Things are going well in Symbolic Logic. Students are mastering truth tables, and they’re symbolizing English sentences into our truth-functional language with increasing facility. (For those who haven’t taken a class like this, or for those who’d appreciate a reminder, please see the note at the end.) Then comes the truth table for the material conditional. It’s usually the bottom half that does it. A false antecedent yields a true conditional overall. The rest of the truth tables made sense. They even imposed an intuitive order on the woolliness of natural language. This truth table does not make sense. If it imposes order, it is not of the intuitive kind. We stare at it awkwardly.
I do my best to motivate the truth table somewhat. Then I explain that, at this point in the class, we needn’t worry too much about why the truth table is the way it is. Once we’ve got a better grasp on the entire logical system, I say, it’ll be easier to see why this is a sensible truth table, given the constraints we have. Indeed, later in the semester, I’ll ask the class to try to construct a better truth table for the conditional. We’ll end up agreeing that the initial one is the best we can do, truth-functionally speaking. We’ll get to talk about the limits of truth-functional languages, and on the choices that are made by those constructing them. These will all be valuable things—later. But right now, someone asks:
“Sure, but why is the truth table like that, though?”
The problem with this question is not that it’s a bad question. It’s a good question, at least along several important dimensions. It’s on topic. The answer is by no means obvious. And answering the question may well improve understanding of important issues. Admittedly, the question undermines my attempt to delay addressing the issue until a later point in the class. But questions are sometimes good precisely in virtue of pushing back on things one is being asked to take for granted or otherwise set aside. Moreover, in this case, we could easily give a plausible-sounding rationale for addressing the issue sooner rather than later. We can imagine the student following up the question with something like, “I just can’t learn something when it doesn’t make sense to me!”
So if it’s not a bad question, what, if anything, is wrong with asking it?
* * *
I teach at a large R1 state university. We have a Master’s program, but I’ll set that to one side. Graduate pedagogy is important and underdiscussed, but it’s a very different context, and I won’t be able to do justice to it here. Mine is a land-grant institution, and most of the Philosophy Department’s student credit hours (SCH) come from teaching medium-to-large general education courses (enrollment of 40–120) to learners whose only contact with philosophy will be that course. About one quarter of our students are first generation. They come from all over the state, many from places where their K-12 education left much to be desired. Many students work at least full-time, as well as going to college. Many students are caregivers. Many students are also highly instrumentally motivated. To them, college has become a cost/benefit proposition. Their goal is to graduate with a GPA that will yield a worthwhile return on the investment of going to college. I don’t judge the students who have this attitude. I judge the system that fosters it and higher education’s own complicity in it.
In general education classes in this context, I typically aim for students to ask more questions, rather than fewer. I often aim to have them ask questions precisely about the point and value of college. For instance, in a class called Philosophies of Life (my department’s main SCH generator), in a unit on environmental ethics, we talk about the history of land-grant universities. Students ask questions like: Where did that land come from? What does the land-grant mission mean today? Is the university living up to what it says the land-grant mission is?
This is all to the good, and I want to try and do more of it in those classes. But experiences like the one I started with have prompted me to think more about helping students know when not to ask questions—even good ones.
What exactly makes for a good question is itself a good question. And part of the value of question-focused pedagogy is helping students think through that. I’m going to leave it intuitive and direct you to further resources (Lani Watson’s (2018, 2021) work is a good place to start; see also Bloch-Schulman (2016, 2024)). Here, I want to explore the idea that good questioning might require refraining from asking a good question. That is, the skill of being a good questioner includes sensitivity to whether to ask a particular question, even a good one. A soccer analogy: the skill of being a good goal scorer includes sensitivity to whether to take a particular shot, even a good one. A good goal scorer doesn’t just take good shots. She also recognizes when taking a good shot is not the best thing to do, such as when she could instead give the ball to a teammate who can take an even better shot.
I think the student asking about the material conditional’s truth table in the context I gave falls into this category of a good question that it was not good (or at least not ideal) questioning to ask. But it’s not obvious why.
Morality provides one important kind of reason for refraining from asking a good question (see Brynn Welch’s contribution to this series). While I make no claims about being able to sharply distinguish moral considerations from pedagogical ones in general, in the logic case, morality does not underpin the problem with asking the question. In asking it, the student needn’t be disrespectful. Nor do they risk opening a morally loaded can of worms.
We can make progress by considering what asking a question does to a conversation. As Austin (1962) showed about speech acts in general, so for asking questions in particular: we can use utterances that sound like questions to do all sorts of things. What’s the worst that could happen? might be a question in a briefing room, but it might be an invitation or an incitement among bored friends. And we can ask a question without uttering something that sounds like a question: They’ve been awfully quiet recently might be an assertion, but it might also be a way of asking whether they should be checked on. What, then, is distinctive about utterances that are genuine questions, rather than assertions or invitations?
Here I’ll follow Watson (2015, p. 122) and think of a question as “a tool for eliciting information.” Sometimes questions, even good ones, undermine their own information-eliciting goal. They can do this in part because questions demand answers (see Roberts (2012) for a formal framework). Once a question is asked, it needs addressing. You might be able to set it aside, but it can’t be ignored. This is especially true in the classroom where, despite our best efforts, it can be hard to get away from an implicit model of students imbibing information from instructors. If questions are tools for eliciting information, and if instructors are implicitly seen as founts of information, then questions in classrooms clamor for answers. Indeed, I find it can be as hard to know when not to answer a good question, as when not to ask one. My impulse in the logic class is to answer that question, even as I suspect that the answer won’t be readily graspable at this point in the course—even though trying to answer it might sow confusion that I do not want to sow.
When, then, should one not ask a good question?
Answer: When doing so might undermine the information-eliciting end that the question is supposed to serve.
A benefit of this answer is that it shows what can be wrong with asking questions (good or bad) insincerely. Someone “just asking questions” uses their utterances not in the service of eliciting information, but in the service of some other end, such as promoting a baseless claim. A different kind of case: one of my high school teachers was well known for answering, at length, any question that wasn’t obviously off topic. If we suspected a pop quiz, we’d get to asking questions and sometimes succeed in taking up the entire class period that way.
We’ve arrived at an answer. I think it’s a good one. But I also think we can go deeper. Further reflection on when not to ask a good question will shed light on fundamental issues in both philosophical pedagogy and philosophical methodology.
* * *
In an appendix essay to his seminal—I do not use the word lightly—book on writing, Writing without Teachers, Peter Elbow (1973) distinguishes between two modes of inquiry. The doubting game is what we tend to do in philosophy and what critical thinking courses tend to try and train students to do. It involves subjecting claims to doubt and scrutiny; Descartes was a master of the doubting game. Like Elbow, I both have nothing against the doubting game and am heavily invested in it. But, like Elbow, I do have something against treating the doubting game as the only game in town, or at least the only one worth playing (see also Dotson (2011) and Wolfe (2022)).
The doubting game needs to be played alongside the believing game, in which “the first rule is to refrain from doubting the assertions [under consideration], and for this reason you take them one at a time and in each case try to put the others out of your head. You don’t want them to fight each other. This is not the adversary method [of the doubting game]” (Elbow, p. 149). Crucially, in the believing game, you’re not just entertaining a proposition for the sake of coming up with objections to it, or even for the sake of coming up with reasons in support of it. Rather, Elbow continues, “there is a kind of belief—serious, powerful, and a genuine giving of the self—that it is possible to give even to hateful or absurd assertions. To do that requires great energy, attention, and even a kind of inner commitment… Try to have the experience of someone who made this assertion.”
We needn’t think that we can believe things at will to appreciate Elbow’s point. There’s a way of giving a claim serious consideration that goes beyond merely entertaining it. There’s a way, that is, of looking through a claim, rather than at it. When you look through a claim in this way, you see the world differently. Seeing the world differently is valuable, but it’s very hard to do if we exclusively play the doubting game. This is a problem for philosophical pedagogy. We often aim for learning outcomes that involve considering others’ perspectives or being charitable. But if Elbow’s right, and I think he is, we and students alike need not only to consider others’ perspectives from without but also to view the world from within them. (Elbow is clear that this is very difficult, even when one is trying to play the believing game. Among other things, it can take a very long time—on the order of a semester and not a class period.) But the typical philosophy classroom often offers students scant opportunity to develop this skill. (Joanna Lawson has rightly pointed out to me that history of philosophy classes can be important exceptions. In such a class, one might wrestle for many weeks really trying to see things from, say, Leibniz’s perspective.)
How might we help students get better at playing the believing game in our classes? Elbow (p. 176) again: “one of the things that must be stressed most as advice for playing the believing game is that you must learn to inhibit your impulse for answers.” And yet one of the ways we express our impulse for answers is by asking questions.
This provides a richer understanding of what’s going on in the logic vignette. It’s not just that the question risks undermining its own information-eliciting end, though it does risk that. In inculcating students into a formal system, I’m inviting them to play the believing game with respect to it. At least at the beginning, I’m inviting them to take on board the syntactic rules, the truth tables, the proof system—without doubt. I’m inviting them to learn the formal system from within, to learn what it’s like to inhabit it, to be fluent in its idioms. I’m inviting them, that is, to see the world from the perspective of the formal system, and not just to look at the system. Later, once they’re good at looking through the formal lenses, we can take them off and look at them and subject them to doubt. But if we start doubting the lenses before we learn to look through them, we might not ever be able to find out what they help (or hinder) us from seeing.
So, when the student asks about the truth table for the material conditional, they’re refusing to play the believing game. That’s not the student’s fault; I haven’t framed things in these terms to them—though I will do so the next time I teach logic. Nonetheless, their refusal to play the believing game risks hindering their progress in the logic course. More broadly, one’s refusal or inability to play the believing game risks hindering one’s progress as a thinker and as a human.
Does this mean that questions have no place in the believing game? I think not. But it does mean that we need to be able to ask questions that further the ends of the believing game. What is information eliciting such that it can bracket, not exacerbate, the impulse for answers?
I was going to finish with a series of questions for further exploration, but really, what I’d like to leave you with is an exhortation: try on the lenses of the believing game for a while. Try them on and try to look through them to a world in which our classes spend more effort on helping students play the believing game for themselves.
Note on Symbolic Logic
A Symbolic Logic class involves symbolizing natural-language sentences in a rigorously defined formal language. For instance, we can symbolize English “and” using the symbol “∧”. The resulting sentence is true in the truth-functional language if and only if it is flanked by true sentences (e.g. “ 𝑃 ∧ 𝑄” is true if and only if both “𝑃 ” and “𝑄 ” are true). That seems exactly right, because English “and” also seems to be true if and only if it is flanked by true sentences: “It’s raining and I forgot my umbrella” is true if and only if it is indeed true that it is raining and true that I forgot my umbrella. The material conditional, which can be symbolized as “→”, is an attempt to capture English “if… , then…”. There are various things that can seem counterintuitive about it, but in the text I focus on the fact that a false antecedent (the sentence before the arrow) yields a true conditional overall. So: “𝑃→𝑄” is true if “𝑃 ” is false, no matter what “𝑄 ” says. The problem is that this seems to give exactly the wrong verdict in some cases. Think back to some hot summer’s day. (You may not have to think far, depending on where and when you’re reading this). Consider the following claim about that day: If it snowed, then it was over 90 degrees. That seems false. How could it have been over 90 degrees if it snowed? But the corresponding symbolization turns out to be true. Let “𝑆 ” symbolize “It snowed” and “𝑂 ” symbolize “It was over 90 degrees”. Then “𝑆 → 𝑂” is true, because “𝑆 ” is false (it indeed did not snow on that hot day).
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