 one. Hello, I'm JJ Joaquin, and welcome to Philosophy in What Matters, where we talk about things that matter from a philosophical point of view. Now in this episode, we will explore life and works of some of the world's greatest women logicians. Now, logic is often thought of as a male dominated field with the likes of Aristotle, Boo, Piers, Fregge, Russell, and Whitehead as acknowledged founders of this area of inquiry. But as our guest in this episode suggests, we should also acknowledge the contributions of women in the development of modern logic. Now, to celebrate these contributions in a way why they matter, we have Sarah Acomman, assistant professor of philosophy at Durham University. She's also the associate editor of the Journal of Logic, Language, and Information, and the Doctor of Logic in YouTube. So, hello, Sarah. Welcome to Philosophy in What Matters. Hello, and thank you very much for the invitation. I'm looking forward to talking about these topics. Okay, so before we get into our main topics, let's first discuss your philosophical background. So, how did you get started in philosophy? It's very interesting because I got into philosophy via logic. So, I had one or two brushes with philosophy in high school. My mom had taken an introduction to philosophy course at university, and her undergraduate textbook was just a collection of articles sat on one of the shelves in our living room for years. And at one point, I pulled it off and I opened it randomly. And I read What the Tortoise Said to Achilles by Lewis Carroll. And I remember reading it and thinking that that's what I want to do. I want to learn how to think like that. And then my senior year of high school, I had the opportunity to take courses at the local university, one of which happens to be Introduction to Logic. And I chose that course because I knew deep down inside that I was not a logical person. Comparing myself to my father throughout my whole life made this very clear that he, well, the picture of rationality and logic. And I was not that. So, I went into this logic class, convinced that I was going to fail, but I was going to enjoy learning about it anyway. And a couple of weeks in, discovered I actually really like this. A few weeks later, discovered I'm really kind of good at it. This is cool. I want to do more. And so when I actually went off to university, I chose my courses and I chose my kind of degree program specifically to maximize how much logic I could do. And as a result of where I went, I was in a philosophy program. And so I also had to take other philosophy courses. But for a very long time, I identified first and foremost as a logician. And if people would call me a philosopher, I'd be like, I'm not a philosopher. I'm a logician. And even after what six years as a professor of philosophy in a philosophy department, I still don't like really being called a philosopher. Okay, so who influenced you to pursue a career in hadamic philosophy or hadamic life? So the probably the most major influence on kind of where, how I got to where I am now was one of my professors at the University of Wisconsin, Madison, Mike Bird. He, one of the like actual philosophy and non-logic courses that I took that I really loved was an upper level class on Frege Russell and Wittgenstein. And that was my first introduction to analytic philosophy. And again, I took this class and I remember thinking this is the way that we should be thinking about things. And so even, even though I'm not necessarily kind of much of a philosopher, I do have a lot of thoughts about philosophical method and like ways of thinking about things and ways of asking questions and ways of answering questions. And this, it fed into my desire to do logic. Professor Bird was amazingly supportive of my desires to do logic. I was in his office hours a lot and he was always happy to answer my questions. And this set me up in a position so that when I went on to do my graduate work at the University of Amsterdam, I was lucky enough to fall into the into the capable hands of another person who was very much interested in kind of supporting people who wanted to do what they wanted to do, even if it wasn't necessarily the mainstream thing to do. So was willing to support somebody who wanted to do logic in the context of a philosophy department. At the University of Amsterdam, my supervisor, Benedict Lever, was much supportive of somebody who wanted to do history of logic in a logic program. And so both of both of those people had a significant influence kind of on what I have enjoyed doing and even my ability to have the opportunity to do it in the first place. Okay, so you specialize not only in logic, but also in the history of logic. So before talking about the history of logic, let's talk about what logic is in the first place. So Dr. Lager, what is logic? Yes, what is logic is what I ask my undergraduate students in their very first logic class, because a lot of them either have no idea what it is, or they have gotten this very pat answer, something to do with valid arguments and things like that. And so they will tell me things about necessary truth preservation and stuff. But actually, my favorite definition of logic is something that belongs to not anything that you'd find in a modern textbook, but in a textbook written round about 1215. So Roger Bacon wrote a book called The Art and Science of Logic. And in it, he gives a definition of logic, which I absolutely love. He says that logic, as a science, is the habit of distinguishing what is true from what is false by means of rules or maxims or dignities, by which we can comprehend the truth of a locution through our own efforts or with the help of others. And logic is so called from logos, which means discourse and lexus, which means reason or understanding. And so as it were, the science either of reason joined to discourse or discourse joined to reason. And what I love about this definition, and I think really kind of encapsulates what I think is the heart of logic, is that it's about separating truth from falsehood. So in order to determine what things are or can be true, we need to know how truths and falsity relate to each other. It's rule governed. There's a systematicity about it. This isn't blind searching. It's not ad hoc. There are features in language that you can look for, features in the world that you can look for. And there is a very close connection between these things and determining acceptability of arguments. But then there's two more things that Bacon includes that a lot of modern logicians might not necessarily, and that is that it's a joint venture, and it's related to discourse. And I think that this is something incredibly crucial to understand about what is really going on in logic, that we are involved in a collective enterprise in trying to figure out what is true and what is false and what are the appropriate rules to be used. And it cannot be separated from the ways in which we communicate with each other. So discourse not just in verbal communication, but in broader ways of exchanging and communicating information. So if I have to give kind of the short answer, I just go to Bacon's answer, I think his is an excellent definition of logic. A longer answer involves a lot more time than we probably have a lot of thought and a lot of study, but the idea that I try to get my students to understand is that broadly speaking, what brings all aspects of logic together is that it is a way of helping us determine what are good arguments. And good can be defined in many different ways, and this is why we have many different types of logic and many different approaches. But at the center, that's what it's all about. What are good arguments? I like the idea by Roger Bacon with regard to the social dimension of logic. So you have discourse, not only the formal thing, but also how we communicate and how we argue with one another. Is that the idea here? That and also the collaborative aspect, the fact that a lot of times people have, maybe philosophers more than others have this idea of logic as being this kind of God given a priori science and that you can sit in the logician or the mathematician, they sit in their office on their own and they have their axioms and their definitions and they derive their theorems. And yes, you can do that, but logic, studying, learning, teaching, researching it is always going to be so much more accessible and easy and understandable if you're doing it in combination with other people. So one of the kind of life lessons that I learned from Professor Byrd UW-Madison was for his lower and upper level logic courses, he encouraged people to submit homework in groups. So two to three people would submit one homework assignment. And this is how you learn to ask questions of other people and you learn to explain things to other people that you understand this is by talking about it and helping other people understand it. And you lose that dimension if you're just sitting in your office deriving theorems on your own. Okay, so you coded Roger Bacon, so that's a 12th century or 13th century philosopher. We're talking about logic, right? So why do we code still medieval philosophers or philosophers in the olden days? That is, why does the history, does the history of logic really matter here in understanding what logic is? So there's the trite answer, which is that yes, of course, the history of a subject always matters because what's that kind of overused quote that everybody always says, those who don't know their history are doomed to repeat and you can see this in the history of logical developments in the sense that propositional logic was independently discovered or independently defined three different times, first by the Stoics, then by Peter Abelard in the 12th century, and then by Frege in the 19th. So if Frege had been reading medieval monks, maybe he would have known that this had already been done. But that's a very trite sort of answer. One of the reasons why the history of logic matters is because I like to make a distinction between history of logic and historical logic. So history of logic is asking questions like who are the people who are working and what texts did they write? Who did they study with? Who did they teach? What were their dates? When were they born? All of these sorts of like things that a historian would do. Now, I have a deep interest in history, but I'm not really a trained historian. So I try not to do as much of that. Historical logic, on the other hand, is logic first and foremost rather than history. It's just logic that happens to be kind of temporarily remote from us. So it might use different methodologies. It might use different vocabulary. There might be different techniques. But it's still logic. And this is something where I think that logic differs from a lot of the other sciences in that you can pick up Aristotle and read the prior analytics. And if you don't know anything about the syllogism, but you're trained in modern logic, you can read the prior analytics and be like, yeah, this is the sort of stuff that I do. This is logic. And same with medieval developments. Again, they might be using different techniques and vocabulary, but at the root, they're still interested in the same sorts of things. And I mean, you might say, well, this is going to be true of like biology or chemistry, that they're interested in like how life works or how chemicals and things work. But logic differs from other sciences in that what the historical people did in these topics is still relevant for today. So you wouldn't necessarily tell a doctor to go out and read Galen or to read a 12th century medical textbook because the sorts of things that you would find in those textbooks are not necessarily things that we would want doctors to be doing nowadays. Whereas you go back and you read historical logic and they're dealing with the same sorts of questions and they're dealing with the same sorts of problems. And sometimes they have things to say that are different from what modern people have figured out, or maybe they have a different emphasis, or maybe there are sometimes there are approaches that they take that seem entirely natural as soon as you realize that this is something that you can do. It's just that nobody has done it that way in the modern period. So history of logic matters for questions of, you know, you don't want to reinvent the wheel, but also because there are genuinely novel developments that are still applicable for nowadays. So I think every logician should have to read a bit of Aristotle, have to read a bit of the Stoics, and then read some of the 13th and 14th century commentaries and textbooks because there's so much to learn, not just about history, but about logic in them. Actually, if you read Aristotle and all the rest of the gang, you see the same themes like moda logic, epistemic logic, and so on. So the developments that we see now were, so to speak, were discovered by them. Yeah, and also multi-agent logic. The Medibles were entirely steeped in this idea that logic is a public discipline. It's a public activity that happens between multiple people, usually with an audience. And so questions about what am I committed to in the course of a disputation, or what can I assume my opponent knows given what has already gone on. You know, these sorts of like dynamic epistemic multi-agent systems, you know, this is what they were doing in the 13th century. All right, the theories of obligations. Okay, so let's move to our concern in this episode. So your current project is to showcase the contributions of women logisticians in the field. So who are these women and what were their contributions in the development of logic, as we know it now. So it's interesting that you asked me a little bit ago what is logic, but you didn't ask the follow-up question, which is what is a logician? Because that's the question that I am grappling with in the context of kind of trying to answer the very broad question of who are the women in the history of logic? So first you need to say what logic is, and I have a fairly clear conception of that. But then if you ask, well, like, what is a logician? There's a number of different aspects and answers that you can give. You could say, well, a logician is somebody who is practicing, somebody who writes textbooks and does research and logic and proves theorems and does all of these things. And this is a legitimate answer to take, but if you take that sort of answer, then of course it's going to end up excluding large portions of history and large numbers of women from ever being able to count as logicians, particularly like up through the Middle Ages and into the early modern period. But if you want to say, well, who are the women who were taught logic or studied logic, even if it didn't necessarily, even if it wasn't something that they went on to kind of do explicitly or publicly, maybe they were working in other philosophical fields or related fields and through reading their work, you can learn about how their training and logic influenced the rest of their ideas. So kind of, if I narrowed my definition of logician to kind of practicing logician, then there probably would not be many women logicians before the 19th century or so. So I like going with the more broad definition because it allows me to stay a lot more about the relationship between women and logic in history. If I allow myself to ask questions like what kind of opportunities were there for women to study logic, but it really is kind of in like the 19th century that women start participating in logical discourse and kind of academic logic spheres in a way that is kind of like clearly identifiable as these women are logicians. And this isn't surprising because it's in the kind of the course of the 19th century that women get to participate in most academic fields. So it's not like this is something unique to logic or mathematics. This is part of a kind of wider trend of women moving into higher education and things like that. Okay, so would you consider, because you have a broader notion of who a logician is, so would you consider Heliouis as a logician? She is a very interesting case. We know explicitly that she had access to a fine logic teacher. Yes. We know that, yes. So at the time that Heliouis would have been being tutored, the kind of the primary set of subjects that were being taught are what are called the trivia. So they are the linguistic sciences, grammar, rhetoric, and logic or dialectic. The two words are kind of used interchangeably. We have explicit evidence that Heliouis learned grammar and rhetoric because the sorts of texts that were used as texts for those fields are texts that she quotes in her letters and things like that. We don't have the more, we don't have kind of explicit evidence that she was taught logic, even though her tutor was one of the most evident logicians of his period, and perhaps in the history of logic. And it's very interesting to see the ways in which she characterizes logic or logicians as being at a very bellicose and very belligerent and very militaristic. And I said earlier this, I highlighted the fact that logic was a very kind of public activity which would not have been accessible to women throughout much of the Middle Ages because they were not involved in these sorts of public activities. So it could very well be the case that she was taught grammar and rhetoric and not logic. It's certainly, even if she did, her later attitude towards it is not very favorable. So while it would be a lovely way to be able to call her a logician, I'm not sure that she is on either of the two possible definitions of logician that I've given. Okay, so let's jump many centuries after and let's talk about this woman philosopher logician and perhaps the mother of computing herself either lovely. So is she a logician in your case, in your definition? Interesting case because on the one hand, the idea of this, you know, the field of modern computing science being founded by a woman is a great idea. And it's the sort of things that people would love to be true. But I'm not, I am not sure that modern kind of historiography of computing science hasn't overstated her role in the developments. It's certainly clear that she, you know, contributed to the, you know, the development of kind of early computer programming and that she was an integral part of that. But the extent to which what she was doing counts as computer science. I mean, all of the questions I've been asking about logic and logician, you could do the same with computer science and computer scientists. But I don't think that I would call her a logician. I don't see evidence that she was kind of formally trained in logic of the time, or that she was talking with people who are logicians, or that she was generating logic. So kind of the question then would be, well, where's the boundary between computation, computing and logic? And I think that actually kind of these two fields at in the early part of the 19th century were not yet connected to each other. That was a more later development. So really cool, not necessarily a logician. Okay. How about Christine Ladd Franklin? Absolutely a logician. Absolutely. I've been working on her specifically for a couple of years now, because there's this kind of reputation that she has of having stalled this long-standing problem in Aristotelian syllogistics, something that's plagued people for 2,000 years. And the first time that I came across this characterization of her and her word, my first thought was, you know, I have no idea about this. But this is kind of embarrassing, because I'm interested in the history of logic, and I'm a champion for women in logic, and I'm not familiar with what her contribution is. And so I found her PhD thesis, downloaded it, started reading it, and wanted to find out. And it's very interesting. So I've got a paper almost done, but it's been almost done for a very long time. But a paper looking at what her solution was, and then going from that back to the question of what was the problem that everybody says that she solved. And the short story is it wasn't a problem of Aristotle's that she was solving. It was a problem of a contemporary algebraist, Jevons. So Lab was very much a logician. She studied under a logician. She studied under a purse. She was interacting with the, she was working in algebras, Boolean algebras, and extended Boolean algebras in the context of other people working in this. And it's also quite clear that she had a significant impact on people after her. So the solution to the problem that she came up with, this antilogism picked, you know, kind of its utility was recognized by other logicians almost immediately. And you can still find a huge amount of kind of later authors referring back to it, citing on it, citing it and building on it. And so she's very easy to identify as a logician. Okay, so some more logicians. How about this particular Vienna, member of the Vienna Circle? Yeah, so Ola Hahn is particularly interesting. People who know about her might primarily know about her as the wife of Otto Neurath. And in fact, a lot of kind of the people who were working in, so kind of between about like 1870 and 1920, I, you know, it's a nice 50 year period, it works good to kind of think about that as a, as an era or an area. Specifically kind of working with logic or foundations of mathematics or foundations of kind of geometry more broadly. A lot of the women working then were closely related, both kind of academically and meritably to other logicians. This isn't surprising. Logicians like talking to other logicians, we get along well with other logicians, you know, so this isn't too surprising. But what's unfortunate is that a lot of these women then end up only being known as wife of so-and-so. Olga Hahn's work, much of it is still only available in German, though a colleague of mine at Tubingen, Justin Vlatsitz, is working on translating some of her work into English so that it can be more accessible. One of the reasons I want to highlight her is she also worked with lads untilagism. So here's a nice case of not only of an earlier woman logician producing something that kind of influenced logic more broadly, but was something that was picked up by another woman. And so you can kind of see this, you know, passing on of development. And when there aren't that many women in a field, you don't often see that sort of kind of academic connection. So it's nice when you do. Okay, so you have another, well, Cambridge woman philosopher and logician. Consider this founder of Cambridge Wood of Analysis. And actually the first editor of Analysis, the journal? Yep. She sends Steving. Yeah, Steving is interesting because she's, again, people who are familiar with her are probably more familiar with her philosophy. So she was kind of steeped in logical positivism and it kind of related fields to that philosophy of science, these sorts of things. But she was actually one of the, one of the first people to write a logical textbook incorporating the new developments of Russell and Whitehead. So Principia Mathematica is not an accessible text. You can't, I mean, you shouldn't use it as a textbook for undergraduates or graduate students or anybody, but she was one of the people who kind of recognized that there's actually really crucially important things in there and took it and created something that could actually be used. So textbooks for the importance of the development of a field should not be underestimated because a lot of people, this is what they're going to be getting as their first introduction to something, not some big research volume, but some textbook that says, here's what this topic is. So even if she's kind of maybe more known for being a philosopher, we shouldn't say, oh, you know, it was just a textbook that she wrote. Textbooks are incredibly important. Actually, she, her textbook seems to bridge Aristotelian logic with the current Russell Whitehead logic as well. Yeah. So one thing that you see kind of in, you know, the 19th century and even kind of into probably about like the 1950s or so, the Aristotelian syllogistic was still considered a fundamental aspect of logic. And I don't, I don't really know why it's kind of fallen out of favor. You know, in at least in American philosophy departments, you often get logic courses that teach propositional and predicate logic. And then you have critical thinking courses. And that's where you stick the syllogism and Venn diagrams and fallacies and things like that. So it's, it's a weird kind of sociological question of why the syllogism lost its central place in the role of logic. But even, you know, even in the early part of the 20th century, if you were going to know logic, you had to know that. And with the new 20th century developments, things like Russell and Whitehead's logic. Okay, speaking of textbooks, here's another, actually, she's not working on a textbook, but she developed recursion theory. How about Rosa Peter? Yes. So, I mean, she's, she is somebody who is a delight to talk about because she basically founded a field. So prior to her work, there wasn't really something that could be identified as kind of recursion theory in modern day. Now, her inclusion here might be considered kind of controversial because you might want to say, well, is recursion theory really logic? Or is it, you know, computer science or mathematics or something else? And this is a point at which I think it's less helpful to try to make disciplinary boundaries to say this person is a mathematician. This person is a computer scientist. This person is a logician because in the intellectual and academic context that they were all working in, these weren't distinctions that were being made. Whereas, so, you know, I made this distinction with Lovelace saying, well, maybe she's an early computing scientist and not a logician. But that's because at that time, these, these developments were happening separated from each other. Whereas by the time that you get to, you know, the early 20th century, where the people who are doing logic are the people who are doing foundations of math are the people who are doing things like recursion theory. So I, I'm happy to call her a logician because notions of recursion are so fundamental to basic logical approaches. So even if you aren't doing mathematical logic, if you're not doing, you know, piano arithmetic or girdle and completeness theorems or anything, one of the first definitions that you get when you are studying propositional logic is the definition of a well-formed formula. And that definition is recursive. So if you don't have recursion, you can't even get started in logic. So yeah, I'll count her as one of us. Okay, here's the other person who wrote a textbook that introduced analytic philosophy and the modern logic, Alice Ambrose. So what's her contribution to logic? So she was very, she was also a student of Wittgenstein's and so is interesting because of the kind of, the ways in which Wittgensteinism could be again made more accessible. One thing that's interesting is how many of these women were writing textbooks, as opposed to say like research papers. So there's very much this sort of sense that I don't want to say it was like women's jobs to make things accessible or things like that, but it certainly is the case that a lot of these women would have had their access to being in academic circles via teaching. So this is kind of what gives them their their credibility to be a part of these kinds of academic contexts as if they were part of the educational side of things. So Ambrose is somebody that I don't know as much about as I would like to, but the kind of close connections between her studying with Wittgenstein and her expositions of his work and also she had connections with GE Moore. So she's kind of on the list of people I need to read more about because there's definitely something in there, the extent to which it will end up counting as logic. Again, depends on how you're going to define logic. And finally, of course, the woman who has her name in a formula, Ruth Barken Marcus. So you know that you've made it when you get a formula named after you. Barken Marcus, she's reached the pinnacle. The other reason I really like her is that she has some absolute wonderful smackdown responses to Kwan. And I think Kwan needs to be smacked down. I think that he introduced far more false issues into the study of philosophical modal logic than he ever solved any issues. So Barken Marcus is kind of the aspirational ideal of whatever you would like a kind of, if you're thinking of women in the history of logic, she's probably going to be one of the first people that you name. In fact, I with my introduction to logic students, the first assignment I give them every year is they need to find three logicians who lived before 1000, three who lived between 1000 and 2000, and then three who were alive after 2000. And when we have our small group discussions meeting, we collect all of the answers, we put together a great big timeline, and then we stand back and end up looking at like, where are all the Chinese logicians? Where are all of the African logicians? Where are all of the women? And kind of interrogating people's biases and blinkers. But if a woman is going to be mentioned, it's going to be Barken Marcus. Okay, so a lot of women philosophers and logicians are working right now. So where do you see academic work on logic heading in the next few years? And who are the leading women logicians paving the way to these developments? So there's, there are plenty. So there's the, there's a new initiative specifically for women in logic. So there's a Slack channel and a Facebook group and a Twitter page for women in logic. And this is very, very broad. So it includes people like me who are kind of on the history and philosophy side. There are, you know, kind of hardcore computer scientists, people working on, you know, machine learning and artificial intelligence and things like that. So nowadays, at least you look for women in logic and you'll find them all over the case. I, I don't really want to highlight any because there are so many and so many leading figures. I don't want to highlight out any one of them because it would give kind of the false sense that here is somebody who is kind of unique or special. While women in logic are still underrepresented, I mean, the, the percentages that you have for kind of women in logic are often lower than women in STEM and women in philosophy. So we kind of inherit the worst of both worlds. But just because the percentages are so bad doesn't mean that our absolute numbers are small. I mean, I, I can, oh, go on then. I will name names just to name a bunch of names so you can see how many there are. Renika Vabruga, Valeria De Piva, Sarah Negri, Nina Geer, sorry, I can't pronounce Polish, I apologize for missing her name. Audrey, Katarina Dutil-Nawaz, Graciana Ciola, I could just go on and on and on. So we're out there. We're not hard to find. Okay. So, but what's the new development coming from women logicians? Katarina Dutil-Nawaz is working on multi-based logic, a lot of stuff on the theories of obligation as well. You're working on a lot of stuff in philosophy and give a logic. And what else? What else is the current trend in logic? Again, it's, it's hard to single out any individual trend because there's so many of us doing so many things. So there are, you know, people working on multi-agent systems. So another name I could have mentioned is Sonya Smets at Amsterdam, who is very much in kind of dynamic epistemic logic, multi-agent logics. There are people working in foundations of AI. So basically one of the brilliant parts about logic in the 21st century is how diverse and prolific it is. So you can be doing kind of hardcore history or hardcore computer science, and it all falls under this umbrella of logic. And in any one of these areas, you will be able to find kind of women at the forefront. So whether you are interested in temporal logics for program verification or an understanding of the role of imagination in logical reasoning in the 14th century, you know, there's, there's going to be some woman working on that area. Okay, so on a personal, on a more personal level. So what's your advice for those who want to get into professional philosophy and logic in particular, especially for women? So yeah, I'm not going to give advice for philosophers because I'm not the right person to do that. I almost feel like I am ill-equipped to give advice to women in logic about being a woman in logic because I was very lucky and didn't really realize this until many years later how lucky I was with the support of the mentors that I had. So most of the classes that I took as an undergraduate or as a graduate student were round about 10 to 15 people. And it was usually like me and another girl and the rest were guys. And, you know, you recognized that this sort of, you know, that this was a very bad gender imbalance. But for me personally, it never really had any, any effect. I mean, I, I liked working with my colleagues. They were interested in the same things I was interested in. They were willing, they were interested in collaborating. I ended up marrying one of them. So, you know, it's not all bad. But I think that's kind of recognizing it. So what, what I would say to, you know, a young woman today who wants to study logic is to recognize that women in this field are underrepresented and that this is just something that they're going to come across. So if they are not happy in kind of all male situations, then this is something that they will probably get more of in, you know, if they were studying logic than if they were studying, I don't know, English literature. On the other hand, it's definitely getting better. So last year, I, one of my small groups for my intro logic class, I suddenly stopped looked around the room, there were eight students and me in the room, four of the students were women. And I paused and I said that in the 20 years that I've been doing academic philosophy, this is the second time that women have outnumbered the men in academic logical context. The other time was at a workshop on feminist philosophy and formal logic where all the invited speakers were women. So not a typical situation. But I had another class again this year where just looking around the room, who was all there, there was like six women and two guys. So it's getting better. And while I never felt the lack of like a female role model, I had plenty of good role models. So I didn't need one that had the same gender as me. I understand that for a lot of people that is important. And so one of the kind of two things that I would say is like, if this, if you want to do logic and this thing is important for you that you have a strong female mentor or strong female role model, well, there are plenty of people out there. So pick where you want to go to graduate school or even where you want to do your undergrad and look for places where there are women teaching logic and then kind of set yourself up for success. But the other thing is that this being in this field provides people with a chance to be that role model, even if they never expected to be in that sort of position. And this can start right away in an introduction to logic class. Find out what you're good at and then help other people to become good at that. So talk with your colleagues, discuss the homework assignments, go over the answers to the exams. And there's, it's not always going to be easy, but there are, it is definitely getting better. I will say that. Okay, but it's an academic career worth it. Would you say that your career is worth it? I mean, I would say yes. But I am somebody who got into grad school, completed my PhD without significant financial or mental burdens. I, you know, I have a job. It's a permanent job. So I am in the best possible situation. Of course, I'm going to say it was worth it because it all worked out for me. I am very hesitant to recommend academia to anybody right now. Because, well, many, many, many reasons, including the financial costs, the mental costs, the lack of job prospects, the fact that it's only going to get worse, the neoliberalization of academia, the increasing workloads. So you name it, it's probably getting worse. On the other hand, if this, if this is what you want to do, and you have the capacity and the support and what you would need to do it, it's, it really is the best job in the world, getting to do research and to think about things that I like and talk about people about things I find interesting and then get to teach them to students. I mean, could it get any better? The best of all possible worlds. Okay. Thanks again, Sarah, Dr. Logic for sharing your time with us. For you guys, join me again for another episode of Philosophy and What Matters where we discuss things that matter from a philosophical point of view. Cheers.