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Contexts and Contest: Propositional (i.e., Sentential) Logic as a Method of Asking Narrow & Focused Questions
Contexts and Contest: Propositional (i.e., Sentential) Logic as a Method of Asking Narrow & Focused Questions

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At the start of every term, I always tell students that my aim is to have them leave class with more questions than answers. As a student, philosophy encouraged me to ask questions that I otherwise never felt I had . . .

At the start of every term, I always tell students that my aim is to have them leave class with more questions than answers. As a student, philosophy encouraged me to ask questions that I otherwise never felt I had the opportunity to ask. And asking these questions often brought more questions. These questions often ended up being abstract and enticing in a way that questions from other courses weren’t. These questions seemed foundational, urgent, and personal. To make sure that the questions my students are leaving with are similarly foundational, urgent, and personal, I try to structure my courses and assignments around skill development. In particular, the skill I try to help them develop is the skill of asking narrow and focused questions about themselves and their relationships (in the broadest sense of the term—e.g., their belonging or opposition to: friends and family, people of the same and different political or religious affiliations, different countries of origin, species, “nature,” ecosystems, etc.).

Philosophy courses aren’t—or at least shouldn’t be—focused on a canon of texts or providing students with content that is to be memorized for some further end. Courses should be focused on skill development and methodology. Focusing on question-skills is a way of helping students to better interrogate and understand the ideas that are important to them (as opposed to trying to give them ideas or questions that we think should be important to them). What’s learned are skills or skill sets that have the potential to help students better understand themselves, their surroundings, and their relationships with their surroundings. I want to help provide this opportunity to students.

Where I teach—West Chester University—has a similar demographic and structure as where I went to undergrad—University of Minnesota Duluth. Both universities are state schools with a predominantly white student population, both universities place a heavy emphasis on teaching, and both universities tend to attract students who prefer to stay in-state and, for a variety of reasons, don’t want to attend one of the larger universities in their respective areas. As such, I feel like I can relate to my students in ways that I wouldn’t be able to at universities where the demographics of the student population are drastically different than my experiences (in terms of socioeconomic standing, levels of education, college-readiness, etc.). This connection with my students, I feel, helps me understand their needs and experiences (to some extent).

Since I have a 4/4 teaching load, and most of those courses are introductory courses, most of the students who take my courses are, more often than not, just trying to satisfy some general education requirements. Given the wide array of life aims, job prospects, ambitions, eagerness to take an ethics course, work ethics, etc., of the students in these courses, I want to be sure to market the course as something that will be beneficial for everyone. To do this, I tell my students that one of my main aims in teaching is to get them to slow down when thinking. This is mainly because slow, careful thinking allows us to identify beliefs or assumptions—in ourselves and others—that we may otherwise not recognize (and, hence, not be able to challenge). This kind of slow, careful, philosophical thinking allows us to ask more focused and poignant questions.

While asking broad or rhetorical questions (e.g., “Why?”) can help students to discover aspects about themselves and their relationships, I find that focusing on the development of question-skills can be a more efficient way of reaching these points. That’s not to say that I don’t encourage or appreciate, or even engage students with, those big, broad questions, but I find it useful to structure courses around asking narrow, focused, or poignant questions. This is primarily because, as V.F. Cordova states, “[i]deas… exist in a context… [and] to fully understand an idea and its implications and ramifications it becomes necessary to understand the context” (p. 54).

Cordova was one of the first two Native American/American Indian women to receive her PhD in philosophy (along with Anne Waters) in 1992. She was a member of the Jicarilla Apache tribe and received her PhD from the University of New Mexico. She was partly responsible for the creation of the APA’s Committee on Native American and Indigenous Philosophers, as well as APA Studies on Native American and Indigenous Philosophy (which she co-edited from its beginning until her death in 2002). Her work is currently archived at the University of New Mexico, and it has been incredibly influential to myself and my Indigenous colleagues.

Following V.F. Cordova, I take philosophy to be “the study of ideas.” Not particular ideas, but ideas in the broadest possible sense of the term. This conception of philosophy helps to explain why we have fields like philosophy of biology, political philosophy, philosophy of disability, etc. These fields seem to be a mix of content and skill. The content comes from their field of study, while the skill is a kind of philosophical question-skill. What makes them areas of philosophy is that they are studying the ideas that are born of, or occur in, a particular field of study.

While Cordova was talking about ideas being shaped by, and developed out of, our cultures, relations, surroundings, etc., I tried to implement this lesson by utilizing a tool of Western philosophy—propositional logic. Studying ideas requires understanding, or at least engaging with, the contexts in which ideas are developed. That being the case, asking questions that are too broad or too general encourages ignoring these contexts. Broad questions (e.g., “What is the meaning of life?”) can be great at producing ideas that are thought-provoking, illustrative, or otherwise engaging, and general (i.e., unfocused) questions (e.g., just asking “Why?”) can be great at helping students to see connections between ideas. However, these kinds of questions can also encourage us to think of our responses as being more general, broad, or universal than they actually are. In other words, they ignore the contexts in which we find ourselves and in which our thinking is already occurring.

This being the case, I focus on question-skills by trying to get students to ask very focused, specific, or narrow questions. The most efficient way I’ve found of doing this is to structure my courses and assignments around propositional (i.e., sentential) logic. While I value logic as a course in its own right, the reason that I focus on propositional logic in other philosophy courses is because I find that it helps students to ask more focused, productive questions. It makes explicit the context of ideas.

After covering the basics of propositional logic (e.g., validity, soundness, premises, objections, etc.), looking at the arguments allows us to ask specific questions about ideas that are important in the context of particular discussions (e.g., abortion, eating meat, trans-rights, etc.), thereby bring those contexts—and contextual thinking—to the fore. To cover the basics of propositional logic, in the first week of a course, I tell students that there are only two ways of disagreeing with an argument. You can either disagree with the structure (i.e., show the argument is invalid) or, if it’s valid and you still disagree, you can disagree with the content (i.e., show the argument’s unsound). Anything outside of this doesn’t technically qualify as a “disagreement.” Then, we discuss how you would formally disagree with an argument—i.e., how you would show an argument is either invalid or unsound. You show an argument’s invalid by coming up with a counterexample—a situation where all the premises are true, yet the conclusion is false (this is why thought experiments are great), and you show an argument is unsound by coming up with a counterargument—an argument where your conclusion is the direct denial or refutation of one of the premises of the argument with which you’re disagreeing. This helps to narrow the focus for students on specific ideas as they pertain to the topic of discussion instead of getting bogged down in ideas that are abstracted from a context.

This also allows for a more productive and efficient way for students to disagree with one another in discussions. In class, we can use contemporary issues as examples that spawn or highlight disagreements between students. Putting arguments on the board regarding, e.g., abortion, eating non-human animals, ambivalence towards poverty and famine, etc., allows us to more efficiently understand how or why students agree or disagree with the argument. If they disagree, then they’re asked to identify which particular premise they’re trying to refute (assuming the argument’s valid). If they want to show the argument’s poorly structured, then they’re asked to provide a counterexample to show it’s invalid. In the course of these discussions, I encourage students to do the same with each other (often in small groups): if someone disagrees with their argument, ask them if they think the structure’s faulty or if they disagree with one of the premises; if the structure’s faulty, ask if they can provide a counterexample; if they disagree with a premise, ask which one, and whether they have a counterargument. This still provides students with an opportunity to emphasize considerations they take to be important, but it helps to provide them with a structured discussion and a structure for thinking about how these considerations fit into a broader context (i.e., an argument). Instead of disagreements spanning an array of considerations regarding a particular topic, discussions centered on propositional logic allow us to focus on particular claims or ideas (i.e., premises). This is often much more engaging and inviting than asking broad questions and receiving a battering of responses that are either unrelated or the relation isn’t clear.

For example, consider the following questions about abortion:

• Is abortion morally permissible?

• Does limiting abortion infringe on a pregnant person’s bodily autonomy?

• At what point, if ever, do fetuses have “moral standing”?

Asking students these kinds of questions can lead students to provide their beliefs about these questions as well as a battering of reasons for their beliefs, but it doesn’t help to explain the connections between those reasons or beliefs. Instead of asking students these questions, getting students to produce or address arguments concerning abortion (in propositional form) helps them to more efficiently find either points of contention or connection. I assume that’s partly because it either provides students with a context in which the idea is being used or discussed, or it merely makes explicit the context in which an idea is already occurring.

Instead of talking broadly about abortion—a situation where we often ignore context (e.g., details, relationships, consequences, etc.)—we can present students with specific arguments as a way of getting them to ask how ideas are related or connected to one another. Consider the following arguments:

1. Killing innocent people is wrong.
2. Abortion kills an innocent person.
Therefore, abortion is wrong.
And 1. Restricting access to abortion violates a pregnant person’s bodily autonomy.
2. A pregnant person’s bodily autonomy shouldn’t be violated.
Therefore, we shouldn’t restrict access to abortion  

With these arguments, we can talk about whether killing innocent people is wrong and how that idea relates to abortion. We can talk about what makes someone or something a ‘person’ and how that relates to the idea of innocence. We can talk about whether restricting access to abortion violates a pregnant person’s bodily autonomy and what, if any, are the limits of bodily autonomy. We can discuss whether it’s possible to believe both arguments (and what it would take to believe both). Most importantly, we can talk about how all of this is relevant in the context of arguments (i.e., discussions) about abortion.

With regards to the basics of propositional logic, in discussions, I would first ask students to determine whether the arguments are valid (i.e., are they able to come up with a counterexample). If they’re valid, then we move on to asking whether they agree with each of the premises. For each of the premises: what’s their support for thinking each of the premises is true? If they don’t, what’s their argument against the premise(s)?

Asking students how they would disagree with these arguments provides them with practice at focusing on specific points of contention (rather than just focusing on the fact that they have a belief that is different from the one in the conclusion of the argument). Instead of asking themselves whether they think abortion is morally permissible, they’re encouraged to ask things like, “Would abortion be morally impermissible if killing innocent people wasn’t always wrong?” Now they’re asking about a particular relationship (i.e., a context) between particular ideas.

Asking them about the structure of an argument (how the ideas in that argument relate to one another) or about specific premises of an argument is a more efficient way of getting them to see how their ideas relate to one another. The drawback of this focus is that students aren’t encouraged to find these kinds of questions themselves. This I take to be a benefit of asking broad, general questions, so I still think there’s a place and benefit for those kinds of questions. My hope and aim are to show that there’s a benefit of asking very specific, narrow, focused questions, and propositional logic can help us do that. The benefit is that using propositional logic can help us see the relationships between ideas by providing a context in which ideas are occurring.

It’s incredibly challenging to bring Indigenous philosophy into Western classrooms and courses in a respectful and effective manner. My hope is that focusing on skill development (e.g., question-skills) as opposed to content, and encouraging students to leave with more questions than they had when they arrived, will help to challenge the idea that philosophy is a Western endeavor or that philosophy can only be done—or was only done—by men of certain cultures. By trying to merge Native American philosophy and Western philosophy through the use of propositional logic, my hope is that students come to better appreciate the complexity of not only their own ideas and their own lives but that they come to appreciate the complexity of trying to understand the ideas and lives of others. And hopefully, this will help to encourage more patience and humility.

While I have only started doing this recently, I’ve so far found that it’s also helped students to focus on skill development if I explain why our assignments and discussions are focused on propositional logic (i.e., if I explain my motivations). Typically, what I’ve done is ask students to consider how difficult it can be to answer broad, open-ended questions—this can be done by asking them, as a class, a broad question (e.g., “what do you all think about the death penalty?”), then asking them what, if anything, they found challenging about answering this question (since this is also a broad, open-ended question, it may help to ask more leading questions, e.g., “Was this difficult to answer because we’re in a group?”, “Was this difficult to answer because you don’t feel like you know enough about the death penalty to answer?”, etc.). Then, I can demonstrate how focusing on argument structure can help us to have a more focused and productive dialogue. Putting a simple argument about the death penalty on the board, I can ask students if they agree with the premises (and, if so, how they would justify each premise) or disagree with the premises (and, if so, how would they object to the premise(s)). Doing these kinds of metacognitive activities with the students helps to demonstrate the benefits of studying propositional logic, but it also helps them to see how ideas exist within a context, and if we’re attentive to that context, we can have more productive, respectful discussions and further our understanding of ourselves and others.

The post Contexts and Contest: Propositional (i.e., Sentential) Logic as a Method of Asking Narrow & Focused Questions first appeared on Blog of the APA.

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