Lecture Notes: Symbolic Logic

By Joe Linstroth / Illustration by David Vogin

Not a day goes by that we don’t hear, make, or assess arguments. From political punditry and advertising campaigns to social media feeds and dinner-table banter, arguments come at us from seemingly everywhere. Often, the ones that resonate most are those that align with how we feel. But how we feel is separate from whether an argument is factually correct. So how can we avoid being taken for a ride? Philosophy professor Janet Folina and her “Introduction to Symbolic Logic” course offer tools to help us sift through the rhetorical cacophony.

There’s a tendency to judge an argument’s effectiveness based on how persuasive it is, but being persuasive isn’t the same thing as being correct. Can you talk about the difference?

When I think about an argument’s persuasiveness, that’s a psychological property. It’s descriptive: When are we, in fact, persuaded or convinced?

What logic gets at is whether we are right to be convinced. It’s not descriptive; it’s not psychological; it’s normative. What logic studies is the correctness of an argument. Logic helps us get past what resonates with us—what we like to hear—to focus on what’s rational and correct.

What types of arguments come to mind that are really persuasive but incorrect?

I think we’ve all witnessed one type of persuasive pattern: repetition. If someone says something ten times, our brains are induced into recognizing the pattern and we may think, “It’s got to be true, right?”

Another example is when someone speaks with authority, which can also be very convincing psychologically.

Then there are fallacies like a misplaced appeal to authority. For example, a toothpaste ad featuring a football player: A football player is not an expert on dental health, yet somehow we’re persuaded because of the star power.

Another troubling one is when we’re persuaded to quickly make a general conclusion. So, someone might say, “Well, I haven’t been vaccinated and I haven’t gotten sick, so I don’t need to be vaccinated.” That’s a fallacy illustrated by the “donkey example”: I haven’t fed my donkey for five days, and he’s fine; after thirty days, he’s still fine. But on the thirty-first day, the donkey dies. Sometimes we can be too quick to leap to a conclusion.

So where does symbolic logic come in?

There are many ways to correct our psychological bad habits. One is to just be more critical in general. Another is through symbolic logic, which helps us to step back and think about the format of an argument—for example, merely distinguishing between an assumption and a conclusion can help. Symbolic logic can make us more cautious about argumentation because of its focus on structural properties. It takes the content and emotion out of the equation, so if you’re just looking at the form of the argument, it allows you to be critical of what you already believe and wary of accepting what other people say.

How would you describe what symbolic logic is?

Put simply, it’s a fun, puzzle-solving activity that studies the forms of correct arguments. It improves our critical reading and writing skills, which helps us be more objective and less psychologically confused. We use symbols to focus on those forms just like we use numerals to do arithmetic. The symbols make it more efficient to study arguments, because when you’re studying the forms, every argument of that form is going to have the same properties. Finding your way from the premises to the conclusion is like finding the best way to navigate to the top of a climbing wall.

How did you develop your interest in logic?

Kind of by accident, but it changed my life. I was a math and religious studies major as an undergrad. When I studied abroad at St. Andrews University in Scotland, I couldn’t find a math class that fit, so I took logic. Someone asked me: “Why don’t you come back and do a masters?” My first response was, “Why would I do that?” Then I thought, “Huh. I really like this stuff.” So I went back to St. Andrews for my master’s degree, and that’s how I discovered philosophy and my career.

What advice would you give to help others avoid being deceived by a poor argument?

Don’t believe everything. Be skeptical and bring a critical lens to the things that people tell you. Consult real authorities on issues, not just those who speak with authority or act like they have it. It’s important to step back, pause, and evaluate, because I think people are responsible for their own beliefs. Some people say, “Well, I have the right to believe whatever I want,” and that’s ridiculous because beliefs have consequences. Your beliefs determine what you do, and what you do has consequences that affect other people. We have a responsibility to try to believe the truth, and logic can help.