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- [00:00]
A
Hi there, it's Bill Gray from Hillsdale College. Before you skip ahead, can I ask you a question or two? If you could teach 50 million Americans one thing, what would it be? Would you teach our great American story that this nation is unique, founded on self government and individual liberty? Maybe you would teach the truth about free enterprise, how hard work and opportunity allow anyone to rise? Or would you teach the gospel and the Christian faith that helps us live good and meaningful lives? At Hillsdale College, we're doing exactly that. Teaching the best that's been thought and said. Through our free online courses, K12 programs, Imprimis, podcasts and more, we reach and teach millions every year with the principles of liberty that make America free. And with your help, we can reach even more. Your tax deductible gift today will help us teach millions more people to pursue truth and defend liberty. Just text the word give to 7 1844. You'll get a secure link to make your donation in seconds. That's give to 718 44. Thank you for standing with us. Now back to the show.
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B
Welcome to The Hillsdale College K12 classical education podcast, bringing you insight into classical education and its unique emphasis on human virtue and moral character, responsible citizenship, content, rich curricula and teacher led classrooms.
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C
Now your host, Scott Bertram. Thanks for listening. The Hillsdale College K12 Classical Education Podcast is part of the Hillsdale College Podcast Network. More episodes at podcast hillsdale.edu or wherever you get your audio. You also can find more information on topics and ideas discussed on this show at our website, k12 hillsdale.edu. we're joined by Paul Mittermeier. He's a teacher at Cincinnati Classical Academy Middle School, Latin Upper School, Logic and Rhetoric. Paul, thanks so much for joining us.
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B
It's great to be with you. Thanks so much for having me.
- [02:09]
C
Discussion today about formal logic. What is it? What is its value? Try to answer those questions today. When people hear the term formal, formal logic, Paul, it can sound intimidating. What exactly are we talking about? How would you explain it to people in plain language?
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B
It certainly is an intimidating element of the curriculum. Also, when you're talking to parents about what is offered in a classical school, you know what most distinguishes a classical curriculum from others? I think it is one of the real points of excitement to which they gravitate. But really, formal logic is. It's an art, one of the three arts of language, and it is the art of proper reasoning and argumentation in language. Language. So it's really, if you wanted to simplify it, it's the Art of argument. But there, there is a little bit more to it. Although it sounds like a very complex, very challenging discipline, it's actually the first of the arts of language that we as human beings begin to learn. Because where it starts is not with arguments, it starts with naming and defining things as what they are. So I teach logic now and just in sort of explaining this to students at the beginning of the course, that you can sort of use an example when you as a young child are just sort of coming to consciousness of the world, when you're just becoming aware of the world around you, experientially using your senses, knowledge is entering through your senses, you start to try and assign names to concepts. So an example that I use with my own students is, let's say that as a young child, you go out on a walk and you see a large brown four legged animal and your mother points to it and says dog. After this experience, immediately you must think a dog is a large brown four legged animal. Until you see a small yappy chihuahua that is white and your mother also says dog. At which point you have now started to make a distinction. Okay, size in this animal does not matter. It's something that's changeable. But maybe it is still a four legged animal and maybe it has to have brown on it somewhere and it makes noise. Until you see any other variety of dog, right, Other breeds, and they're also named dog. So in this whole process, what you're doing is you're learning to distinguish between what is essential to a thing and what is accidental to a thing. You're learning to figure out what is the actual essence of this thing, what is the definition of it, what are the qualities that can be changed or removed in the thing. And then after I've figured out what this thing is, what do I call it? What name do I give it? So that's really where logic begins, is with naming and with defining things. And then it gets more complex from there. The next thing you'd want to do is make a statement about the things that you've named and defined. And after you make statements about those things, you want to make arguments about them. And so this is where argument ultimately comes from, is defining terms all the way up through assessing arguments themselves on whether they're actually good.
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C
So how does formal logic differ from the kind of everyday reasoning that we all use in normal conversations?
- [05:11]
B
Yeah, it's an interesting question, and it might be a question of privation because unfortunately in a lot of our everyday conversations we misuse logic or there's an absence of logic. So in, I would say, the way in which it differs is that it actually gives structure to the way in which we're arguing, and it teaches us to do this with precision. In logic, if you're trying to assess whether an argument is actually good, there are a couple criteria according to which you do this. If an argument itself is actually true, in other words, what you're actually talking about or what you're actually discussing corresponds with reality, then we say that it's a true argument, but that's actually different from being a valid argument. A valid argument is when the conclusion that you've reached follows from the premises that you've outlined. So in other words, if A is true and B is true, must C be true based on A and B? So there's a difference between truth and validity. And then if an argument is both true and valid, it's a sound argument, which is the best kind. So I would say just in learning these formal rules, right, this is why we call it formal logic, because we're learning these formal rules of the argument. It helps to structure our arguing and ensures that it is actually done precisely. And.
- [06:29]
C
Well, logic plays a central role in classical education, especially in the middle school years. Why has logic traditionally been placed at that stage of a student's education?
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B
This is because middle schoolers tend to be very argumentative. And so the great fear of every parent in a classical school community is when they are already dealing with contention at home and they come in to learn about the classes their child will be taking that year. And you tell them, logic, the art of argument, instills dread in the heart of every parent until you inform them. No, what we're trying to do here is we're trying to put some guardrails on this instead of at this sort of contentious stage of a child's development, which is natural. Right. They want to understand the world around them. They're pushing on the limits of reality, not because they are just rotten or trying to cause trouble, but because they want to understand truth. They want to understand the world around them. And so helping them to do that in a responsible way with some formal rules so that they can structure their thought and structure their argument. I think that's why we place it at this stage in a child's development.
- [07:39]
C
What are some of the core skills that students do learn when they begin to study formal logic?
- [07:45]
B
Yeah, it's. I really take it in three stages. So what's. This is sort of interesting, but what I. What I always Characterize with my students is that arts themselves are always a form of making or creating. So when you're practicing an art, no matter what the art is, you're always making something or you're creating something. And this is different from a science which doesn't deal principally with making or creating, but with studying something and understanding something. And so arts in this sense, they're man made, they're created, right? You think about an art like oil painting. This is not something that was naturally occurring. This is an art that was created and developed over time. Human beings figured out what media must be used in oil painting, what is the medium that must be painted on, what are the media that are used to paint. And then over the course of history, they developed better techniques for doing this. Different styles, there were different movements to it. So really, in a certain sense, although it comes from a natural inclination, the art is man made. But this is not true of logic. And logic is sort of unique in this respect. Logic is not man made. Logic is just the activity of our intellects doing what it should do. So our minds or our intellects. Really what it does is threefold activity. First, the first act is called simple apprehension. And this is what I described just before. It's this act of apprehending reality by defining things and naming things. The second act is judgment, where we then predicate one thing of another, right? So we make a statement, statement about those things that we've named and defined. And then the third act is actually coming up with those arguments. This is logic in its full exercise when it's come to fruition. But I would say that it's in that early stage, the way a logic class starts, and the skills that students are actually learning is how to name things and define things with precision. In a logic class, students will always think at the outset that you're sort of patronizing them. One of the first questions I ask them in a logic classroom is define a pencil. And the reaction is always priceless. Students just sort of gape at you like, are you serious? Are you patronizing me by asking me what a pencil is? But you would be amazed once they try to do this, how few of them can actually define a pencil. They do a great job at describing it, they don't do a great job at defining it. So this is one of the first skills that they learn is how to identify a thing's essential qualities, how to define a thing's accidental qualities, and. And if you can differentiate, then you can define it, and then it goes from there. Right. So beyond that, making statements about these things and then finally weaving those statements into arguments and then analyzing whether those arguments are actually true, actually valid and sound. Those are just a few of the skills.
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C
Now, for parents who haven't studied logic themselves, what does a typical formal logic class actually look like?
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B
If I would characterize it, at the height of it, once you've got a lot of the skills under your belt and then you're sort of working in that third stage of logic, it will look very complex in a certain sense because there's sort of a, almost mathematical looking notation that is used in formal logic. What we do in our schools is study what they call the figure and the mood of the syllogism. So a syllogism is a three part argument. I'll give you an example and I'll kind of walk through it at all three stages. Let's say that we want to define three different objects. Again, at the very outset of logic, we might want to define what a man is, we might want to define what it means to be rational, and we might want to define who Socrates is. Now I'm going somewhere with this, right, that they seem like three sort of strange things to select. But if we select these three things to define, you know, we, we might spend some time actually defining them on the basis of essence and accident. What is man? Students will debate about this. Well, a man is a biped who has the ability to speak, which is actually pretty good. But then after you go through, maybe you arrive at a more complex definition like Aristotle's, man is a rational animal. Where this eventually goes is you can make statements about the things that you've defined. So instead of just defining man, you can then make a statement, man is rational. When you make this statement, what's implied is that you have to understand what a man is and what reason is. And then finally you can weave all of this together in an argument. So an example of a syllogism or a three part argument using these terms would be all men are mortal. Socrates is a man, therefore Socrates is mortal. This is sort of the classic example that's used in a logic classroom to introduce this concept. And so what would a class actually look like? It would be taking arguments, arguments like this, and figuring out, number one, is this argument valid. So if we assume the first premise to be true, if we assume the second one to be true, must the third one be true? And really, no matter what we plug in for those three terms, there are rules to these arguments that determine whether they must be valid or not. We would also look at the arguments to see if they're actually true. Like, aside from the argument, does this correspond with reality? Is this actually true? And then we would start looking at the argument and asking, okay, maybe we've determined that this is a valid argument and a true argument, but is there a better way of saying it? Is there a more simple, more clear or straightforward way of saying it? So in that way, we're not just looking at arguments to see if they're true or not. We're comparing different arguments that are arguing the same thing in order to figure out how they can be articulated in the clearest and the most beautiful way.
- [13:33]
C
What changes do teachers usually see inside of students once they begin studying logic?
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B
It's a great question. I think that it will sound sort of cryptic, but logic is an art that once you see it, you cannot unsee it. Any student who has taken logic, anyone who has gone through a course like this, will know this to be true. It's almost an indescribable phenomenon that once you have taken a logic class and you've really invested in, just transforms the way that you think about the world. You, you are always sort of in, you know, listening to arguments, whether you're reading something in a newspaper or listening to something on the news, or whether you're even pulling an argument that's sort of hidden in out of a text of literature or something like that. You always sort of have this innate desire to analyze it and to figure out is this true, is this valid. So in a certain sense, it makes you more argumentative. It gives you sort of this heightened keen awareness of arguments and of where they're being used, but it also, I think it makes you not just argumentative in the sake that in the sense that you'd like to be contentious, it makes you argumentative in the sense that you really would like to know the truth. So I would say it makes you argumentative, but it also really cultivates in the student this desire to know and this desire to have the truth at all costs.
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C
How does the study of logic help students read texts more carefully and make stronger arguments?
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B
Yeah, it helps, I think, because after you've studied these formal, logical rules and after you've looked at all of these different types of syllogism and types of argument and you've given names to them, then immediately, as I said, it's as if when they're looking at a text of literature or they're reading about something in history, they're looking at it through this lens of logic. And so they. They want to find these arguments that are hidden in texts or embedded, and they want to pull them out. And so we also practice doing that in a logic class. And this also carries over into other courses like rhetoric, because, of course, in. In speeches and orations, you can find a lot of these sorts of arguments, but what they'll want to do is find language or verbiage that almost concludes something, pull that conclusion out, and then work backwards to find out what the premises were so that they can actually map that out and then analyze it according to the rules of formal logic. So this is really a tangible, measurable way of assessing the argument of somebody, whether in print or in writing or spoken verbally. You can actually sort of pull the argument out, isolate it, and use these rules of formal logic to determine, well, maybe this person made an argument that was true, but it wasn't actually valid. Maybe this speaker in his speech offered an argument that was valid, but it's not actually true. So to look at it with that, again, I think it just helps us to better discern the truth in a
- [16:30]
C
world full of information and claims and arguments. Can training and logic help students navigate what they hear in the media and in public debate?
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B
Absolutely. I would say that in a classical school, you know, we often encourage students to stay away from the minutiae of contemporary politics and the contemporary discourse. You know, unfortunately, a lot of it is just sort of a bad model or a bad exemplar of what it is that we would like them to know. Too often, contemporary discourse embodies the absence of logic rather than the formal rules of logic itself. And so it's, you know, for better or for worse, however, this is where we find ourselves. This is the situation in which we live. So for me, as an educator, you know, I sort of view my job as helping students learn these formal rules. I also am aware that teachers in my own school and throughout our network are bringing students into contact with great works of literature. They're bringing them into contact with great speeches and orations that have made through history. So if we can look at these great speeches in a rhetoric class, for example, we might read the Gettysburg Address. We might read the speech of Empress Theodora, the royal purple is the noblest shroud, or the speech of Pope Urban II at the outset of the first Crusade, right? These are great speeches that altered the course of history. So if we can look at these speeches, use those as models and exemplars, find examples of great logic in Those speeches, then we're all the more prepared to go out into our own world in which we find ourselves situated today, and sort of not only use these formal, logical rules, but also weigh the contemporary examples against these great examples from the tradition, these great examples from antiquity. This will give us a clear standard by which to judge. You know, is. Is what we're hearing today in the media, is this actually good? Are these arguments good? Is this speech that this politician gave actually a good speech? So, again, knowing the formal rules, but also having these great exemplars that have stood the test of time will help us better assess the things that we find in our own time.
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C
You touch on it a bit there, but sometimes people assume logic is only useful for philosophy or only useful for public debate. Where else?
- [18:52]
B
Absolutely. I mean, it's. It shows up certainly in politics. I mean, politics is probably the place in which it's most pervasive today because whether we want to participate in it or not, we find ourselves immersed in it. And maybe we should participate in it and try to do what is right and what is good, seeking the truth and using the laws of logic. But I would say, I mean, it carries over in other areas as well. When you're looking at an argument in logic, you're not just looking at it for the sake of argument itself. It also attunes you to just the very notion of order and perfection. Right. When you look at an argument and you look at its form, right? How the terms in the argument are laid out and how the layout of those terms results in the argument being true or valid, you actually see a real beauty. There's a structural beauty to it. And I would almost use the word there's a geometry to it. So this. This brings me to sort of, you know, the direct answ to your question. In logic, you find geometry, and in geometry, you find logic. As students are learning mathematical rules and principles, they see a logic, right? When they're learning geometry and they're studying, for example, Euclid and his propositions, this is a form of logic. It's just carried over into the realm of mathematics. And you can see where that is then extrapolated, right? In order to build great buildings and have great architecture in our cities, what's used geometry. And so this, you know, these great Euclidean proofs that have been derived through laws of formal logic are then translated into physical architectural constructions. And I would say to all of that, right? In looking at a good or a beautiful building, there's a music to it. It's. It's sort of musical because it's a harmony of a proportion of beautiful features. So that would be something I would suggest is that the more familiar you become with the liberal arts, the more you start to realize that they're all sort of interchangeable. All of the liberal arts have a beauty about them. They have a harmony about them, an order about them. They're sort of like a symphony. They're all very musical and they all give us insight into beauty.
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C
Final question for Paul Mittermeier as we talk about formal logic. So when students graduate from a classical school, having studied logic or what lasting habits of mind do you hope that
- [21:10]
B
they take with them above and beyond all else, simply that they, they really have a precise and a refined desire to pursue and to figure out the truth? Right. We don't, we don't want them to harp so much using formal logic that they are just browbeating people with it because we understand that in entrusting them with this art, we are sort of giving them a powerful weapon. They're able to pull arguments apart, they're able to tell people that they are either what they're saying is true or valid or neither. Right. So we don't want them to use this irresponsibly, we don't want them to do this in sort of a brow beating way, but we do want that real desire for the truth to still remain for the rest of their lives. And so I would say from logic itself, having that desire for the truth, that precision, but then also sort of curbing and checking that with sort of a curiosity and a charity, I think is really helpful because again, we also want to assume that in the world of academics and in learning, everybody desires the truth. So when somebody says something that is not true or not valid, they ought to be corrected so that they can get closer to the truth. But we also ought to give those corrections with charity, assuming the best of everyone and doing it with sort of a collegial spirit. This is the spirit that you should really have in an institution of learning, understanding that it's a partnership, that we're all pursuing the truth together. So let's check and correct each other when we're wrong, but let's also do it charitably and lovingly.
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C
Paul Mittermeier is a teacher at Cincinnati Classical Academy, teaching Latin to middle school and logic and rhetoric to upper school students. Paul, thanks so much for joining us here on the Hillsdale College K12 Classical Education Podcast.
- [23:02]
B
Really, my pleasure to join you. Thank you so much for having me.
- [23:05]
C
I'm Scott Bertram. We invite you to like us on Facebook. Search for Hillsdale College K12 classical education. You also can follow us on Instagram hillsdalek12. That's hillsdalek12 on Instagram. Thank you for listening to The Hillsdale College K12 classical education podcast, part of the Hillsdale College Podcast Network. More at Podcast Hillsdale Edu or wherever you get your audio.