Logic 101 · Philosophy · Series

Logic 101: Two Basic Types of Arguments

In my last post I discussed what arguments are and are not. Arguments are supported opinions, meaning some claims (premises) are used to support another claim or opinion (the conclusion).

But knowing what arguments are isn’t enough to be able to recognize them. We also have to be able to recognize what kind of argument is being put forward.

There are many different kinds of arguments. Each type of argument also comes with its own distinctive rules for determining whether it is a good one or not. For now I will only describe the two most basic kinds of arguments: deductive and inductive.

Deductive Arguments

An argument is deductive if its conclusion is guaranteed to be true if the premises are also true. This is another way of saying that there is no imaginable case where the premises are true and the conclusion is false. If we can’t imagine such a case, then the way the argument is arranged (or what “form” it takes) is said to be “valid” and is therefore deductive. Only deductive arguments are formally valid arguments.

As a side note, notice that the definition of valid that I’ve just given is not a synonym for “good.” Validity is a matter of truth-preservation in an argument. Whether or not a deductive argument is a good one is a different consideration altogether.

To see this difference, take a look at the following argument:

  1. Either God exists or 7+5=13.
  2. 7+5 does not equal 13.
  3. Therefore, God exists.

If premises (1) and (2) are both true, then it is impossible for (3) to be false. This means that the argument is formally valid. (I’ll explain the form this argument takes in a later post.) But is this a good argument? Not at all, seeing how the only reason you would accept (1) is if you already accept (3). In other words, the argument is already assuming what it needs to prove. That means that, even though this argument is valid, it is not a good argument.

By the way, if an argument is both valid and has premises that are true, we say that the argument is “sound.” 

Inductive Arguments

An argument is inductive if it is formally invalid. All inductive arguments have conclusions that could be false even if all of its premises are true. But this isn’t a strike against inductive arguments, seeing how they are the most common types of arguments we make. Most of our beliefs are based on inductive arguments.

Let’s consider another argument:

  1. If it is raining outside my home, then my front lawn is wet.
  2. It is not raining outside my home.
  3. Therefore, my front lawn is not wet.

Based on what I said at the beginning of both the last section and this one, do you think this argument is valid or invalid? Can you imagine a scenario where (1) and (2) are true, but (3) turns out false? Try to do this for a moment before you read on.

You’ve probably come up with more than one scenario that shows why this argument is invalid, but one is enough. The conclusion could fail to be true, for example, because it’s summer time and I’m running a lawn sprinkler. It is structurally invalid.

If I were giving this argument to you in person to assure you my front lawn wasn’t wet and really believed it wasn’t, then I would probably be assuming the truth a few things I didn’t state before. Any premise that is assumed and not explicitly stated when an argument is given is called a suppressed premise. Here’s a more convincing form of the original argument that includes some suppressed premises:

  1. If it is raining outside my home, then my front lawn is wet.
  2. It is not raining outside my home.
  3. I am not watering my lawn.
  4. I don’t have an automatic sprinkler system installed.
  5. None of my neighbors have ever watered my lawn for me.
  6. Therefore, probably, my front lawn is not wet.

The suppressed premises that I’ve listed here actually claim that several things are not the case. What I’m denying is that the scenarios you probably imagined a moment ago are true. These are called rebuttal premises because they answer potential objections to the original argument I gave you.

Since I’ve addressed the concerns we had about the original argument, I’ve given an inductive argument that is strong. I’ve given you good reasons to accept that the conclusion is probably true.

Summary

In this post I’ve illustrated the difference between two basic argument types. If an argument is intended to be formally valid, then it is deductive. If the argument is formally invalid, but with additional information provided may give us reason to believe that the conclusion is probably true, then the argument is inductive.

In the next post in this series I will begin to discuss the method that we will use to analyze arguments.

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