1.7: Validity and Soundness

The idea of a valid argument is one of the most important concepts in critical thinking, so you should make sure you fully understand this topic. Basically, a valid argument is one where the premises entail the conclusion. What this means is that if the premises are true, the conclusion must also be true. So here is a valid argument with two premises and a conclusion:

• Moby Dick is a whale.
• All whales have fins.
• So, Moby Dick has fins.

This is another argument with just one premise and a conclusion:

• Barbie is 90 years old.
• So Barbie is older than 20.

In both of these arguments, if the premises are all true, there is no way that the conclusion will be false. So the arguments are indeed valid. Notice that the validity of the argument does not depend on whether the premise is in fact true. Consider the second argument above. Even if Barbie is actually only a ten-year-old, the argument is still valid. Validity only requires that when the premises are true, so is the conclusion. It depends only on the logical connection between the premises and the conclusion. It does not depend on their actual truth or falsity. A valid argument can have false premises and a false conclusion. A valid argument can also have a false premise but a true conclusion, as when Barbie is 30 years old.

This, however, is not a valid argument. It is invalid:

• Barbie is older than 20.
• So, Barbie is over 90 years old.

The argument is not valid because it is possible that the premise is true and the conclusion is false. For example, Barbie could be 21. Or she could be 80. These situations are counterexamples to the argument. Basically, a valid argument is an argument with no possible counterexamples.To sharpen your skills in evaluating arguments, it is important that you are able to discover and construct counterexamples. Giving a counterexample can help you convince other people that a certain argument is mistaken.

There are a few important points worth remembering:

• An invalid argument can have true premises and a true conclusion. In the previous argument, both the premise and the conclusion are true if Barbie is 99 years old. But remember that true premises and a true conclusion are not sufficient for validity, because the logical connection between them is missing. This means that an argument with true premises and conclusion can still be a bad argument.
• Notice that we are making a distinction between truth and validity. Statements (the premises and the conclusion) can be true or false, but they are not valid or invalid. Arguments might be valid or invalid, but they should never be described as true or false.
• It is possible to have a valid argument where the premises are false but the conclusion is true. Validity only guarantees that when you start with true premises, you end up with a conclusion that is true. So we should never say things like your assumptions are false, so even if you reasoning is logical your conclusion cannot be true.

Soundness

Given a valid argument, all we know is that if the premises are true, so is the conclusion. But validity does not tell us whether the premises or the conclusion are true or not. If an argument is valid, and all the premises are true, then it is a sound argument. Of course, it follows from such a definition that a sound argument must also have a true conclusion.

In discussion, it would be nice if we can provide sound arguments to support an opinion. This means showing that our argument is valid, and that all the premises are true. Anyone who disagree would have to show that not all the premises are true, or the argument is not valid, or both.

To improve critical thinking, these are good habits to cultivate when it comes to argument analysis:

• Identify clearly the premises of an argument. Can we state the assumptions clearly?
• Check whether the assumptions are true or not.
• Evaluate the validity of the argument. Even if the premises are true, the logical reasoning of the argument can still be quite bad. The evaluation of the premises and the reasoning are two separate tasks.
• When arguing for a certain conclusion, always see if you can find more than one argument to support it. This would make your case more convincing. Being able to count the number of arguments in support of a position is an important thinking skill.

Hidden assumptions

When people give arguments sometimes certain assumptions are left implicit. Example:

• It is wrong to create animals with human DNA because it is unnatural.

This argument as it stands is not valid. Someone who gives such an argument presumably has in mind the hidden assumption that whatever that is unnatural is wrong. It is only when this assumption is added that the argument becomes valid.

Once this is pointed out, we can ask whether it is justified. We might argue for example,that there are plenty of things that are unnatural but are not usually regarded as wrong (e.g.cosmetic surgery, going to the Moon, contraception, etc). Pointing out the hidden assumption in an argument can help resolve or clarify the issues involved in a dispute.

In everyday life, many arguments have important hidden assumptions which have not been made explicit. It is part of good critical thinking to be able to identify these assumptions. One way to do this is to see what additional premises are needed to add to an argument to make it valid.