Section Progress:

3.3  Soundness and Premise Truth

It's time to return to our detective story. Raquel made this argument.

1. Quinn is innocent.
So:
2. There was false evidence in the file.

When she says some of the evidence is false, she is talking about the original evidence you gleaned from the file:

1. One or more of these people is guilty: Pia, Quinn and Raquel.
2. No one else was involved.
3. If Pia is guilty, so is Quinn.
4. Raquel never works alone.

She's saying that one of those claims must be false, because Quinn isn't guilty.

But this is confusing, because our original argument was valid too, which entailed that Quinn guilty.

So is he innocent or guilty? What is going on?

Here's the key realization that will clarify the situation: validity doesn't care about actual truth values.

Validity is a hypothetical or conditional property. It says what must be the case IF the premises are all true. But it says nothing about whether they are actually true or not.

Validity is not a matter of actual truth values.

This hypothetical nature of validity is easy to overlook, but it is essential to grasp in order to understand the concept.

Remember: validity concerns the structural relations between the premises and conclusion.

Truth, by contrast, concerns the relation between the premises and the facts in the world.

Truth concerns the relation between the premises and the world.

So if you learn that some argument is valid, you have no idea whether the premises are actually true or not.

There's key lesson here: validity is the fundamental concept of logic, but it's not the only thing that matters!

Two things matter in logic: validity and truth. This point is so important there's a name for it.

Sound = valid + true premises

We call an argument sound when it is valid and has true premises.

Try applying the idea: are the following arguments sound?

Now let's see if you can do some reasoning about the concept of soundness.

Soundness can help us understand what is going on with Raquel's testimony.

We have a valid argument that Quinn is guilty. But that doesn't mean he actually is guilty! We still need to know whether the premises are true.

We took the evidence in the file to be facts, but sometimes we're given incorrect information.

So when Raquel tells us Quinn is innocent, she's not disputing the validity of our argument; she's disputing the truth of the premises.

The first argument entails Quinn is guilty. The second argument entails there is false evidence. Both of those arguments can be valid. But they can't both be sound.

Let's see if you can explain why they can't both be sound. Drag one sentence into each container below to show the problem. Only drag the sentences you need to; leave the others in place.

Here's a final question to consider: if validity and truth both matter, why did we say that validity is the fundamental concept of logic? Why not say truth is?

Logic studies principles of reasoning that apply to any domain whatsoever: from physics to politics.

No matter how specialized the subject matter, we can use the tools of logic to evaluate the reasoning.

But we can't use the tools of logic to evaluate the truth of the premises: that's for the physicist and political analyst to figure out.

So truth matters to logic, but it isn't just up to logic to figure out the truth. That's where these other areas of knowledge come in.

But it is up to logic to tell us when an argument is valid or not, and mastering argument analysis and evaluation is one of the key skills you'll learn in this book.

3.3 Soundness and Premise Truth