Toward Arguing Better: A Trusty Tool

Read Part 1.

Teachers are supposed to discover things ahead of time and then share them with students. But sometimes the discoveries come during the teaching. It’s part of the compensation package.

A month or so ago, I experienced one of these moments of discovery during the 9th grade class I teach three days a week—a class in formal logic. (Yes, logic. I dare you to read a short essay about formal logic. What are you afraid of?)

My light bulb moment was not the discovery that evangelical and fundamentalist Christianity are desperate for more constituents capable of thinking clearly about hard questions. That reality struck home a couple of years ago, and I’m reminded almost daily. (Often enough, the guy in the mirror is the evidence.) Nor was my light bulb moment the realization that if we start teaching kids logic again, as in the good old days, we might see a generation of better Christian thinkers succeed the “this feels true to me” generations we’ve raised up in America over the last century or so. I already believed that. It’s why I’m teaching the class.

The light bulb came on when an idea I’d accepted as true in theory became “real” by experience. The students and I were working through some exercises sixteen chapters or so into our textbook1 when we arrived at this question:

Smith said, “Pro-lifers don’t care about children who are already born. All they care about is their stupid political agenda.” Jones disagreed by saying, “No, there are many pro-lifers who are involved in caring for children.”

The assigned task was to analyze the paragraph, “isolate the related statements, and put them into categorical form. Assign abbreviations to the terms, place them on the square of opposition, and determine their relationship.” In this case, the available relationships were contradiction, contrariety or subcontrariety.

Sounds daunting, but trust me—the kids made it look easy. And, if you’re sixteen chapters into the textbook, it is easy.

But don’t get distracted by the technical stuff about squares and contrariety and the like, or you’ll miss the good part. The light bulb came on for me when I realized that by working through this exercise, my students were beginning to learn how to do something priceless: they were learning how to look at emotional statements about a highly sensitive topic and identify accurately (a) what is actually being claimed and (b) what sort of reasoning is involved in it. As they left class, I told them, “I’d be surprised if one in ten thousand Americans knows how to see that little bit of dialog as clearly as you can now see it.”

We can’t fly through sixteen lessons of formal logic here. But for those who haven’t glazed over or found something warmer and lighter to read yet, here’s a rough approximation of what we did to complete the exercise (and I do mean “we.” I’m learning this along with them!).

Step by step

1. Isolate the related statements.

Only two statements are related—“Pro-lifers don’t care about children who are already born,” and “There are many pro-lifers who are involved in caring for children.” They are related because they share all the same terms.2 The unrelated statement (“all they care about is their stupid political agenda” is actually part of a second argument).3

2. Put the statements in categorical form.

The results of this step sound weird, but several rules determine how to do it correctly, and there is definitely a method to the madness. I’m going to take the liberty of paraphrasing a bit to avoid lengthy, hyphenated noun phrases (like “care-about-children-who-are-already-born pro-lifers”).

Conversational form Categorical form
Pro-lifers don’t care about children who are already born No pro-lifers are care-about-children pro-lifers.

Here, the process is already proving to be insightful, because it’s only when we put Smith’s statement into categorical form that we realize what he is really saying. His generalization is a universal negative: there are no pro-lifers who posses a certain quality—caring about kids. (He might deny that this is what he meant, but if his statement means some (or even many) pro-lifers don’t care about living children, he is leaving open the possibility that some pro-lifers do care and no longer has a point.)

Expressing Smith’s words categorically not only helps us see more clearly what he’s claiming, but also reveals how vulnerable his claim is. You only need one contrary example to disprove a universal negative.

The second related statement, Jones’ reply, is also more clear in categorical form.

Conversational form Categorical form
There are many pro-lifers who are involved in caring for children. Some pro-lifers are for-children-caring pro-lifers.

3. Assign abbreviations to the terms.

This step is just a bit of arbitrary shorthand. We’ll make the first statement “No P are C” and the second, “Some P are C.”

The remaining steps involve displaying the relationship between statements using a graphical tool. Positioning the statements on a square of opposition4 shows that their relationship is that of contradiction (if one is true the other must be false and vice versa. They go at opposite corners of the square of opposition, diagonal to each other).

But what if we didn’t have Jones’ rebuttal (the second statement)? We could put the first in categorical form, place it on the square and determine what form a contradictory statement would have to take. It’s a great way to develop and analyze the soundness of arguments.

How useful is it?

If you have an intuitive pull toward logic but have never really understood how it works, seeing a process like this starts making a host of possible uses click in your brain. For me, it was quite exciting.

But the discovery may also make you wonder, as I did, “Why in the world didn’t somebody teach me this in high school?!” It’s sad to be just learning it at age 45. But better late than never. These tools are too interesting and helpful to go unappreciated.5

Just for fun, see if you can put these generalizations in categorical form—and see if it doesn’t open your eyes a bit to why we’d all benefit from learning some formal logic.

  • Calvinists don’t care about reaching the lost.
  • Those who develop eclectic Scripture texts do so outside the believing community and without the aid of the Holy Spirit.
  • Parents who punish their children assume children have to feel bad in order to learn.
  • Fundamentalists don’t really care about truth or love. They just love to fight.
  • Capitalists think greed is good.
  • People who oppose gay marriage just feel threatened by people who are not like them.

These statements are not all equally easy to put into categorical language, and they are all portions of larger and more complex arguments. But taking statements apart and reassembling them can go a long way toward understanding what kind of argument is being made and what kind of argument (what kinds of statements) will effectively counter it.

A word of caution though. Effective logical arguments are really for “the people in the middle.” That is, we shouldn’t expect solid logic to convince an abortion-rights activist to change his mind. He is unwilling to do so and—as far as I can tell—logic does not reach the will. Logical argument is only effective when the hearer (or reader) is already willing to be persuaded.


1 The book is Introductory Logic for Christian and Home Schools, by James B. Nance. Canon Press.

2 In logic, a “term” is the smallest unit of meaning and is always a noun or noun-phrase (nominative phrase). In categorical logic, a term is always either a subject or a predicate and an “argument” is always a set of premises and a single conclusion—though premises are sometimes unstated.

3 It may also be a very loose paraphrase of the first statement. Either way, because it’s a universal regarding what “pro-lifers” “care” about (two of the same three terms), Jones’ reply counters it also.

4 The first half of the Wikipedia article is fairly accurate and helpful:

5 As the logic class has progressed, we’ve learned how to analyze a wider variety of normal-language statements and convert them to various kinds of categorical statements.

[node:bio/aaron-blumer body]

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There are 15 Comments

ChrisS's picture

My son, now a HS junior, has taken a love to apologetics, and along the way, has necessarily studied logic in his studies. I'm with you, why didn't we learn this in high school? Dr. Jason Lisle, of Answers in Genesis, has written a small book called Discerning Truth, taking the reader through the many fallacies we tend to use when we debate/argue.

Our dinnertime discussions often end up centered on Christianity-related articles with the generalizations you listed, identifying well-put points as well as fallacies that leave some authors' stated positions rather empty. We would do well to better stated our own beliefs and positions so as not to generalize.

Aaron Blumer's picture


I agree... generally. Wink

Sometimes communicating efficiently requires that we generalize. Can't specify every qualification in every case. And sometimes a generalization is precisely true: humans are sinners; sinners resist God; nobody can save himself (in categorical language these are all universals: all sinners are humans; all sinners are God-resisters; no human is a self-saver).

But in the heat of debate, universals are really handy blunt instruments and definitely overused.

Edit... want to mention, too, that the study of common fallacies is mostly a branch of "informal" logic. There are some formal fallacies (these mostly have to do with syllogisms in which the premises do not support the conclusion--even if they are true premises--or do not necessarily imply it. In formal logic, "imply" means something like "require.")

Charlie's picture

During the middle ages through the dawn of modernity, logic was the only game in town. Especially after the rediscovery of many Aristotelian texts, a complete Christian-Aristotelian synthesis began. In many ways, the C-A synthesis outlasted even the Cartesian revolution. Where it really began to fall apart was after the inductive (scientific) method got off the ground. Francis Bacon's Novum Organum is a critique of logic, or at least of its applications. (The title is a challenge: Aristotle's collection of logical writings is known as the Organon, meaning tool or instrument. Bacon was proposing new tools.)

According to Bacon, all the logic comes too late. Logic pertains only to generating valid inferences and exposing invalid ones. If one starts with false premises, logic will generate valid but false inferences. Thus, a new method for confirming premises is necessary. So on, so forth.

In our post-critical era, I think we've reached the point where we understand that all knowledge cannot be written as a complete logical system from indubitable premises. Logic doesn't often help us get new information. Further, logic generally does not establish the truth or falsity of things, but only of arguments. Showing a logical error in an argument does not necessary show that the conclusion is false, only that that particular route won't reach it. But, logic can still play a very important role. It can point out where we've gone off-track in our thinking, and as Aaron pointed out, it can help us sort out what someone is really saying. Worthy goals, to be sure.

My Blog:

Cor meum tibi offero Domine prompte et sincere. ~ John Calvin

Aaron Blumer's picture


In the essay, I didn't lay "Smith's" argument out completely. Like most arguments, his leaves at least one premise unstated (if one of a syllogistic argument's statements is left unstated, the argument is called an enthymeme. If more than one is unstated, that term might still apply, or there may be another--can't remember at the moment.)

Smith said, “Pro-lifers don’t care about children who are already born. All they care about is their stupid political agenda.”

Unstated premise: All people who don't care about children are people who are wrong about abortion.
Stated premise: All prolifers are people who don't care about children
Unstated conclusion: Therefore, all prolifers are people who are wrong about abortion.

The structure of the syllogism is valid (the conclusion is necessarily implied by the premises).

But the argument fails because the minor premise (the stated one) is untrue. So, we really don't have any kind of "fallacy" here. Just an unsound argument.

For ease of analysis, we might reduce the syllogism to a schema ("S" is the minor term--the subject of the conclusion, "P" is the major term--the predicate of the conclusion, and "M" is the middle term... the one that links the other two terms and links the two premises).
All M are P
All S are M
:. All S are P

This syllogism only proves its conclusion true if both of the premises are true. In this case, the argument/syllogism fails because in reality, some S (prolifers) are not M (people who don't care about living children).

Aaron Blumer's picture


Charlie wrote:
Showing a logical error in an argument does not necessary show that the conclusion is false, only that that particular route won't reach it. But, logic can still play a very important role. It can point out where we've gone off-track in our can help us sort out what someone is really saying.

Thanks, Charlie... and the history on Bacon's response is helpful too.

I'd only add that while defeating a particular argument (or set of arguments) doesn't prove a conclusion false, it does--in the context of a particular piece of writing or speaking--prove it unsupported. Since we always interact in chunks (a speech, an essay, a book), it is possible to use logic to neutralize a chunk's primary claim(s). Since these pieces of communication are the main way we interact with ideas and arrive at conclusions, being able to do that is more powerful than many want to admit in our post-Bacon point of view.

I think Bacon had a point that logic comes late (you have to have true premises first). For Christians, that only underscores the value we place on revelation. We get all of our weightiest premises from Scripture then reason from those... and from that, gain a solid system for using induction to learn more.
I'm putting it all in pretty simple terms because that's basically where my understanding is at this point.

Charlie's picture

One of the more interesting problems of modern epistemology is that of foundationalism vs. post-foundationalism. For most of Western history, knowledge has been conceived as a foundationalist enterprise. Classical logic reinforces that idea.

As you pointed out, a conclusion is proved true only if both its premises are true and if it is in valid form. Great. But, each of the premises rely on (or rest on, hence the metaphor of the foundation) other premises, which in turn rest on others. So, to know the truth of any conclusion, we must be able to trace it all the way back to first principles. According to Aristotle, there are a few intuitive first principles - law of non-contradiction, whole is greater than part - and each science (scientia, a defined realm of inquiry) has its own first principles that function axiomatically within that realm. See Thomas Aquinas, Summa Theologiae I.1 for the classic exposition of theology in the form of an Aristotelian scientia. In the 20th century, Gordon Clark tried to do something similar, using the Bible as a set of first principles. There's also Cartesian foundationalism, in some ways a whole different animal.

Many post-moderns and even what I rather awkwardly call partial post-moderns have embraced non- or anti-foundationalist epistemologies. Many of them are reacting against Cartesian foundationalism, and their critiques may or may not apply to other types. But the debate is interesting and relevant, since the role of logic in a non-foundationalist epistemology is going to be a bit different.

My Blog:

Cor meum tibi offero Domine prompte et sincere. ~ John Calvin

Aaron Blumer's picture


Where would you locate yourself in that landscape?

I don't know what Cartesian foundationalism is--and can't really even imagine what anti-foundationalism is... so I must be an old school foundationalist?

(Edit: Ah... Cartesian as in Descartes... I think I get it more or less now.)

Charlie's picture

Aaron, I'm still looking for where I belong, while trying to do some good where I am. One of the things that certain types of postmodernism have accentuated is the secondary nature of theory. For example, when a child learns his native language, he does so not by tables of grammar rules, but by imitation and imagination, all wrapped up in a process of trial and error. By the time he gets to the point where he is learning grammar rules, he already has a vocabulary of hundreds (thousands?) of words, as well as thousands of actual communication experiences. Thus, the theory becomes an after-the-fact tool that, in many ways, merely clarifies what he already knows and puts the finishing touches on his ability.

So, the question of epistemology is not so much, "How will we learn things?", but, "How can we explain the fact that we have already learned so many things?" By the time anyone reflects on the justifications of belief, she has already had countless experiences of forming, confirming, and disconfirming beliefs.

I find myself nodding in agreement with many of the criticisms leveled at foundationalism, particularly at Cartesian foundationalism. Certain philosophers have tried to incorporate aspects of criticism, promoting "weak" or "moderate" foundationalism. I am also interested in theories of truth that move in a pragmatic direction, that is, they validate themselves by working. In theology, George Lindbeck has moved down this path. Certain theologians of the Radical Orthodoxy persuasion have as well, and with liberation theologians it is presumed. One problem I find with strong foundationalism is that I could theoretically prove everything before trying it, since I can prove premises merely with more premises. It's all in my head. Certain weak or non-foundationalist accounts that move in a pragmatic direction offer more interplay between doing (or experiencing) and knowing. This appeals to me as a Christian: "Taste and see that the Lord is good."

My Blog:

Cor meum tibi offero Domine prompte et sincere. ~ John Calvin

Aaron Blumer's picture


For me, the weaknesses of foundationalism--to the degree I'm aware of it, which is pretty minimal--is failing to account for the human soul/spirit/mind (as opposed to brain). Some of what you say resonates with me because, as I see it, the heart is involved in the process of knowing in all sorts of ways that we can't pin down. I tend to think that this is because they are so complex and diverse and because of the difficulty of finding any way to step outside of them and look at them carefully (if we could actually step out of the influences of the heart, would there any longer be anyone to do the looking?).
But, at the same time, I firmly believe that we arrive at some knowledge by deduction from other things we know. How much... not sure.

It seems to me that it's impossible to escape some kind of dynamic where what we know beforehand shapes our experience and what we experience shapes what we know. We know what revelation (as in Scripture here) means because we already know what the words and grammar mean, yet we know more words and grammar because of the revelation we accept and so on.

The one thing that impresses me most about the whole process (of knowing) is that it so stubbornly refuses to be completely understood and explained (we've been trying for how long now?). So, relying on a bit of deduction, that seems to prove not only that we are ultimately dependent on something (Someone) greater than we (all of us) are to give us knowledge, but also that "real" is so much bigger than the slice of it we think we're apprehending in our little lifetimes under the sun.

But, being deeply conservative in disposition, I'm just about always inclined to trust the thinkers who have been dead the longest. Smile

Charlie's picture

Aaron Blumer wrote:

But, being deeply conservative in disposition, I'm just about always inclined to trust the thinkers who have been dead the longest. Smile

Right, that's why you're a dispensational Baptist...

Cheap jabs aside, if you want one book that shows what anti-foundationalism might look like for theology, you should check out The Nature of Doctrine by George Lindbeck. It's not very big, and you can even skip one or two chapters. Reading Lindbeck should give you a good feel for what's going on in a lot of mainline Protestantism, particularly those sections that identify more with analytic than continental philosophy.

For an evangelical treatment, see Beyond Foundationalism by Grenz and Franke. For a critical evangelical review, see this JETS article:

Also within evangelicalism, D. A. Carson and James K. Smith have gone back and forth on postmodernism, although I don't know that either of them are sufficiently nuanced. It's hard to critique postmodernism; you really need to pick a specific idea or stance and work from there.

I also know that David Wells has written a book on postmodernism, Above All Earthly Powers. I haven't read it, but it's been highly recommended by conservative evangelicals I know. It probably isn't that precisely focused on the foundationalism issue though.

Postmodernism: A Beginner's Guide by Kevin Hart is a fantastic intro. He's a Catholic English professor with a strong philosophical background. He specifically discusses anti-foundationalism.

My Blog:

Cor meum tibi offero Domine prompte et sincere. ~ John Calvin

mbruffey's picture

The problem with postfoundationalism is that it proves too much, i.e., "All foundationalists have a defective epistemology."

Charlie's picture

mbruffey wrote:
The problem with postfoundationalism is that it proves too much, i.e., "All foundationalists have a defective epistemology."

I'm unclear as to what the example is supposed to prove. If you're suggesting that postfoundationalists can't or shouldn't make categorical statements with universal terms, you've really misunderstood postfoundationalism.

My Blog:

Cor meum tibi offero Domine prompte et sincere. ~ John Calvin

Aaron Blumer's picture


Charlie wrote:
Aaron Blumer wrote:

But, being deeply conservative in disposition, I'm just about always inclined to trust the thinkers who have been dead the longest. Smile

Right, that's why you're a dispensational Baptist...
Cheap jabs aside...

I really begged for that one! It is admittedly awkward at times. But while I'm always inclined to trust the thinkers who have been dead the longest, I don't think they're always right or that the newer idea is always wrong.
There's just a much higher persuasion threshold for the new stuff.

Thanks for the links. I don't know when I'll have time to read up on these things, but they are pulling me.

I think mbruffey's point is that the PFs have prematurely or too comprehensively abandoned foundationalism. ... but of course they see foundationalists as having a defective epistemology--this is why they are striving to develop something they believe is better.

mbruffey's picture

Aristotelean logic will be around long after both foundationalism and postfoundationalism are long gone. Mark

mbruffey's picture

At the same time, it might be useful, Charlie, to opine about the strengths and weaknesses of postfoundationalism. What are its primary strengths, and how do you go about articulating those to a hostile audience? What are its weaknesses, and how will you confront those? Mark

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