010 – How to Build an Argument Matrix

Last episode I introduced an important concept for critical thinking, what I call an Argument Matrix.

In this episode I talk about the mindset, the tools and the literacy skills that are required to successfully build an Argument Matrix.

In This Episode:

  • How should we go about building an Argument Matrix?
  • Recap: What is an Argument Matrix?
  • Three parts to my answer:
    • Mindset
    • Technology
    • Literacy
  • Mindset issues: confirmation bias, psychological barriers, fear
  • Technology issues: capturing and organizing the right kind of information
  • Literacy issues:
    • media and information literacy
    • argument literacy
    • reading and writing literacy
  • Why public education doesn’t teach critical thinking


“If you want to build an Argument Matrix, you need to have the right mindset, you need to have a system in place for capturing and processing the information that you come across, and you need to have the right literacy skills, developed to a level that is sufficient to support the activity.”

“There’s no shortcut to any of this. It’s better to think of it as a lifestyle choice, that reflects a commitment to life-long learning and the values of critical thinking.”

“I don’t know if it will ever be a popular choice, to support education for critical thinking and personal development, rather than for economic value. It may always be a minority lifestyle choice. But the tools are in our hands, and there’s nothing to stop us from developing our own programs and support systems.”

References and Links

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This is the Argument Ninja podcast, episode 010.

Hi everyone, this is Kevin deLaplante and you are listening to the Argument Ninja podcast.

Last episode I introduced the idea of an Argument Matrix and the important role it plays in critical thinking, and I got a lot of enthusiastic feedback on it. The image resonated with a lot of you, and I’m happy about that.

I got a couple of emails asked about the best way of building an Argument Matrix. How do you go about acquiring the background knowledge that gives an understanding of all the relevant arguments involved on a topic or in a debate?

And I got another couple of emails about you would use this knowledge to actually persuade someone. Once you’ve got this knowledge, how can you apply it in a strategic way?

These are both great questions. In fact, they’re both central to the Argument Ninja program that I’m developing.

What I want to talk about on today’s episode is the first question. How do we go about acquiring this kind of knowledge? How do you build, or expand, your Argument Matrix?

In this episode I’m going to walk through how I approach this question and share the advice I give when I’m asked about it.

But before we get into that, I think we should do a bit of a recap for those who missed last episode, so that we’re all on the same page in terms of what we’re talking about.

So, what do I mean by an Argument Matrix?

Well, take any interesting claim. Any claim for which it might make sense to offer reasons to believe or accept it. Or it could be an action, a decision, it doesn’t matter.

Abortion should be illegal.

Abortion should be legal.

There is a God.

There isn’t a God.

I should take this new job offer.

I should have a kid before I finish graduate school.

We should invest in the goal of establishing a human colony on Mars within the next twenty years.

String Theory is our best hope for a grand unified theory in physics.


Whatever you want. These are all claims for which reasons can be given either for or against. And they’re claims about which reasonable people can have different opinions.

What I’m calling an Argument Matrix is a conceptual tool for thinking about what it means to really know what you’re talking about when you’re arguing about claims like these.

You start building an Argument Matrix by looking for arguments in favor of a claim, that offer reasons to accept the claim.

You also want to be looking for the strongest natural objections to the argument you’re considering. An objection is itself an argument. The conclusion of the objection is that the argument you just gave is a bad argument.

To say that an argument is bad is just to say that the premises don’t offer good reasons to accept the conclusion.

There several different ways that arguments can be bad.

They can be bad because they rely on premises that are false or dubious. And they can be bad because they rely on weak logic. By weak logic, I mean that even if the premises were all true, they still wouldn’t give us good reason to accept the conclusion.

There are other ways that arguments can be bad, but these are the two ways that connect directly to the formal structure of arguments.

So, an objection is an argument that says that the logic of your main argument is weak, or one or more of the premises are false or dubious. Or both.

If the objection is a good objection — if we judge it to be a good objection — then what we’re saying is that it provides good reason to believe that your original argument was bad.

Now, if you want to defend your original argument — and if it’s a defensible position, then you should want to —  you need to come up with a reply to the objection. That reply will be another argument.

What’s the conclusion of the reply? The conclusion of the reply is that the objection that was just given is a bad argument. The reply is an argument that criticizes the objection.

Now, notice that there are three arguments in this group: a main argument, an objection and a reply. These form a natural unit. It’s the minimal unit to have an argumentative dialogue.

The term I use for this is a “dialectic” unit. It’s the unit that describes the back-and-forth of a debate where, to use a tennis metaphor, there’s an initial serve, a return of serve, and a volley. I whack the ball over the net, you whack it back, and I return the volley.

The important thing about these volleys is that they’re on point. You’re directly addressing relevant argumentative points, and responding to these points. You’re not avoiding the objections, you’re facing the objections head on.

Now, from here you can go on and build out the Argument Matrix in different ways. You can go deeper, and explore the grounds of the premises that you’re relying on; and you can go broader, by considering different kinds of arguments that bear on your subject.

But this basic dialectic structure, of argument, objection and reply, is the minimum you need to have a genuinely productive argumentative dialogue.

It’s also, no coincidence, the minimum number of arguments you need to see in a good argumentative essay, and it’s the natural structural unit of most academic papers, for all the same reasons.

Now, if you were to diagram this out, and start including possible objections and replies at different levels, and different types of arguments in support of your root claim, then our diagram would quickly start to look like a branching tree, a hierarchically ordered web of inferential relationships.

And it’ll be a bushy tree. You won’t be able to draw it all out explicitly so you can see it all at once, it’ll be too tangled and complex.

But this web of inferential relationships is what I’m calling an Argument Matrix.

When I was watching the Disney movie Frozen there’s that scene in the big song, “Let it Go”, where Elsa is building her ice castle and she stamps her foot on the ground and a branching crystal structure bursts outward from that point on the ground.

In my head that’s sort of what I see when I visualize an Argument Matrix. Or that burst initiated by something like Gandalf planting his staff in the ground in front of him. It’s too pretty and symmetrical to be a realistic representation of an Argument Matrix, but as a depiction of an idea that captures some essential features, it works for me.

Your personal matrix is defined by whatever portions of the matrix you can reconstruct and navigate, on the topic in question. So these will vary from person to person. If you know a lot more about a topic than someone else, your matrix will be broader, deeper and more articulated than that other person’s.

But there’s also the much larger matrix, defined by the collection of arguments of everyone who has dedicated time to thinking about and engaging with the topic. Our personal matrices will always be limited and incomplete in comparison to this larger matrix.

So, that’s basically were we left off last episode.

I want to reiterate that this structure that I’m describing isn’t anything that we would expect a person to formally reconstruct on paper. You could try to outline portions of it, and there can be reasons to do that. But more commonly it’s the kind of understanding that is revealed in conversation, when someone is talking or writing about a particular topic.

And the main point is that, this is the kind of understanding that is central to the goals of critical thinking. The greater your command of the Argument Matrix surrounding a topic, the more likely you are to be right when you make a judgment on the topic, and the greater your ability to claim ownership and responsibility for those judgments.

Now, from a debate standpoint, it’s also clear that the person with the deepest and broadest Argument Matrix has a material advantage over everyone else, in the sense that they have a better understanding of the issues that are actually relevant to judging the truth of the claims in question.

However — and this is vitally important — that advantage doesn’t automatically translate into successful persuasion. There’s a big difference between being right and convincing someone else that you’re right.

Arguments don’t advocate for themselves, people do. And that means that even if you’ve got the best arguments at your disposal, you and your audience are still human beings, with all the foibles and vulnerabilities that come with that. You will always be dealing with cognitive biases and the psychology of resistance.

That’s why persuasion skills need to be developed independently, alongside the kind of argumentative understanding that we’re talking about here.

But the issue of persuasion and argumentation is another topic, for another day. What I want to focus on now, is the question about what is the best strategy for developing an Argument Matrix.

If I’m starting from a place where I know my knowledge is limited, and probably one-sided, how should I go about broadening and deepening my understanding of the arguments on all sides of a debate?

When I give advice on this question I find that my answers tend to fall into one of three categories.

1. Sometimes the advice I give is about mindset, what kind of psychological attitude is most conducive to this process.

2. Sometimes I talk about technology, about the amazing tools that we now have at our disposal for finding and capturing information.

3. And sometimes I talk about the different kinds of literacy that are important for recognizing and processing and interpreting this information.

So, my answer to this question, about the best way to acquire information about the argument structure surrounding an issue or a debate, has three parts: a part about mindset, a part about technology and a part about literacy.

So let’s talk about each of these in turn.

I’ll start with mindset issues.

One of the biggest obstacles we face when looking for information is that we self-segregate into groups of like-minded people that share a similar worldview. On the internet we tend to visit the same small number of information sites over and over again.  And on social media, we’re fed a curated, filtered stream of information, determined by our search history and the history of articles we’ve clicked on, that reinforces our old viewing habits.

So our information environment isn’t as rich or as diverse as it could be, or as it needs to be if our goal is build an argument matrix.

We’re also subject to confirmation bias, which is a cognitive bias that makes us prone to remember, to search for and to interpret information in ways that reinforce our expectations, and makes us prone to forget, ignore or otherwise downplay information that challenges our expectations.

These are all mechanisms that are working to keep us inside the information bubble that we’ve constructed for ourselves. So we need to find ways of getting outside this bubble.

Another mindset issue involves our attitude toward the whole process of becoming educated about different points of view.

There’s a lesson to be learned from the history of cultural anthropology. 19th century European and American anthropologists were preoccupied with categorizing the cultures they encountered as either “primitive” or “civilized”. So they would go into a technologically less developed culture, or a tribal culture, and document what they learned, but all of it was filtered through a lens that ranked cultures as civilized to the degree they shared key traits with their own culture, which was assumed to be the pinnacle of civilized culture, and primitive or backward to the degree that they lacked the traits they regarded as essential to civilization.

This filter gave rise to an ethnocentric bias in how Western anthropologists described and theorized about the cultural phenomena that they were observing. Quite apart from the role that all of this played in reinforcing colonialist and racist views, the resulting science, even at the basic level of just describing what you’re seeing right in front of you, was seriously compromised, because of this bias.

Anthropology has worked hard to purge these ethnocentric biases from its methodology. One approach, for example, involves cultivating a sense of distance from one’s own cultural worldview, and through extensive engagement in the target culture, actively trying to perceive the activities of the culture as natural, to the point where the anthropologist comes to see how those activities are perceived and understood and have meaning within that culture.

Now, there are limits to how far one can go in adopting the worldview of another culture, when you weren’t born and raised into it. But the point is that some effort like this is necessary just to get the descriptive facts halfway right.

And the same is true for a lot of issues that are held by people within particular sub-cultures, that are part of a group identity, even within our own culture. Think about abortion rights issues from the perspective of richer communities versus poorer communities, or men versus women. Think about gun control issues from the perspective of liberal urbanites versus the rural poor, or the inner city poor.

The arguments that we’re trying to understand are held by people with their own motivations and histories, that reflect their point of view on the world. It may not be your history, but to really understand the issues as others see them, we need to develop an ability to sympathetically inhabit a different worldview, as best we can, for a period of time.

This is much easier said than done, especially if we feel committed to the view that we want to defend. Because the stronger we feel that commitment, and the more drawn we are to identification with the group on the “right side” of the issue, the more vulnerable we become to a host of cognitive biases that can distort our perception of reality.

So we need to find ways of empathizing with other people and their point of view. Not for the sake of multiculturalism or other liberal political values, but to maximize the clarity and accuracy and completeness of our understanding.

This is more important than you might think at first. It’s easy to underestimate how challenging it can be to immerse ourselves in a worldview that is very different from our own.

Part of the challenge is the fear that, if we stay in that place for too long, it may change the way we think about the issue, and maybe more than that. We may lose faith in the beliefs and values that define who we think we are.

I’ve been a teacher in classes where we’ve spent three or four weeks on a unit on the philosophy of religion, or political philosophy, and students come to see me in office hours and confess that they’re having a hard time with this material. No because it’s hard, but because it’s forced them to consider a point of view that runs counter to everything they’d been raised to believe, and they’re struggling with the feeling that they’ve lost their bearings.

That feeling, of not knowing what you believe anymore, can be very stressful. Our brains don’t like it.  We look for ways of making sense of our experience, and if we don’t have an interpretation ready at hand to do the job, we’ll try to manufacture one, just to relieve the stress.

I’m just as subject to this as anyone. But there are ways of cultivating a mindset that doesn’t recoil from doubt and uncertainty, that finds purpose and meaning and value in the critical journey itself, in the search for answers, without always having to settle on an answer.

I’d like to do a whole episode on mindset issues because there’s a lot more to say about this topic.

In the Argument Ninja program that I’m developing, I’ll be including some units on mindset, for all these reasons.

But this is enough for now.

Let’s move on to talk about technology.

We’re living in an unprecedented age of access to information. Say what you will about Google as a company, there’s no denying that it’s brought a universe of information within the reach of ordinary people.

Are you a pro-gun-control person? You’re familiar with at least some of the gun control arguments? But to build out your Argument Matrix on gun control, you need to look carefully at the anti-gun-control arguments too. Maybe you’re not as familiar with those.

Well, today, I can type into Google the words “arguments against gun control”, and Google will give me over a million results, ranked by Google’s judgment about the importance of a site with respect to those search terms.

The first hit on Google, on my browser at least, is from a site called “Listverse”, and it’s a list article called “10 Arguments Against Gun Control”. In the first line it states “This list serves as a rebuttal of the Listverse list “10 Arguments for Gun Control” by Morris M.”, and it give a link to that article.

So right away you’ve got two articles, pro and con, with the con list framed as a rebuttal to the pro list.

This is not a bad place to start.

But you could lose a couple of hours reading just these articles and chasing down the dozens of supporting links inside each one.

It’s better to approach this more systematically. You’re on the Google search results page for “arguments against gun control”. Most people will click on the first or second link on the search page and stop there. That’s a mistake. The top ranked articles aren’t necessarily the most comprehensive or the best written or the most fair-minded. Google has given you ten links out of a million. Trust me, there are gems further down this page.

Also, you need to look at multiple sources, and compare the arguments across multiple sources. The ones that show up on every list you know are central to the debate. And it’s only by looking at multiple sources that you’ll find the best objections and replies.

Now, some of the links will look like they’ve done all the work for you. They’ll give you a systematic ordering of pro and con arguments. There’s a site called “procon.org” that does this for dozens of controversial social issues. It’s a great site, you should check it out.

But these sites, and most internet sources, quite frankly, are still quite shallow, from an argumentative depth standpoint. They give you an argument, and an objection to that argument, and then they move on. Pro and con.

What’s missing is how a supporter of the pro argument would reply to the con objection.

If all you’re given is an argument and an objection, you don’t yet have a dialogue. Remember what I called a “dialectic unit” is a three-argument structure: argument, objection and reply.

When you start looking at the issues in terms of these kinds of dialectic units, you’re modeling a real argumentative exchange. And you’ll also notice how rare it is to find online.

The risk of these sorts of pro-con lists is that they give you the feeling of understanding, but they do that by feeding your confirmation bias. They make you feel satisfied that you can now say something in defense of your view.

But if that’s all you’ve got, it’s the argumentative equivalent of junk food. Someone who really knows their stuff will know how to identify the areas of weakness in your argument, and if you don’t know to respond back, then you’re stuck.

So, you’re going to need to spend more time on this than just perusing the first article you come across.

You’re going to want to bookmark the search page, and you should bookmark all ten links on this page, so you can go back and look at them more thoroughly at your leisure.

Now, right away, we see a need to have some system for capturing and recording and organizing links to internet sources, ready to go, at any time, when you’re online.

This is why software apps like Evernote were built. It’s a dedicated app that you can use for capturing and organizing web content. It comes with a browser toolbar extension so that if you’re in Chrome or Safari and stumble on a web page or an article that you want save or bookmark, you can just hit the Evernote button on your browser toolbar.

You can also use your browser’s toolbar to create folders for bookmarks. In Chrome I can create a folder, right on my browser toolbar, called “Gun Control”, and whenever I find an article or a website I want to save, I just highlight the URL and drag it into the folder. I can create sub-folders inside, for pro and con arguments, if I want to.

There’s a dozen other services or apps you can use to capture and organize links. Which ones you use doesn’t really matter, as long as you have something set up that makes sense and is convenient and does the job.

I really like an app service called Workflowy. It’s a browser-based list-making app. I use it almost every day, and when I’m on a research mission I’ll often start making lists here and leave it open as a tab when I’m working, so when I find something I just cut and paste the url from one tab into my Workflowy list, and then organize the links into different headings and subheadings, and make notes to myself inside the list items.

If I’m writing something on this topic, I’ll generally switch over to Scrivener, which is a writing app, and load up the links in the research folder, so I can look at the original source and open up a panel for taking notes, side by side.

With a list organizer you can start to build out the structure of an Argument Matrix, by intentionally focusing on arguments, objections and replies.

As you work through the articles in your link list, you’ll see the same issues brought up about over and over, and you’ll see how the common argumentative moves are presented and framed, and you’ll learn to anticipate how each side will respond to these moves.

Along the way, you should allow yourself to comment on what you’re reading, and ask yourself questions that you might want to follow up on.

In Workflowy, when I’m making notes on a source that I’m reading, if I want to add a comment or a question of my own I’ll put it as a list item in square brackets. If I think the objection I just summarized is a weak objection, I’ll say that, and add a line or two about why I think so. This is like making notes in the margins of a book. It’s a way of inserting myself into the dialogue, and developing my own point of view on the issue.

So, these are some of the ways that I go about the process of researching and organizing information about a topic. In most cases, the argument structure of the debate doesn’t reveal itself as plainly as you would like. You need to impose that structure yourself — you need to demand to see it — by setting up those argument categories in the system you’re using and actively work at reconstructing how those exchanges would go, based on your current understanding of the positions. As your understanding grows, you’ll tweak how you present these arguments, you’ll add levels to them as you go deeper, and you’ll add branches to your argument tree that you had never considered before.

And it’ll change the way you think about the arguments, and the issue. Your own positions will evolve over time, as a result of this process.

But that’s how you build an Argument Matrix.

In the pre-internet days you would do this using books and library sources and photocopying articles and making notes by hand or on a desktop computer. Now we have different tools, but the process is the same.

And I’m sure there are academics listening to this and saying to yourself, this is nothing new, this is just research. This is what research looks like.

And that’s exactly right. What I believe is informative in what I’ve been describing here, what many students don’t appreciate, is how real research isn’t so much about learning facts as it is about reconstructing arguments. That’s not something that students are told, and in my experience it takes a long time to figure out.

Okay, we’ve talked about mindset issues, and we’ve talked about technology and the mechanics of reconstructing the argument structure surrounding a debate, using the tools we now have at our disposal.

The third item on my list of topics that are relevant to building Argument Matrices is literacy.

This process that we’ve been talking about is not an easy one. When you’re searching for information online, you have to make judgments about what’s a quality site and what’s not a quality site. Then you have to read the sources and figure out what they’re saying and reconstruct the reasoning behind it. Then you’ve got to find some way of presenting and recording this information for yourself, in such a way that it will still makes sense to you if you come back to it a year from now.

None of this is easy.

When we’re searching for information on the web, and we need to make judgments about the information we find in different sources, that requires media literacy and information literacy.

Do you know what kind of information is found in dictionary entries versus encyclopedia entries? Do you know how Wikipedia entries are written and edited, and how that affects the quality of the content? Can you judge the reliability of a website resource by the way it looks? How do you find the resources that experts rely on for reliable information? What are the pros and cons of YouTube as a source of information? How can we assess the quality, or the objectivity, of a YouTube channel? Do you know what a “filter bubble” is? Do you know how corporate control of web platforms affects the content that you find there?

This is media and information literacy and it takes time to develop.

Then you’re asked to read a text or watch a video or listen to a podcast, and from that experience, extract the argument structure. Do you think that’s easy? It’s not. This is argument literacy, and despite what the public education teaching profession wants you to believe, you get almost no training in this in school. Only about 1 in 5 graduating high school seniors can pass an argument literacy test at a reasonable standard. Many high school seniors can’t read a newspaper editorial and consistently identify the conclusion of the editorial. They misjudge the main point that the editorial was trying to communicate. And even when they do get it, they have a hard time reconstructing the reasoning behind it.

If you don’t have a good sense of what an argument is or how to identify premises and conclusions or how to extract the argument structure from a text that has a lot of other things going on at the same time, then you’re going to struggle with this process. There’s no getting around it.

There are other forms of literacy that can affect how easy or hard it is to reconstruct an Argument Matrix on a given topic.

Science literacy is important, when you’re trying to investigate a topic that has a science component. If your science literacy is poor, and most people’s is, it can be very hard to interpret scientific information correctly.

And you can’t underestimate the significance of basic reading and writing literacy. Do you understand the vocabulary that’s being used? Do you have a habit of looking up words that you don’t understand, as you read?

Can you process the meaning of more complex sentence structures, that use logical connectives, like “if A then B, otherwise C or D”.  Or sentences that use nested clauses?

Can you follow shifts in voice, when the author stops speaking for him or herself and starts speaking for someone else, like when an author is summarizing the views of someone else, before commenting on it. I can’t tell you how common it is for students who aren’t reading carefully to miss these shifts, and think that the view that an author is presenting is the author’s own view, when it’s not.

And when you write, or speak, can you efficiently summarize or paraphrase what you’ve just read, in your own words?

All these different kinds of literacy tend to hang together. Basic reading and comprehension skills are a prerequisite for most other forms of literacy. Argument literacy feeds back and make it easier to read and understand more complex forms of writing. As people become more educated these different forms of literacy develop together, mutually supporting one another. This process, the evolution of literacy, is the scaffolding that makes more advanced forms of learning possible.

So, let me sum up.

Building an Argument Matrix is a sophisticated intellectual activity. Any reasonably intelligent person can do it, but you should think of it as a skill that takes discipline and commitment to develop. Like learning to play chess well, or become proficient on a musical instrument, or become a good writer.

If you want to build an Argument Matrix, you need to have the right mindset, you need to have a system in place for capturing and processing the information that you come across, and you need to have the right literacy skills, developed to a level that is sufficient to support the activity.

There’s no shortcut to any of this. It’s better to think of it as a lifestyle choice, that reflects a commitment to life-long learning and the values of critical thinking.

Now, do I think that schools are doing a good job of developing the foundational skills and mindset and values that support this lifestyle choice?

Absolutely not. But the mistake is to think that this was ever their job. Raising critical thinkers has never been the primary function of formal schooling, and certainly not public schooling.

The primary function of public schooling, just for the record, has always been to develop a labor force that can support the economic activity that government and business finds valuable, and to instill a set of shared social and political values within the population. The goal, in other words, is to produce good citizens, not independent critical thinkers.

Once you realize this, it explains a lot about how school curricula are determined, and why there’s such a preoccupation with test scores and performance rankings.

And you see that there is no social institution that we can hand our kids over to that is responsible for educating critical thinkers.

That burden falls on us — individuals, parents, teachers, all of us.

I don’t know if it will ever be a popular choice, to support education for critical thinking and personal development, rather than for economic value.

It may always be a minority lifestyle choice. But the tools are in our hands, and there’s nothing to stop us from developing our own programs and support systems.

I’m working on a program of my own. Not the Critical Thinker Academy, as it operates right now. Something more structured, that takes advantage of the features of a true learning management system, with assessments and assignments and level upgrades and gamification features.  A real, structured education program that is organized around the Argument Ninja and martial arts themes that I’ve been developing in this show.

I’ll let you know more about the program as it develops, but if you want to keep on top of updates, I urge you to visit ArgumentNinja.com and sign up for the Argument Ninja newsletter, where I’ll send you information about updates as they come out, including how you can lock in a subscription to the Argument Ninja program at a fraction of the rate that it will go for when it’s launched.

That’s it for this week’s episode. Thanks very much for listening. Take care, and I’ll talk to you next time.

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