One of the most difficult insights for students to grasp about the concepts of soundness and cogency is that they cannot always be determined. I have noticed that when students evaluate arguments they sometimes feel the need to state that an argument is sound or unsound, cogent or uncogent when they cannot possibly have any means of truly determining this. Let’s look at the concepts closer and try to understand why they sometimes cannot determined.
The definition of a sound argument is one that is valid and has true premises. A cogent argument is one that is strong, has true premises, and does not omit any premises that would entail a different conclusion from the one drawn in the argument. In deductive arguments that are valid, the determination that the argument is unsound simply means that the premises are false. In an inductive argument that is strong, the determination that the argument is uncogent simply means that the premises are false. Of course, an invalid argument is automatically judged unsound just as a weak argument is automatically uncogent.
With these parameters in mind let’s look at some examples.
Since Moby Dick was written by Shakespeare and Moby Dick is a science fiction novel, it follows that Shakespeare wrote a science fiction novel. In this deductive argument the premises (assumed true) necessarily entail that the conclusion is true so the argument is valid. Once we determine this we ask whether the premises are really true or false. In this example the premises are false so the argument is unsound. That should be easy enough.
But, consider this example. Since Agatha is the mother of Raquel and the sister of Tom, it follows that Tom is the uncle of Raquel. Again this is a valid argument so we need to determine (if possible) soundness. But, ask yourself the question: Are these premises really true? You might say yes, but how do you know? You might say we don’t know so the argument is unsound. But wait! Judging an argument unsound simply means that the premises are false. Do you know this to be the case either? No. Here is a case where the truth of the premises cannot be determined so soundness cannot be determined. What would be the proper answer to this question then? We would say it is deductive and valid but the soundness cannot be determined. Sometimes in logic “I don’t know” is the right answer!
This also occurs in inductive arguments. Consider this example. Coca-Cola is an extremely popular soft drink. Therefore, probably someone, somewhere is drinking a Coke right this minute. Assuming the premise is true the conclusion is probably also true so it is a strong argument. Now, is the premise really true? Sure. So, the argument is also cogent.
But what about this one? Harry will never be able to solve that difficult problem in advanced calculus in the limited time allowed. He has never studied anything beyond algebra and in that he earned on a C minus. Here is another strong argument since if we assume the premise is true (that he never studied anything beyond algebra and in that he earned on a C minus) the conclusion is probably also true. But, when it comes time to assess cogency we no longer assume the premise is true. We need to determine whether the premise really is true. Is it? Again, I would ask you to consider how you would know this. Do you know Harry? No. So, here is a case where cogency cannot be determined.
To this some students will reply: Well, then soundness and cogency can never really be determined. But, we’ve already seen examples where we can easily determine soundness and cogency so this is not the case. My only point is that there are arguments where the truth of the premises cannot be established. That is to say, no one could know whether they are true or false. Please note that this is different from the problem you may run into in some examples where you personally do not know whether the premises are true or false. If you personally do not know, that does not necessarily mean that soundness or cogency cannot be determined. It may simply mean that you cannot determine them. In practical terms, this may be a problem for you on the exam since I will expect that in cases where soundness or cogency can be determined, that you be able to determine it. A few examples may clarify this point.
Every map of the United States shows that Alabama is situated on the Pacific coast. Therefore, Alabama must be a western state. This inductive argument is strong since the conclusion follows from the premise assuming the premise is true. Is it a cogent argument? You may not know and so you may think the answer is that cogency cannot be determined. However, this is a case where cogency can be known (whether you know it or not). It is false that every map of the United States shows that Alabama is situated on the Pacific coast. In fact, it is quite likely that no maps show this (and you should know this as you should know where Alabama is really located!). So, this argument can be determined and is uncogent.
How about this one? The United States Congress has more members than there are days in the year. Therefore, at least two members of Congress have the same birthday. This deductive argument is valid since the conclusion necessarily follows from the truth of the premise. So, now we need to determine soundness. Can we? Yes. The premise is true so the argument is sound.
But, what is the difference between these examples and the ones above that were undetermined? Look at the example with Raquel and Tom. There is no reason anyone should be expected to know who these people are. How could you ever know this? This is why soundness cannot be determined. However, in the example about Congress it is clearly knowable by someone and I maintain it ought to be known by everyone in the class as an educated person.
So, please be aware of these issues as you work through section 1.4 in the text. Take care to note the cases where soundness and cogency can be determined but also be aware of cases where they cannot. In such cases recognize that there is no logical basis for making a determination of soundness or cogency and refrain from doing so.
