3. Valid vs Invalid Arguments

An argument has to satisfy the Logic Condition in order for it to qualify as a good argument. But there are two importantly different ways in which an argument can satisfy the Logic Condition.

One way is if the argument is valid. Another way is if the argument is strong.

"Validity" and "strength" are technical terms that logicians and philosophers use to describe the logical "glue" that binds premises and conclusions together. Valid arguments have the strongest logical glue possible.

In this lecture we're going to talk about "validity" and the difference between "valid" versus "invalid" arguments. In the next lecture we'll talk about "strength" and the difference between "strong" versus "weak" arguments.

Together, these two concepts, validity and strength, will help us to specify precisely what it means for an argument to satisfy the Logic Condition.

Valid vs Invalid

We've seen valid arguments before. Recall the Tom Cruise argument:

1. All actors are robots.
2. Tom Cruise is an actor.
Therefore, Tom Cruise is a robot.

This is an example of a valid argument.

Here's the standard definition of a valid argument:

An argument is VALID if it has the following hypothetical or conditional property:

IF all the premises are true, then the conclusion CANNOT be false.

In this case we know that in fact the first premise is false (not all actors are robots) but the argument is still valid because IF the premises were true it would be IMPOSSIBLE for the conclusion to be false.

In other words, in a hypothetical world where all actors are robots, and Tom Cruise also happens to be an actor, then it's logically impossible for Tom Cruise NOT to be a robot.

THAT is the distinctive property of this argument that we're pointing to when we call it “valid” — that it's logically impossible for the premises to be true and the conclusion false. Or to put it another way, the truth of the premises guarantees the truth of the conclusion.

These are all different ways of saying the same thing. Validity is the strongest possible logical glue you can have between premises and conclusion.

Here's an example of an INVALID argument:

1. All actors are robots.
2. Tom Cruise is a robot.
Therefore, Tom Cruise is an actor.

The first premise is the same, "All actors are robots". But the second premise is different. Instead of assuming that Tom Cruise is an actor, we're assuming that Tom Cruise is a robot.

Now, if these premises are both true, does it follow that Tom Cruise HAS to be an actor? No, it does not follow. It would follow if we said that ONLY actors are robots, but the first premise doesn't say that.

All we can assume is that in this hypothetical world, anyone in the acting profession is a robot, but robots might be doing lots of different jobs besides acting. They might be mechanics or teachers or politicians or whatever. So in this hypothetical world the fact that Tom Cruise is a robot doesn't guarantee that he's also an actor.

And THAT is what makes this an invalid argument.

An argument is INVALID just in case it's NOT VALID.

What this means is that even if all the premises are true, it's still possible for the conclusion to be false. The truth of the premises doesn't guarantee the truth of the conclusion.

That's ALL it means to call an argument "invalid".

In particular, it doesn't imply that the argument is bad. As we'll see in the next lecture, invalid arguments can still be good arguments. Even if they don't guarantee the conclusion they can still give us good reasons to believe the conclusion, so they can still satisfy the Logic Condition.

But like I said, we'll talk more about this later.

A Cautionary Note About the Terminology

I'll end with a cautionary note about this terminology.

We're using the terms "valid" and "invalid" in a very specific technical sense that is commonly used in logic and philosophy but not so common outside of these fields.

As we all know in ordinary language the word "valid" is used in a bunch of different ways. Like when we say "that contract is valid", meaning something like the contract is “legally legitimate” or that it's “executed with proper legal authority”.

Or when we say "You make a valid point", we mean that the point is “relevant” or “appropriate”, or it has some justification behind it.

These are perfectly acceptable uses of the term "valid". But I just want to emphasize that this isn't how we're using the term in logic when we're doing argument analysis. It's important to keep the various meanings of "valid" and "invalid" distinct so there's no confusion.

Note for example that when we use the terms valid and invalid in logic we're talking about properties of whole arguments, not of individual claims.

If we're using the terms in the way we've defined them in this tutorial then it makes NO SENSE to say that an individual premise or claim is valid or invalid.

Validity is a property that describes the logical relationship between premises and conclusions. It's a feature of arguments taken as a whole. Still, it's very common for students who are new to logic to confuse the various senses of valid and invalid, and make the mistake of describing a premise as invalid when what they mean is simply that it's false or dubious.

So that's just a cautionary note about the terminology. If you keep the logical definition clear in your mind then you shouldn't have a problem.