Diagramming Arguments

When the diagramming technique described in this section was first developed, many people saw it as a more flexible substitute for propositional logic. That’s what I thought when I started using it. However, I have come to believe that all of the basic components of diagramming can be effectively translated into propositional logic. Nevertheless, I think diagramming is an important supplement to logic, because it provides a streamlined way of mapping long and complex arguments that would be very difficult to map with horseshoes and wedges. In this section, I will be making connections between diagramming and propositional logic. You may not need to understand the relationship between diagramming and propositional logic to master the skill of diagramming. However, seeing this relationship will give you a deeper understanding of both systems.

Suppose someone argues that Sam will win the race because he has better endurance than the other contestants. Written as a modus ponens, the argument would look like this.

E= Sam has better endurance than the other contestants

W=Sam will win the race

Using the diagramming technique, we would write this argument this way.

1)Sam will win the race because 2)Sam has better endurance than the other contestants.

The propositions are now symbolized by numbers instead of letters, except for the proposition “if E then W”, which is “symbolized” by the line that connects (1) and (2). You can see that with this simplified notation, it becomes much easier to map longer and more complicated arguments. The notation with the standard logical operators functions rather like microscope, enabling you to focus precisely on one logical connection at a time. That’s very useful when you’ve finally found the weak spot in an argument and want to explain in detail why it is a weak spot. The diagramming technique operates more like a macroscope, (if there were such a thing). It gives you a sense of the overall structure of long complex arguments, enabling you to see the forest instead of just the trees.

There is one other basic building block used when diagramming arguments. Sometimes a conclusion is supported by what are called conjoint premises. These are premises which rely on each other to support a conclusion, and which by themselves provide little or no support for the conclusion. Let’s expand our argument a bit further to show how conjoint premises work.