The Anatomy of an Argument

§1.2

As the term is used in philosophy, an argument is a set of related propositions (called premises) that is given as a reason for believing a further proposition (called the conclusion). Consider, for example, the following, simple argument:

Whoever murdered Carl had to have access to his rose garden at midnight, and the only person who did was Natalie, therefore Natalie must be the murderer.

Here the conclusion is that Natalie murdered Carl, and there are two premises: (1) that whoever murdered Carl had access to Carl’s rose garden at midnight, and (2) that only Natalie had such access.

There are a few ways in which we can represent an argument that make its structure clearer. One popular way is called standard form. Here’s what the argument we have been discussing looks like in standard form:

1. Whoever murdered Carl had access to his rose garden at midnight. 2. Only Natalie had access to Carl’s rose garden at midnight.

3. Natalie murdered Carl.

Each proposition has been written on its own line and labeled with a number. The premises are written first, and a line is drawn to separate them from the conclusion. This line represents the inference—the mental act of moving in thought from the premises to the conclusion.

You will occasionally find arguments written out in this way in some of the readings for this class. However, we will be making more use of a newer way of representing the structure of arguments, which is called “argument mapping.” Here’s a map of the argument we’ve been discussing.

Map 1:

In the map, each proposition is written in its own box and labeled with a number. The inference is represented by a green circle and labeled with a letter. Thin lines connect the circle to the boxes containing the premises, and a thicker line with an arrow at the end connects the circle to box containing the conclusion.1

Both of these ways of representing the argument are meant to make it easy to see that Propositions 1 and 2 combine to provide a reason to believe Proposition 3. Another way we can express this point is to say that Propositions 1 and 2, taken together, are meant to help us to tell that Proposition 3 is true.

Notice that neither of these propositions on its own provides any reason at all to think that Natalie murdered Carl. If someone had no idea that Natalie had access to Carl’s rose garden at midnight, then learning that the murderer had access to the garden at this time, wouldn’t give him any reason to suspect Natalie of the murder. Likewise, if someone had no idea that the murderer had access to the rose garden, then knowing that Natalie was the only one with access wouldn’t give him a reason to think she committed the murder. It’s only when we put the two propositions together that they give us a reason to believe the conclusion. This argument map represents this relationship by having the lines from the two premises meet at the circle representing the inference, and then having a single arrow go from the circle to the conclusion.