009 - The ARGUMENT MATRIX (or, How to Know What You're Talking About)

In this episode I introduce an important concept, what I call the Argument Matrix, and two related concepts associated with the Argument Matrix, which I call “argumentative depth” and “argumentative breadth”.

These concepts are central to my views on the role of background knowledge in critical thinking.

Or to put it more plainly, they’re central to my understanding of what it means to really know what you’re talking about.

In This Episode:

  • How do we know that we know what we're talking about?
  • Critical thinking education's Dirty Little Secret (critical thinking can't be taught)
  • The definition of an argument
  • Basic principles of argument analysis
  • The challenge of evaluating the truth of premises
  • The definition of an Argument Matrix
  • Objections and replies
  • Argumentative depth vs argumentative breadth
  • Example: the fossil record and common ancestry
  • Example: the ethics of abortion
  • the Argument Matrix and the goals of critical thinking
  • Expertise is relative
  • pro tip: assume we know less than we think
  • Two kinds of Argument Matrix: the Map vs the Terrain


"Logic is great, logic is important ... but all the logic in the world can’t make up for ignorance. "The Argument Matrix gives a model for a certain kind of background knowledge that is very important for critical thinking. It’s a model of the space of intellectual debate on a topic. The more of this space you can access, the greater your background knowledge. "

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This is the Argument Ninja podcast, episode 009.

Hi everyone, this is the Argument Ninja podcast, where we talk about the art, science and ethics of rational persuasion and what it means to be a true Argument Ninja.

I’m your host, Kevin deLaplante, and in this episode we’re going to turn our discussion back toward the argument part of “Argument Ninja”.

I’ve talked a lot about the need to take seriously the psychological and social dimensions of persuasion and argumentation. And in my martial arts analogies, like the one I developed last episode, I’ve argued that at the center of the Argument Ninja approach to rational persuasion must be a set of core principles that aren’t primarily about winning arguments, but rather are about cultivating the intellectual virtues that direct our innate capacity for rational thought toward the goals of critical thinking.

But so far I haven’t said much about these intellectual virtues yet, or the role that argumentation plays in relation to the goals of critical thinking.

So that’s what I’m going to talk about this episode.

And in this episode I’m going to introduce an important concept, what I call the Argument Matrix, and two related concepts associated with the Argument Matrix, which I call “argumentative depth” and “argumentative breadth”.

These concepts are central to my views on the role of background knowledge in critical thinking; or, to put it more plainly, they’re central to my understanding of what it means to really know what you’re talking about.

I can say with confidence that if you know what you’re talking about, the quality of your reasoning is going to be higher than if you don’t know what you’re talking about.

The question is, how do we get to the point where we actually know what we’re we’re talking about it?

And hiding inside this question is a deeper and maybe more troubling question:

How do we know that we know what we’re talking about? How do we know that our knowledge is sufficiently broad and deep that we can be confident that our judgment is reliable, that it’s informed by all the relevant facts? How we do know that we’re not still reasoning from a position of ignorance?

What I want to do in this episode is introduce the Argument Matrix concept as a tool for addressing questions like this.

Okay. One of the dirty secrets of critical thinking education is that, in spite of the thousands of critical thinking courses being taught in colleges and universities around the world, critical thinking can’t be taught in a single class.

Let me explain.

I can teach basic logic in a classroom. I can teach logical fallacies and cognitive biases in a classroom. And these are important components of critical thinking.

But in a critical thinking class, I can’t teach students the necessary background knowledge that is required to make critically informed judgments about all the topics they might care about.

I can if my course is dedicated to a specific topic, and that’s the topic they want to think critically about. If I’m teaching the evolution/creationism debate, sure I can teach them the necessary background, if I’ve got a whole term to dedicate to it.

But in a general critical thinking class, that’s not possible. There are some general level skills and knowledge you can teach, but in the real world, critical thinking is always critical thinking about some particular subject or domain. You need to know something about the subject in order think critically about it.Otherwise you’re going to make all kinds of mistakes, that will never go away until you’ve acquired the right sort of background knowledge.

Logic is great, logic is important, but I’ve said it before — all the logic in the world can’t make up for ignorance.

So what can I do in the classroom, to help students with this problem?

Well, I can help them understand why having the right background knowledge is important, and what kinds of background knowledge are particularly important if our goal is to become good critical thinkers about a particular subject.

And I can help them understand how easy it is for us to delude ourselves into thinking we know enough when we really don’t.

So let me tell you I approach this problem.

The first important point is that any solution needs to focus on arguments. Facts are important, but it’s only in the context of arguments that facts become relevant to the kind of understanding that we’re going for.

So let’s back up and review the definition of an argument.

As we use this term in logic and argumentation, an “argument” is a set of statements that are being offered as reasons to accept or believe some other statement, which we call the “conclusion”. The statements that are being offered as reasons, we call the “premises”.

So, schematically, an argument is a set of premises and a conclusion, with the assumption that we should interpret the premises as offering reasons for accepting the conclusion.

Now, in any real argument there’s some context that frames how the argument is going to be interpreted.Typically there’s some issue over which there’s disagreement, and we’re to imagine that the premises are being offered to some audience that isn’t already convinced of the conclusion.

The issue could be, whether smoking should be banned in public spaces, or whether the United States should build a wall on the border with Mexico to help deal with illegal immigration, or whether sugar is better or worse for yourhealth than saturated fats.

The conclusion of the argument usually expresses a stand on the issue, a contention, like “Smoking should not be banned in public spaces”, or “Sugar is worse for your health than saturated fats”.

The persuasive goal of the argument is to get the audience to accept the conclusion, or to otherwise become more favorably disposed toward the conclusion, on the basis of the reasons given in the argument.

Now, in argument analysis we have to distinguish two very different features of arguments.

The first is about the truth-status of the individual premises of the argument. Are the premises true or not? Does our audience have good reason to think they’re true?

The second is about the logical relationship between the premises and the conclusion. If the premises were all true, would they give us good reason to accept the conclusion? In other words, does the conclusion “follow from” the premises?

It turns to that this second question is much easier to answer than the first question.

Here’s a very simple example. Consider this argument:

1. All swans are white.

2. My friend Julie bought a swan.

Therefore, Julie’s swan is white.

Now, let’s ask the second question. Does the conclusion follow from the premises? In other words, in a world where all swans are in fact white, and Julie bought a swan, do we have good reason to think that Julie’s swan is white as well?

And the answer, of course, is “yes”. It follows as a matter of brute logic. If all swans are white, and Julie bought a swan, then her swan has to be white. To deny this implies a contradiction somewhere. If the conclusion is false, then one of the premises must be false. Either not all swans are white, or Julie didn’t buy a swan. There’s no escaping this.

This is the kind of basic logical intuition that we rely on in our audience when we deploy arguments. In this case, we’re relying on our audience’s ability to recognize a logical contradiction when it’s explicitly presented to them, and we rely on their intuition that if a set of statements entails a contradiction, then they can’t all be true — at least one of them must be false.

And for the most part, people are pretty good at recognizing simple logical relationships. And most people are not comfortable indulging in contradictory beliefs when the contradiction is presented to them in an obvious way that they can’t escape. This is why certain kinds of logical moves, like showing that a set of beliefs entails a contradiction, can be persuasive for real audiences.

Now, when I teach students logic, I’m teaching them to recognize the logical properties of different patterns of reasoning. Some patterns are like this one, where the conclusion follows with necessity from the premises. In logic we call these “valid” arguments. In some patterns of reasoning, the conclusion only follows with high probability from the premises; we call these “strong” arguments. And in some patterns, the conclusion doesn’t follow either validly or strongly, and we call these “weak” arguments. This is the category of arguments where the conclusion does NOT follow from the premises.

And all of this, students can learn in a classroom setting, or out of a textbook. It’s like learning the rules of chess. You learn which moves are legal and which are illegal, and then you learn how to assemble sequences of legal moves that push the game in the direction you want it to go. As long as your opponent is playing by the same rules, you can have a productive match.

But now let’s go back to that original argument. All swans are white, my friend Julie bought a swan, therefore Julie’s swan is white.

The logic is valid, but we’re not done with the analysis. All we’ve said is that IF all the premises were true, the conclusion would follow. But now we have to ask — ARE the premises all true?

And there’s one premise in particular that we need to look at: is it actually the case that all swans are white?

Now think about this. What am I asking you to do? This question has nothing to do with the logic of the argument. This question has to do with the relationship between what the premise is asserting about the world, and the facts of the matter in the world. Does it accurately describe the facts, or not?

And how do we answer questions like this? I’ll tell you how. We consult our experience and our background knowledge about the subject.

What do I know about swans? Are they all white? Do I know they’re all white? Have I ever seen a swan that wasn’t white? How confident am I that all swans are white? How confident should I be?

These are questions about the facts of the matter, whether our beliefs accurately correspond to these facts, and whether our degree of confidence in a belief is properly calibrated to the degree of uncertainty that’s appropriate to that belief.

In general, these are very hard questions to answer. Much harder than the purely logical questions.

Now, if you survey people about their beliefs about swans, some will be very confident that all swans are white, and some will be unsure, and some will be very confident that not all swans are white.

It turns out that not all swans are white. In the northern hemisphere, swans are typically all white, but in the southern hemisphere there are mixed black and white swans, and in Australia there’s a species of all-black swan appropriately called the Australian black swan.

If you grew up in the north it’s easy to go your whole life never encountering or learning about non-white swans, so it would be understandable to assume that all swans are white. But you would be wrong about this.

And this highlights the problem of teaching this component of critical thinking. Assessing the truth or falsity of premises is a fundamental part of argument analysis. But how well you can do this depends on the extent and the quality of your background knowledge.

And in a critical thinking class you can’t teach all the background knowledge a person might need to think critically about all the subjects that interest them. A single teacher doesn’t have the time or the expertise to do that.

This is the dirty secret of critical thinking education. There’s a real sense in which critical thinking can’t be taught.

Now, in spite of these limitations, there is a lot that can be taught in the classroom that can be very helpful for students who are looking for the most efficient way of acquiring the background knowledge they need.

The approach that I favor, as I said earlier, places arguments at the center of our understanding.

What I’m going to do now is introduce a concept that I call an Argument Matrix.

The answer that I want to propose to our problem is this: what it means to know what you’re talking about, on a given subject, is that you’re able to navigate the structure of an Argument Matrix that is rooted in the subject in question.

But let’s get the basic idea on the table first.

When you’re asked to justify or defend one of the premises in an argument, what you’re asking for is another argument, with that premise as the conclusion. It’s an argument that offers good reasons to accept that premise. It’s an answer to the question, “but why should I believe that?”.

So, there’s the level 1 argument, the main argument, with a certain set of premises.

And then you can imagine a series of level 2 arguments, radiating outward from the level 1 argument, that are designed to support the premises and assumptions of the level 1 argument.

But then we can ask the same questions about the premises of the level 2 arguments. Why should we believe them?And we can imagine a series of level 3 arguments, radiating outward from each of the level 2 arguments. And so on.

This hierarchical ordering of arguments is the basic structure of what I’m calling an Argument Matrix, that is rooted in the conclusion of the level 1 argument.

The conclusion itself is level 0. The argument for the conclusion is level 1. The arguments that support the premises of the level 1 argument are level 2. The arguments that support the premises of the level 2 arguments are level 3, and so on.

Now, in practice, when you’re engaged in an argument and you’re trying to persuade an audience to accept your conclusion, there are always natural objections that your audience might raise and that you need consider, and you need to think about how you would reply to those objections.

This is how good argumentative essays are organized. You’ve got a main argument, and then you need to raise the strongest natural objections to your argument, and you need to offer some kind of reply to those objections. You’re building into your argument an imaginary dialogue with someone who is skeptical of your conclusion, but open to reason. You’re anticipating their objections and how you would defend your argument against those objections.

So, in our Argument Matrix, in addition to the main arguments, we need to add the natural objections to a given premise or a given line of reasoning, and the best replies to those objections.

The whole thing will still have a roughly hierarchical structure, but it’ll be a more complicated structure, a messier structure, than the strict hierarchy that I was describing originally, because objections and replies are themselves separate arguments, and they can cross-cut and be multiply-connected in various ways.

But you get the idea. The basic elements of the matrix are propositions or statements, collected into sets and related to other statements by relations of logical entailment, either positive or negative. Positive means it gives reason to raise one’s confidence in the entailed statement, negative means it gives reason to lower one’s confidence.

You could call this an Argument Web if you wanted, but in my head I call it a matrix, so I’m sticking with that.

Now, some of you who are familiar with the technique of argument mapping might say that all I’ve described is an argument map, and there are formal tools for constructing such maps, like the program Rationale (which is a very good program by the way).

So, am I talking about argument maps? Yes and no. An argument map is one way of formally representing the kind of structure that I’m talking about.

But argument maps have to follow certain rules for how the arguments are represented, and I don’t believe that everything relevant to argumentation can be captured by a formal tool like this.

Let me finish my introduction to the Argument Matrix, and maybe then it’ll be more obvious how I’m using this concept.

There are two features of an Argument Matrix that I want to talk about now. I call them argumentative depth and argumentative breadth, and we can use them to describe different types of background knowledge and how they relate to the fundamental goals of critical thinking.

What I call argumentative depth is the ability to answer questions of the form “but why should I believe that?”, at increasingly deeper levels.

So for example, if we’re talking about Darwinian evolutionary theory, I might claim that the ordering of different types of fossils in geological rock strata — where fish appear first, then amphibians, then reptiles, and then mammals —counts as evidence for evolution from a common ancestor. If I really understand this claim, then I should be able to fill in the argument for this conclusion.

In response to this argument, you might ask, “what reason do we have to think that the rocks that are lower in the geological strata are older than rocks that are higher in the geological strata?”. This was a presupposition of my argument. Now I’m being asked to justify this presupposition. That’s pushing me to a second level of argumentative depth.

Now, let’s say that I can answer this question, and my answer appeals to radiometric dating methods for estimating the ages of rocks. Now, if you ask me, how do I know that those dating methods are reliable, that would push me to a third level of argumentative depth, and so on.

All other things being equal, the farther you can go in justifying the premises and background assumptions of your arguments, following the chain of justification backwards, the better your understanding of the arguments in question.

That’s argumentative depth.

In our Argument Matrix, argumentative depth is easily represented by identifying the central claim and then moving outward, starting with the level 1 argument and then moving out to the level 2 arguments that support (or challenge ) the level 1 argument, and so on. How far you can go is a measure of argumentative depth.

Argumentative breadth is different. Argumentative breadth is about understanding the range of relevant arguments that bear on a subject.

For example, it’s common for people to think that the fossil record is the primary source of evidence for the hypothesis of common ancestry, the belief that all species of organism on earth are evolutionarily descended from a single ancestral species, a common ancestor.

But it turns out this is false. There are many other sources of evidence that are much more compelling than the fossil record. Now, if you didn’t know this, then your understanding of the arguments for common ancestry is too narrow. For one reason or another you’re failing to consider important arguments that are directly relevant to the subject.

Let me develop another example that illustrates all of these concepts. Let’s talk about abortion.

In debates about the ethics of abortion, the issue often focuses on the moral standing of the unborn fetus. Does the unborn fetus have a right to life? If so, does it supersede the rights of the mother to make choices about her body, or is it subordinate to those rights?

So you can imagine a root claim: the unborn fetus does or does not have a moral right to life. And then imagine different lines of argument that could be offered to support or challenge this claim. These different lines of argument could be seen as branches radiating outward from the central claim, and then splitting into smaller branches as you start to consider objections and replies at different levels of depth.

Now, in the abortion debate there’s a line of argumentation that is explicitly religious or theological.If you believe that human beings are endowed by God with a divine soul at some point between conception and birth, and that the possession of this divine soul is what grounds the special moral status of human beings — what makes it morally wrong to kill a human being — then the issue becomes, what reasons do we have to think this is true, and when in the developmental process does the fetus acquire a divine soul? The moral issue is going to turn on the answers to questions like this.

So you can imagine arguments over these questions, and there is in fact a long history of theological argumentation on these very questions.

One can imagine becoming something of an expert in this line of argumentation — the intellectual history of debate over the moral status of the unborn fetus, within different theological traditions.

When the subject comes up and is framed in this way, the person who is familiar with the line of reasoning can be said to know what they’re talking about.

But notice that expertise on this topic is confined to this particular branch of the Argument Matrix.

There are other lines of reasoning on the ethics of abortion that are non-religious. One such line focuses on the concept of personhood, and whether the fetus can be said to be a person, because on this view, the concept of moral rights, like a right to life, is attached to the concept of a person. So the issue becomes, what characteristics does a thing have to exhibit to qualify as a person, and does the fetus have those characteristics?

These questions define a whole other branch of arguments that radiate outward from the central claim, a different branch of the Argument Matrix from the religious arguments branch.

Now, let’s say you become familiar with the structure of this branch of the Matrix. You learn the standard arguments and the standard objections and replies, and you can move down a couple of levels along a particular branch.

You can say, with respect to the abortion issue, when framed as a question about the personhood status of the unborn fetus, that you know what you’re talking about.

But notice that this person may not know what they’re talking about when it comes to the religious arguments. And vice versa. An expert on the religious arguments may not have much exposure at all to secular debates over the personhood status of the fetus.

In both of these cases, the background knowledge of the expert may be deep, but not necessarily broad. You know your way around your local branch and its various sub-branches, but you haven’t spent much time investigating that other branch over there.

Now, if someone becomes familiar with both branches, the secular arguments focusing on whether the fetus counts as a person, and the religious arguments focusing on whether the fetus possesses a divine soul, then their understanding is both deep and broad — broader than each of the other’s understanding, at least.

So, argumentative depth is about how far along a chain of reasoning you can go — how far from the center you can travel along a particular branch.

Argumentative breadth is about how many different branches you’re familiar with, how wide your field of vision is, how many different kinds of considerations you’re able to recognize and reason about.

And you can play around with different combinations. My knowledge might be deep in some areas but more shallow in others, and broader in some areas and more narrow in others.

And here’s another possibility.

We’ve got our two experts on each of the individual branches. And we’ve got our third expert who has mastered both. Each of them can legitimately claim to know something, and the third expert definitely knows more than the first two.

Now, assume that each of these experts is only aware of their local branches of the Argument Matrix. It’s a bit unrealistic with these particular topics, in this day and age, but for the sake of the point let’s imagine it’s true.

Religious Arguments Guy thinks that his branch of the Argument Matrix is all there is, there’s nothing more that we need to think about, when considering the ethics of abortion.

And Secular Personhood Expert thinks that her branch of the matrix is all there is.

And Double Branch Guy sees both branches, but doesn’t see anything else beyond that.

From the perspective of Double Branch Guy, the other two experts are ignorant of the true size and structure of the Argument Matrix. They know their local branch, but their reasoning, from his standpoint, is always going to be limited and incomplete.

But this observation should raise a question in the mind of Double Branch Guy.

If these two experts can be so mistaken in their beliefs about the structure of the Argument Matrix, how does he know that he’s not in a similar position?

How can he be sure that he’s not sitting in a small corner of a much larger Matrix — that there aren’t many other branches that he’s not even aware of — and from this perspective, his knowledge of the abortion issue is narrow and incomplete?

What I’m describing is a very real situation for many people who are raised to have certain beliefs and to think about issues in a certain way, and are never exposed to other ways of thinking that in fact may be quite common in certain segments of the public, or among experts.

This is certainly the case with the abortion issue. I don’t know how many times I’ve taught the abortion issue in an ethics class and encountered smart students who are very confident in their views and in their sense of what questions are important to consider.These students are surprised and sometimes dismayed to learn that there are other ways of framing the ethical issue that are taken very seriously by many people.

For example, there’s a whole branch of argumentation that focuses on the rights of the state to intervene in the rights of individuals, in the service of the common good.

In this case, the question is about the state’s interest in regulating practices that involve the killing of human beings, and whether those practices promote or undermine social norms about the value of human life, all human life.

I won’t get into the details here, but these arguments tend to be non-religious and they don’t engage the debate over personhood. It’s a different branch of the Argument Matrix.

And there’s another whole category of explicitly feminist arguments that focus on the relationship between the legality of abortion, the history of patriarchal oppression, the role of state control of women’s bodies and reproduction in enabling that oppression, and the concept of group or class rights — rights that women may be entitled to claim as members of an oppressed group, that they would not be entitled to claim if they were not so oppressed.

For some feminists, abortion rights fall within this category, and the arguments for allowing abortion and providing state funding for abortion services have nothing to with religion, nothing to do with personhood, and nothing to do with state’s interests per se. They have to do with the moral status of women’s interests, as a class.

So, arguments that relate to this line of reasoning define a whole other branch of the Argument Matrix.

Now, in the classroom it’s not surprising that students aren’t familiar with all of this, because almost no one is.

But it’s easy to find real life experts in some of the branches of the abortion debate, like constitutional scholars on abortion rights law, whose understanding of the arguments in the other branches is very shallow or non-existent.

I suppose this is just a byproduct of specialization, but there’s a lesson in humility to be learned here, for all of us.

Now that we’ve got this concept of an Argument Matrix on the table, let me say a few things about the role that I think this concept can play in our critical thinking practices.

1. The Goals of Critical Thinking

The first point is that this concept helps to show why argumentation is central to the goals of critical thinking.

Critical thinking has two main goals. The first is to improve the quality of our beliefs and decisions. The second is to be able to claim ownership and responsibility for our beliefs and decisions — to be able to say that these are my beliefs, my choices, that I can thinking independently and critically about this topic for myself, that I’m not just parroting the opinions of parents or peers or the media.

If this is our goal, then just knowing the facts isn’t enough. Having true beliefs isn’t enough. We also want some understanding of why they’re true; we want to be able to give an account of why it’s reasonable to think they’re true.

This ability, to give an account of our beliefs, an explanation for our beliefs, a defense of our beliefs — it all comes down to argumentation in one form or another.

The Argument Matrix provides a model for what this ability looks like, in practice. It’s about being able to navigate the various branches of the Argument Matrix that are relevant to a particular subject or topic.

It’s clear to me that if you’re in command of the best arguments in favor of a position on a particular topic, and those arguments exhibit both depth and breadth, then your judgments about that topic are going to be better than if you aren’t familiar with these arguments, and you’re in a better position to claim ownership and responsibility for those judgments.

2. Expertise is Relative

The second point is about the quality of our background knowledge and the nature of expertise.

The Argument Matrix gives a model for a certain kind of background knowledge that is very important for critical thinking. It’s a model of the space of intellectual debate on a topic. The more of this space you can access, the greater your background knowledge.

But the Argument Matrix model, by itself, doesn’t tell us how large this space is, or how much of that space we can access. It allows us to make a number of concrete judgments about how deep or broad one’s understanding is, relative to the branches of the matrix that we’re familiar with.

Like with the abortion example, we can say that Double Branch Guy is better informed than Religious Arguments Guy or Secular Personhood expert, because he has access to both branches of the matrix. But Double Branch Guy was unaware of the existence of several other branches of the Argument Matrix. So relative to the perspective that includes all four the branches that we talked about, he’s not nearly as informed as he could be.

The upshot is that we’re justified in making comparative judgments about the quality of our background knowledge, and consequently the level of our expertise. Expertise, in this sense, is always relative.

But we should be much more cautious about making categorical judgments about how much we know, or how much there is to know, about a subject.

That would imply that we have access to the maximal Matrix, as it were, with respect to that topic. We’ve got access to the whole history of intellectual debate on a topic. But for any substantial topic, we don’t have this. In general, we only have access to some portion of the Matrix.

If you dedicate your life to a topic, more and more of the Matrix opens up to you, and your knowledge becomes deeper and broader over time. But there are limits to how much any single person can learn and retain. And we should expect the Matrix to continue to grow and evolve over time as people come up with new arguments.

3. Useful Defaults Assumptions

The third point that I think is useful has to do with useful default assumptions about our own standing in relation to the whole Matrix.

Our general human tendency is to overestimate how much we know about a topic, and to be overconfident in the rightness of our judgments. There are several distinct types of cognitive biases that drive us to these conclusions. These biases make us less likely to seek out new perspectives or to explore an issue more deeply.

Another way to think of this is that we’re probably accessing a much smaller portion of the Argument Matrix than we think we are — it’s very likely that there are branches of the matrix that we aren’t even aware of.

And within the branches that we do have access to, our understanding is often much more shallow than we think it is. We can’t move outward along a branch as far as we think we can.

Let me give a couple of examples.

I ask you, is stealing wrong? You say yes. I ask why. You say that it’s on one of the Ten Commandments - thou shalt not steal. That’s a level 1 answer — it’s wrong because God says it’s wrong. Now I ask you, why should I believe that the Ten Commandments are a reliable guide to right and wrong? You say, because God wrote the Bible, and what God says is true. That’s a level 2 answer. And now I ask, why should I believe that God wrote the Bible, and even if he did, why should I believe that everything in it is true? That’s a level 3 question, and that’s a much harder question for most people to answer. You’re entering into the world of Christian apologetics, which you can spend years studying, but which most people don’t study.

But the limits of our knowledge are even more obvious if I ask you about objections and replies. Because remember, these are supposed to be part of the Argument Matrix too. So if you say, it’s wrong because the Bible says it’s wrong, and the Bible is the Word of God, I might ask you, what’s the best argument against the view that the Bible is the Word of God, that the Bible is divinely inspired?

There, I’m testing how broad your understanding is. And this isn’t a trick question. If someone is really confident in their understanding, they should be familiar with the best and most common objections, and have some idea of how they would respond to those objections.

Now, it’s just a fact that most people are not well-versed in the best arguments against their cherished views. Confirmation bias draws our attention to arguments that reinforce our beliefs, and we tend to ignore or diminish arguments that run counter to our beliefs.

This is bad enough, but it’s made worse by the fact that we tend to be very confident that we do understand the opposing side. If I ask you what the opposing side believes, people are often very confident that they know what it is. But more often what they’ll give you is a straw man version of the opposition’s position, not an accurate reconstruction of their actual reasoning.

So, from a critical thinking perspective, it’s just wise to assume that our knowledge is narrower, and shallower, than we intuitively feel it is. It’s wise to assume that the true Argument Matrix is bigger and more complex than the one have in our heads, and that it will take time and effort to reveal these unexplored branches.

4. The Map and the Terrain

The fourth point I want make follows directly from this this distinction between what a person knows and how much there is to know. This is important.

This is like the difference between a map of the terrain, and the terrain itself.

So yes, some Matrix explorers have mapped out more of the terrain than others. But the terrain itself is going to be much larger. Why? Because it’s a product of many minds.

I’ve been using this term, the Matrix, to refer to two very different things. So let’s clarify this.

On the one hand, you can talk about the network of arguments that you, as an individual, are carrying around with you in your head right now, on a particular subject.

That’s the map — your personal map — that represents the state of your background knowledge about the subject.

On the other hand, we can talk about the network of arguments on a given subject that are contributed by people all over the world, from all historical times, that constitute the history of intellectual debate on the subject.

That’s the terrain. That’s the world of ideas to be explored and discovered, through learning and experience. And it’s the world that is continuing to grow as people come up with new arguments and contribute to the dialogue on that subject.

Both the map and the terrain have the structure of what I’ve called an Argument Matrix, because that’s how I’ve stipulated it — argument structure is the structure I’m interested in.

But your personal map, your personal Argument Matrix, is much smaller and more limited than the Matrix corresponding to the terrain, because it represents your understanding of the terrain from your limited point of view. For any substantive topic, the terrain itself is inevitably going to be much larger and more complex structure.

Imagine, for example, the difference between what a Phd in physics has learned by the time they get their doctorate, and the collective body of knowledge that constitutes physics as a whole.

That’s the scale of the difference that I’m asking you to imagine, between the Argument Matrices we carry around in our heads, and the Argument Matrices that comprise our collective reasoning about the world.

Now, if you circumscribe a topic narrowly enough, then you’ll reduce the scale difference for sure.

If I’m an expert on the physics of neutrinos and neutrino detectors, and specifically on the operation of the detectors at the Sudbury Neutrino Observatory in Canada, and someone asks me a specific question about the operation of these devices, then the gap between what I know, and all there is to know, about the operation of these devices, is going to be much smaller than if the question was about neutrino physics in general, or physics in general. The map and the terrain will be closer in scale.

But they’re still two very different things.

Well, I’ve gone way past my usual time, and I think this is a convenient place to stop. So let’s stop here.

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