The Structure of Arguments

In my last few posts, I talked about clarifying the language of arguments. Now I want to talk look past the words and sentences, to examine the underlying scaffolding or structure of arguments. Arguments can take many forms and combine in different ways. For example, a conclusion for one argument can become a premise for another argument

Consider the following argument. 

“There’s a lot of snow in the mountains this winter. That means there will be a lot of snowmelt in the spring. So the rivers will be full in the spring and summer, and full rivers make for good kayaking. It’s going to be a great year for kayaking!”

One way to look at the structure of this argument is to make an argument map, which looks like the one on the right, with the conclusion at the top (this is arbitrary--some argument maps show the conclusion at the bottom). The map shows that this is what’s called a chain argument. Each premise supports a conclusion, which also functions as a premise in a further conclusion. 

Other arguments have a different structure. For example:

“I think Joe is short on money. He sold his kayak, and he’s been working a second job.”

Here, the two premises don’t connect in a series, as in a chain argument. Each supports the conclusion separately, so we can map it as a convergent argument. 

Sometimes, two or more premises have to work together to support a conclusion, because they can’t do it by themselves. We see this with the following syllogism:

P. All cats are predators.

P. Fluffy is a cat.

_________________

C. Fluffy is a predator.

Here the two premises are linked, because neither can support the conclusion alone. The first can’t support it because it says nothing about Fluffy, and the second can’t because it says nothing about predators. This kind of argument can be mapped by linking the premises together, as in the map below.

Oftentimes, when you find unstated premises, they combine with stated premises to form linked premises. In the argument above about Joe, there are actually two unstated premises: 1. If Joe is working a second job, he probably needs the money. 2. If Joe sold his kayak, he probably needs the money. So, we actually have two sets of linked premises, which then converge to support the conclusion that Joe is short on money. This means our argument map is now a combination of convergent and linked premises:

Another thing argument maps can show is objections. For example, Joe’s other friend could object to the premise that “Joe sold his kayak” by saying he didn’t actually sell it, and then support his objection with a premise like “He left it at Lisa’s house.” Objections can contradict a premise, or they can contradict a conclusion directly. For example, someone could object directly to the conclusion by pointing out that Joe just bought a new computer, which suggests that he has money. But then you can object to objections, perhaps by pointing out that the computer was a gift. An objection to an objection is called a rebuttal. All this can turn into a complex, branching tree of arguments, sub-arguments, objections and rebuttals, as in the argument map below, with objections shown in red, and rebuttals shown in orange.

So what’s the point of all this mapping? While there’s no need to do all this with every argument you see, mapping arguments is useful for at least two reasons. First, it makes the underlying structure of the argument clear, which helps in evaluating it. Second, it helps to keep track of all the premises, arguments, and objections, and to review they fit together. Think about a long debate thread on a social media site. Even if all the contributors are using crystal-clear language and stating arguments (not just naked claims), it can be hard to keep track of what points have been made, and what reasons and objections have been made to them. An argument map can show at a glance how the argument unfolded. Like a map of a city, it gives an overview of the terrain being covered. 

One thing to keep in mind is that a map like this could represent two people debating a question, or it could represent a single person debating with himself. And debating with yourself is a good thing to do (as long as you don’t do it out loud in public) because as we’ve discussed in previous chapters, it’s as important to question your own reasoning as the reasoning of others. It’s important to think of objections to our own ideas, because confirmation bias makes it easier to think of supporting evidence than contradictory evidence. If the argument map above does show a single person’s reasoning, then he’s putting some real thought into whether his friend Joe is short of money. He’s not just jumping to that conclusion. 

In fact, “Joe is short of money” doesn’t necessarily have to be considered a firm conclusion. It could also be seen as a contention, a hypothesis, or an issue under debate. If you’re putting forward a firm conclusion in order to convince someone to accept it, you’re making a persuasive argument. But if you’re trying to decide what conclusion is best supported by the premises and objections at hand, then you’re using logical arguments as a means of reasoning. While making arguments for a position is a good skill to have, reasoning is a higher goal. That’s an important thing to remember. Critical thinking isn’t about defending arguments--it’s about evaluating them. It’s not about casting around to find support for your pre-existing conclusions. It’s about deciding what conclusions really are supported.