, but just because we are definitely pursuing puzzles in this sort of intense way. We have the same. Of similar conversations to the kinds of conversations that these characters have in the novel, right? Like conversations that, again, were so divorced from daily life for me in the past, when I was a kid, when I was living in Cuba, that I could not believe that anyone would actually speak like that or anyone would. I thought that this was made up, right? Like that maybe people spoke like that the 19th century, but not in today's world, right? So, yeah, so there is a little bit of that aspect. And in my own work, basically at the moment, what I'm interested in is applications of logic in computer science, right? In particular in database theory. And we are Certainly, looking at puzzles, these puzzles are of a relatively technical nature. But generally speaking, these puzzles have to do with the things that you can use logic to say, okay, in the context of information of database, how can I use logic effectively to ask questions about the database and get answers in an efficient manner in a short period of time? What kind of questions would be more effective to ask? If you have something that you want to ask, maybe instead of asking that thing, as it comes to your mind, there is a reformulation of the same question that is less costly for the computer to ask from the database, and the computer is going to find faster ways of answering that question instead of the original one. So this is a question of equivalence between two propositions in a way. So it's a lot about the expressivity of language, but the expressivity towards this kind of application that you want to have. You want to have logic be, in a way, if possible, useful for something. Right.
- [27:29]
Pat McConville
So those Cuban administrators weren't quite. Right, not so useless as they thought.
- [27:33]
Dr. Guillermo Badia
Not saying exactly that, but, you know. Yeah, that's. Yeah, that's what it is. Yeah. So these are kind of technical puzzles of the sort. Oh, can I ask this question rather than this other question? Right. Is this a question that I can ask in this language? Is it possible for me to formulate this question in this language at all? Right. Sometimes you cannot do that. There are languages that are too poor for you to formulate X or Y question, but you don't know this until you prove a theorem that tells you, okay, how rich these languages. So you need to do this using proper mathematical tools. You have to have something that actually gives you the truth about it. But, yes, certainly, my work is most certainly searching for the truth in the only possible way in which you can do it in life, in my opinion, which is in the realm of mathematics, Right. This is the only realm where truth exists at all. Of course, it's truth. Even in that realm, there is a certain level of. You have to be careful because it's truth with respect to a given language. Again, right? So a given language, a given framework. But once you have a fixed framework, once you have a fixed language, then you can definitely ask very precise questions and you can get certain answers. All right? Of course, that is if you believe the traditional logic. But in this little realm of mathematics, of theoretical computer science and so on, you can be a lot more reassured that what you are doing is actually true. Unless, of course, you make a mistake, but then you didn't do anything to begin with. And this unfortunately, is quite common. I mean, many of my colleagues and I have definitely had significant mistakes in the things I have published. But it is what it is. It's a process of doing, unlearning sometimes. And you have to retract proof, proofs, you know, you have to retract claims sometimes. It's life. This is science as it progresses, Right. It will be like that in every sphere.
- [29:29]
Unidentified Host
Yeah.
- [29:30]
Pat McConville
So, Guillermo, what are you currently working on?
- [29:33]
Dr. Guillermo Badia
So at the moment I'm writing a couple of papers, right. I'm writing a book on many value logics, right, which is logics where essentially you can have more possibilities than just truth or falsehood.
- [29:47]
Pat McConville
You're working on this book and you're working on these papers and I see that you've also got a book on mathematical logic about to come out. Is this an update for that dusty 1960s book that you picked up?
- [30:01]
Dr. Guillermo Badia
No, a different one. This is an update to a different one. Yeah. So this is called what is Mathematical Logic? And this book is a second edition of a very old book that was an Australian production from 1974. And this book was originally by a couple of colleagues of mine that are still alive, which are my co authors in the new edition and some other people that now, you know, they have passed away because it was a long time ago, right. The new edition, of course we rewrote, everything is double the size. And it's definitely an update to that original little book, which when that book came out, I should say it was a. Again, it was an Australian production. But logic here existed more seriously in philosophy departments, but not really mathematics departments. Right. And my colleague John Crossley was the first one to start this out and they decided to write this little book as a product of some lectures that they gave out. I mean, they gave a freak in Melbourne during some period, right, it was him and some other guy, the University of Melbourne. And they gave these series of lectures to the open public. And you know, people came and they wrote a little book, right, from these lectures. And so I thought that this was a wonderful, lovely story. And I, yeah, I just wanted to do a second edition of that. So then I told you we should do this. It took us some time because I should say, you know, it was such an old book that getting the, you know, they didn't even have contracts or anything. Oup had not preserved any of the original documents because it was, you know, like a. For the times of computers. But eventually we got there. It took us about two years to get the contract. And all of this stuff right. And to get the right people to listen to us and then now the book is coming out. So I'm very happy about that and I hope that you know any student that is curious about what mathematical logic is can read the book to see finally how it's very satisfying. Also as a gift for my friend right. Like my two co authors right. The oldest of them is in is 88. You can't imagine what this means to them. This is sort of the 50th anniversary edition of the original book. Right. So it was very emotional for them. So it was a beautiful thing to be part of.
- [32:14]
Pat McConville
Listeners can find links to Dr. Badia's work and some of the art we've discussed on the concept art website. Dr. Guillermo Badia, thank you for joining
- [32:23]
Dr. Guillermo Badia
Concept Art thank you so much Pat. It was wonderful to talk to you.
- [32:39]
Pat McConville
Concept art is produced on Milanina country La Truita Tasmania always was, always will be aboriginal land.