Irrelevant premises

Now we’ll talk about irrelevant premises, and that’s a tricky subject. It’s tricky because it’s difficult to decide when a premise is irrelevant. The impact that irrelevant premises can have on arguments also varies. Sometimes, it makes the argument bad. Sometimes, it doesn’t do any damage. Some arguments may be good even though they have irrelevant premises, and some are bad because they only have irrelevant premises. But first, what do we mean by an irrelevant premise? A premise in an argument is irrelevant if the truth or falsity of the premise has no bearing whatsoever on the question of whether or not the conclusion is true. Let’s see some examples of arguments that have irrelevant premises.

Willi is my cat, and she’s agreed to take part in this video. Willi is a cat. All cats like to hide in boxes. Some dogs also like to hide in boxes, therefore Willi likes to hide in boxes. This argument is valid. If all the premises are true, then the conclusion must also be true. The argument is still valid if we remove the third premise. Some dogs like to hide in boxes is probably true, but it offers no support for the conclusion. Being present doesn’t make the argument valid, and the argument is still valid even if we remove it. The third premise does no proper work in the argument.

Contrast this with the following argument about buildings here in Auckland. The Sky Tower is taller than the Vero building. The Vero building is taller than the Metropolis. Therefore, the Sky Tower is taller than the Metropolis. The argument is sound. It’s valid, and both its premises are true. And the premises are relevant to the conclusion. If you remove either premise, the argument becomes invalid. For instance, the Sky Tower is taller than the Vero building, therefore the Sky Tower is taller than the Metropolis. Hence, for deductive arguments, a premise is relevant if removing it makes a valid argument invalid. But what happens to valid arguments when they have irrelevant premises?

Let’s try the same example again, but this time, we’ll add an irrelevant premise. The Sky Tower is taller than the Vero building. The Vero building is taller than the Metropolis. The Metropolis is on the moon. Therefore, the Sky Tower is taller than the Metropolis. The third premise is irrelevant. If you remove it, the argument is still valid. But it’s false, so strictly speaking, the argument is not sound. As you can see, irrelevant premises do not make arguments bad by making them invalid. They make them bad when they are false. So what should you do with irrelevant premises? Apply the principle of charity and remove them from the argument. Call this, pruning an argument.

[FOOTSTEPS] For non-deductive arguments, the idea is pretty much the same. A premise is irrelevant if having it in the argument does not make it stronger and removing it from the argument does not make it weaker. We’ll use this theatre as an example. Here at the Maidment theatre at the University of Auckland, there is limited wheelchair access. Row H in the stalls, as indicated on the seating plan, has space for wheelchairs. Please contact our box office, and we will book these seats for you. The circle is not wheelchair accessible. Consider the following argument. All theatre-goers should be treated equally. All theatre-goers should have equal access to the circle. The best views from the theatre are from the circle.

The circle does not have wheelchair access. Therefore, probably, wheelchair users don’t have access to the best views in the theatre. The argument is strong. However, the same conclusion is equally supported from all but the first two premises. Remove P1 and P2, and the argument is just as good. The conclusion says that wheelchair users don’t have access to the best views, but it doesn’t say if this is a good or a bad thing. P1 and P2 are about how theatre-goers should be treated, not about whether they all have access to the best views. If you prune the argument, you will be left with– the best views are from the circle. The circle does not have wheelchair access.

Therefore, probably, wheelchair users don’t have access to the best views in the theatre. And the cogency of the argument is no longer threatened by the first two premises. A debate about them would also be pointless, because they are irrelevant. Finally, irrelevant premises are sometimes the main culprit of logical and critical thinking mistakes, and they have their own fallacies. You might want to revise the ad hominem and red herring fallacies before you proceed.