The Inductive/Deductive Distinction

As mentioned in the last post ("So What Makes an Argument Good?"), the two main criteria for the success of an argument are that 1. the premises are true and 2. that the truth of the conclusion follows from the premises. However, what does it mean for the truth of the conclusion to "follow from" the premises?

There are two primary ways to think of this 'follow from' relationship:
1. They provide good evidence that the conclusion is true.
2. They prove that the conclusion is true.

The first of these is the goal of what we call inductive reasoning; the second is the goal of deductive reasoning. Whether or not the arguments succeed at these intentions is another story, but those are the goals. Accordingly, here are the definitions that we are using:

• An an inductive argument is one in which the premises are intended to provide good evidence for the truth of the conclusion. 
• A deductive argument is one in which the premises are intended to guarantee the truth of the conclusion. 

Here is an example of each:
Inductive: "Every dog I have ever had likes to eat bread. Therefore your dog probably will like to eat bread as well."
Deductive: "All dogs like to eat bread. Rover is a dog. Therefore, Rover likes to eat bread."

We don't know whether the premises are true in each case, but we do know that if the premises are true in the inductive example, then there is evidence that the conclusion is true. And in the deductive example, we know that if the premises are true, then the conclusion must be true. This leads to another important distinction:

• An inductive argument that succeeds in its intention: one that provides good evidence that the conclusion is true, is called strong. 
• A deductive argument that succeeds in its intention: one whose premises, if true, would guarantee the truth of the conclusion is called valid. 

Inductive strength is a matter of degree; An argument is strong according to the degree to which the premises make the conclusion likely to be true. Deductive validity is not a matter of degree. If there is any possible way that the premises could be true and the conclusion false, then the argument is invalid. 

Here is an example: "I left my key under the welcome mat. My laptop is gone now. Mike was the only one I told about the key. Therefore, Mike must have stolen my laptop."

This argument is invalid for at least a couple of reasons: The laptop could have been misplaced, or someone else might have found the key (even though they weren't told about it). As long as there is any possibility that all of the premises could be true and the conclusion false, we know that the premises don't guarantee the truth of the conclusion, so the argument is invalid.

One more important note: This distinction has nothing to do with whether the premises are actually true. An argument can be strong or valid even with false premises. The distinction above is based on whether the conclusion would be true if the premises were true. This leads to one more important distinction:

• An inductive argument that is strong and has all true premises is called cogent. 
• An argument that is valid and has all true premises is called sound. 

For example, this argument is strong but not cogent: "A random sampling of a million dogs shows that 99% are green. Therefore, most dogs are green."

This argument is not cogent because the premise is false; but it is strong because if it were true, then the conclusion would probably be true as well.

This argument is valid but not sound: "All dogs are green. Rover is a dog. Therefore, Rover is green."

This argument is not sound because the first premise is false. But it is valid because if both premises were true, then the conclusion would have to be true as well.

There will be more about strength and validity in future posts.