### Validity and Soundness

The terms, “validity,” and, “soundness,” can only properly be applied to deductive arguments. It is a category error to say that an inductive argument is valid or invalid, or that it is sound or unsound.

The certainty we expect from deductive arguments means that the relation between the premises and the conclusion must be so tight that *the truth of the premises guarantees the truth of the conclusion.* With inductive arguments, *the truth of the premises only makes the truth of the conclusion likely*, and that is not a tight enough relation for certainty!

So, just remember that only deductive arguments can be valid or sound!

### Validity

A valid argument is not like a valid driver license. The term, “valid,” when it is applied to arguments refers to a specific relationship between the premises and the conclusion. There are a number of ways of stating this relationship, but these various ways all mean the same thing:

*** If all the premises are true, then the conclusion must be true.**

*** The truth of the premises guarantees the truth of the conclusion.**

*** It is impossible for all the premises to be true and the conclusion false in the same scenario.**

Of these three ways of stating the idea of validity, we will use the third. That is because the third way of defining validity most *carefully* expresses the idea that the relation between premises and conclusion is a hypothetical relation! To really understand this, we must consider the notion of a scenario.

### Scenarios

A scenario is just a way the world could be. It is just a possible state of affairs. For example, it might be raining, or it might not be raining. It might be 100 degrees outside, or it might not. It might be 100 degrees and raining, or it might be 100 degrees and I own a white, Ford Escape. A scenario is just a possible state of affairs, a possible way the world could be.

The way a scenario comes into play when we consider validity is this: Imagine some scenario that would make all the premises of an argument true. Then, hold that scenario fixed and ask yourself this question: “Is there *any* way in this scenario that the conclusion could *possibly* be false?”* If there is any possibility of the conclusion being false in the scenario in which all the premises are true, then the argument is invalid.*

If it is *impossible* for the conclusion to be false in any scenario that makes all of the premises true, then the argument is valid. For a valid argument it is *impossible* for all of the premises to be true and the conclusion false in the same scenario.

So, validity guarantees the truth of the conclusion in any scenario in which the premises are true. But… this is a hypothetical relation, because there is no guarantee that any of the scenarios are the actual, present, real-world scenario! Here is an example:

**1) If it’s raining, then the streets are wet.**

**2) It is raining.**

**——————–**

**3) The streets are wet.**

Imagine any scenario in which it is raining. That scenario makes the second premise true. Imagine that in that same scenario the first premises is also true, because (as in the real world) rain makes the streets wet. So, now we have a scenario in which all of the premises are true. Notice that in that scenario the conclusion also must be true! In fact, you *cannot* dream up a scenario in which both of the premises are true and yet the conclusion is false in that same scenario. So, this argument is valid.

However, none of those scenarios you dream up are the same scenario as the present, real-world scenario is (at least for me, here, right now). As I dream up these various scenarios, all of them fail to reflect the present real world, because where I am right now as I write this, it is not raining. The present, real-world scenario for me has the second premise false.

*For validity, we don’t care about the present, real-world scenario!* There is nothing special about that scenario when we consider validity. Validity is merely a *hypothetical* relation between the premises and the conclusion: Is there any scenario in which the premises could be true and the conclusion false? If there can be such a scenario, then the argument is invalid. If there cannot be such a scenario, then the argument is valid.

So, in a valid argument, we know that for any state of affairs that would make all of the premises true, in that same state of affairs the conclusion would have to be true. *Validity merely establishes this hypothetical relation between the premises and the conclusion, ensuring that the truth of the conclusive is guaranteed from the truth of the premises.*

### Soundness

Once we know that an argument is valid, then we can ask the next question about the argument: Are all the premises *actually* true in the present, real-world scenario? A sound argument must be valid *and* all of the premises must actually be true in the real world. Soundness has two parts: validity and actual truth (of the premises).

Remember that when we consider validity, the present, real-world scenario is just one of many; it doesn’t have any special place in our thinking. But for soundness, we must also consider the present, real-world truth of the premises. So, for that we care *entirely* about the present, real-world scenario! The present, real-world scenario tells us whether or not the premises are in fact actually true.

So, a sound argument is a valid argument that has all true premises.

### Form vs. Content

We can now distinguish the notions of validity and soundness in another very important way: validity is about the *form* of an argument, while soundness adds a concern about its *content*.

Validity is a *formal* relation between premises and conclusion, where present, real-world truth is not a consideration. Soundness assumes validity and concerns itself with present, real-world truth. To assess validity, you don’t really need to know what the premises and conclusion even mean (the form of the argument can be symbolized)! But we must know what the premises and conclusion are really saying, what they mean, to know if they are true in the real world.

So, validity is a formal, hypothetical relation between premises and conclusion, while soundness concerns truth!