Mapping the Relations Between Arguments

Our thinking isn’t usually made up of single, isolated arguments, but of complex sets of interrelated arguments. And argument mapping helps us to visualize and understand these relations. In this section we’ll consider how the argument we looked at earlier concerning Natalie might be related to other arguments. Before we do that, let’s review the simple map of that argument and get clear on how we are going to refer to each of its parts.

Map1

Each box contains a numbered proposition. We’ll refer to them as “Proposition 1,” “Proposition 2,” and “Proposition 3.” The green circle represents the act of inference, and we’ll refer to it as “Inference A.” We’ll use the phrase “Argument A” to refer to the whole argument, which includes the inference, along with its premises and the conclusion.

With this terminology under our belts we can look at and discuss more complex maps that show relations between arguments.

One way in which arguments can be related is by sharing the same conclusion. Here’s an example:

Map 1:

Argument B has the same conclusion as Argument A. They are two distinct arguments because they give separate reasons for believing the conclusion. To see that the reasons are separate, pick one of the premises from either argument, and think about what other premises you would need to combine it with before it would give you a reason to think that Natalie murdered Carl. You will see that in order for Proposition 1 to convince you that Natalie murdered Carl, you would need to also know Proposition 2, but that you wouldn’t need to know Propositions 4, 5, or 6. Likewise, in order for Proposition 5 to convince you, you’d need to also know Propositions 4 and 6, but not Propositions 1 or 2.

A second way arguments can be related is that a premise of one argument can be the conclusion of another. Here’s an example of that:

Map 1:

Notice that Argument A (from Map 1) is part of this larger map. One of its premises is now the conclusion of another argument, labeled C. So, we can think of C and A taken together as a larger, two-step argument for Proposition 3.

Now let’s consider a larger map that includes all the arguments we’ve looked at plus two others.

Map 1:

Argument D is a third argument for Proposition 3. I expect you’ll agree that it a bad argument. We will discuss what makes some arguments better than others in the next section.

Inference E is represented by a red circle instead of the usual green one because Argument E is an argument against proposition 3, rather than for it. The conclusion of the Argument E is “Natalie did not murder Carl.” We could write this out as its own proposition in a separate box, but since this conclusion is equivalent to saying that Proposition 3 is false, it’s nice to have a way to relate Argument E to Proposition 3 on the map. That’s what we use the red circle for. It helps us to see at a glance that Argument E is arguing against the very same conclusion that Arguments A, B, and D are arguing for.

The point of an argument is to help us tell what’s true. So, if we end up in a situation where we have arguments with opposite conclusions as we do in Map 4, then there must be something wrong with at least one of the arguments. Let’s turn now to the things that can go wrong with arguments, and why some arguments are better than others.