Let’s talk about logic for a moment. When you hear the word argument, you may think of a heated exchange of opinions. It’s emotional and angry. A logician would call this a quarrel rather than an argument. In the world of logic, an argument means that you offer reasons to support a conclusion.
An argument can be valid or invalid and sound or unsound. Here’s an example of an argument in a classic form:
Premise 1: All women have freckles.
Premise 2: Suellen is a woman.
Conclusion: Suellen has freckles.
We have two reasons that lead us to a conclusion. In other words, it’s an argument. Is it a good argument? Well, that’s a different question.
Let’s look first at validity. An argument is valid if the conclusion flows logically from the premises. In this case, we have a major premise and a minor premise and – if they are true – the conclusion is inescapable. Suellen must have freckles. The conclusion flows logically from the premises. The argument is valid.
But is the argument sound? An argument is sound if the premises are verifiably true. The second premise is verifiably true – Suellen is indeed a woman. But the first premise is not verifiably true. All we have to do is look around. We’ll quickly realize that the first premise is false – not all women have freckles.
So, the argument is valid but unsound. One of the premises that leads to the conclusion is false. Can we safely assume, then, that the conclusion is also false? Not so fast, bub.
This is what’s known as the fallacy of fallacies. We often assume that, if there’s a fallacy in an argument, then the conclusion must necessarily be false. Not so. It means the conclusion is not proven. The fact that something is not proven doesn’t necessarily mean that it’s false. (Indeed, in technical terms, we’ve never proven that smoking causes cancer in humans).
Our example demonstrates the fallacy of fallacies. We agree that the argument is valid but not sound. One of the premises is false. Yet, if you know Suellen, you know that the conclusion is true. She does indeed have freckles. So even an unsound (or invalid) argument can result in a conclusion that’s true.
What’s the moral here? There’s a big difference between not proven and not true. Something that’s not proven may well be true. That’s when you want to consider Pascal’s Wager.