Section Progress:

2.1  First Weird Case of Validity

You can learn a lot about something by seeing how it behaves in extreme conditions.

Want to know if steel is a good building material for a bridge? You'd better know how it behaves in extreme heat or cold.

We'll do the same for validity, by seeing how it behaves in unusual situations.

Let's start with this argument:

1. The Sergeant is a Martian.
Thus:
2. The Sergeant is a Martian.

Circular reasoning is a type of extreme case: the premise and the conclusion are the same thing.

It strikes us as suspicious--we realize there is something odd about reasoning in a circle.  But notice the following: if the premise is true, so is the conclusion.

Weird case #1: Circular reasoning is valid.

Consequently, all circular reasoning is valid.

If that makes validity seem like an odd concept, you're right. But don't discount it because of that.

The quirky features of validity are part of what make it powerful. We'll see the utility of validity once we start proving that arguments are valid or invalid. Our goal here is just to understand the concept and how it applies to difficult cases.

Circular reasoning: Assuming what you are trying to prove.

Circular reasoning doesn't just occur when one sentence is both the premise and conclusion. Circular reasoning is any case of assuming what you are trying to prove, even if it's put in slightly different terms.

Let's practice the idea.

Now, don't misunderstand the point that circular reasoning is valid: we're not telling you to start reasoning like this in your life.

You won't convince anyone to believe that the moon is made of green cheese by pointing out that it follows from the premise that the moon is made of green cheese.

Circular reasoning is often called a fallacy, which is the name for tempting but flawed forms of reasoning.

Fallacy: A tempting but flawed form of reasoning.

Circular reasoning is often flawed. But we want you to understand exactly why that is. Now you know it isn't flawed because it's invalid.

Furthermore, there are some circumstances in which it's not actually bad at all.

Imagine that someone doesn't understand what a fallacy is, and you are trying to demonstrate to them that George committed one. Then you might reason in a way that the premise just restates the conclusion, but in a more illuminating way, such as this:

1. George's reasoning was tempting but flawed.
So:
2. George committed a fallacy.

This counts as circular reasoning. We are basically assuming what we are trying to prove, since a fallacy is flawed reasoning by definition. But if someone didn't grasp that, then this argument might actually be helpful.

Whether circular reasoning is good or bad depends on the circumstances one is in.

The point is that whether a case of circular reasoning counts as bad partly depends on the circumstances one is in. Specifically, if someone understands the premise better than the conclusion, circular reasoning can be good.

Circular reasoning is problematic, by contrast, when someone rejects the premise just as much as the conclusion. Because then it can't be helpful in persuading your audience; it could only be helpful in tricking or manipulating them.

Learning about circular reasoning might seem like an abstract academic exercise, but it can actually help us understand some of the most contentious debates in current society.

For example, it's not uncommon to hear arguments like this:

1. Abortion is the killing of an innocent life.
So:
2. Abortion is murder.

Or:

1. Abortion is not the killing of an innocent life.
So:
2. Abortion is not murder.

Even though these arguments are diametrically opposed, from a structural point of view they are similar. Both of them are circular: they assume their conclusion in slightly different words.

Here's what you have to figure out:

Both sides of this debate know what abortion is in the medical sense--what kind of procedure it is--and they know what murder is.

That's why neither of these arguments is going to convince someone who is skeptical of the conclusion.

Try the test for problematic circularity: for these arguments, would someone disagree with the premise just as much as they do the conclusion? I think the answer is yes, which is why neither of these arguments is particularly helpful.

Studying unusual cases of logic might seem like an abstract exercise, but it can give us a better understanding of important current debates.

If these arguments are not productive ways to argue about difficult moral topics, you might be wondering, then what are productive ways?

Later in the book we'll answer that question. We just need to build more skills before we get there.

2.1 First Weird Case of Validity