Complex Arguments 1

Chapter 1, Tutorial 4
Complex Arguments and Tree Diagrams

In this tutorial, we look at arguments that are slightly more complicated and more realistic. It's best to see what's in store with an example.

Dark chocolate not only tastes great but is healthy.

So, we have an argument. Let's give it our standard diagram:

Dark chocolate tastes great (to many humans).
Dark chocolate is healthy (for humans).
Dark chocolate is a good food (for humans).

But, if you're thinking rather than just salivating, you might wonder:

Why on earth would anyone think that dark chocolate is healthy? So, we need to give reasons to believe premise two: Not only does the conclusion need reasons, but so does a premise. Hence, we need another argument; here's one that's popular as of 2006:

Dark chocolate is loaded with health-promoting polyphenols -- anti-oxidants that may help lower blood pressure and promote vascular health. Cocoa has more polyphenols than red wine or green tea. So, dark chocolate is a superfood that contributes to long-term health. (Source: Source: San Jose Mercury News.)

So...

Let's oversimplify the reasoning for the moment as this:

Dark chocolate is loaded with health-promoting polyphenols.
So, dark chocolate is healthy (for humans).

Hmm...but now we have two arguments. They are interconnected: the conclusion of the second argument is the same thing as the second premise of the first! But it's hard to see the connection with these standard diagrams. This thinking just begs for a tree diagram!

Let's start with the second argument. It's tree diagram should look like this:

There's only the one premise and the arrow shows how it's supposed to lead to the conclusion.

Next, the other argument gives two independent reasons for the conclusion that dark chocolate is good for us:

Dark chocolate tastes great (to many humans).
Dark chocolate is healthy (for humans).
Dark chocolate is a good food (for humans).

These two reasons are independent because either, standing alone, would give its reason for the conclusion. We draw such independent reasoning with a single arrow.

So, the above can be tree-diagrammed as:

Now, notice that these two diagrams have something in common: the area with blue highlight. The conclusion of the first tree diagram is a premise of the second tree diagram. We can put the two together.

This tree diagram shows the different ways the evidence leads to the conclusion.

OK?

Let's look at some of the basics of these more complex tree diagrams. To get started, which of the following arguments have premises that independently support the conclusion?