Introduction: soundness and cogency

We’ve already talked about how to evaluate the structure of an argument. This involves thinking about what kind of connection there is between the premises and the conclusion. The terms we have used for talking about the structure of arguments are valid and invalid (for deductive arguments) and strong (for non-deductive arguments).

There is more to a good argument than validity or strength, however. A valid or strong argument might have premises that you know to be false – in that case you definitely shouldn’t believe the conclusion on the basis of the premises, in spite of the validity or strength of the argument. A good argument, as well as being valid or strong, must also have all true premises. When you are deciding whether you should be persuaded by an argument, you need to think about whether it is sound (if it is a deductive argument) or cogent (in the case of a non-deductive argument).

Some definitions:

A sound argument is an argument that is valid and that has all true premises.

A cogent argument is an argument that is strong and that has all true premises.

In this chapter we are going to talk about how to assess whether the premises of an argument are true.

Remember: to be sound, an argument has to be both valid and have true premises.

We already know how to assess the validity or strength of an argument. So in order to determine whether an argument is sound or cogent, we need to rule on whether its premises are true.

It is common for people to shy away from making a firm determination of the truth value of a statement. People say things like “it’s just an opinion”, or “there isn’t really one truth”. Assessing the truth of statements is a necessary task in argument assessment, and it’s important to make an effort to do it.

Is there such a thing as truth?

A statement is true if it describes the world as the world is, and false if it describes things differently from the way the world is. That is a common-sense account of truth, and it is the one we will be using in this course.

Some statements are true in a totally uncontroversial way.

Squares have four sides

is  true.

Some statements are equally straightforwardly false.

Squares have three sides.

No matter how forcefully the arguer asserts this, it is simply false.

Some statements are true at some times and false at others. That doesn’t stop them from being true or false, in just means that sometimes the world changes, and that will affect the truth of claims about the world. Consider this claim:

Joe Biden is the President of the United States.

At the time of writing, this statement is true. At some time in the future it will be false. This feature of the statement does not stop it being true at the moment.

This way that the truth of claims can change transfers into the soundness or cogency of arguments in which they occur. So,

P1) Joe Biden is the President of the United States.
P2) Joe Biden is a man.
                                          
C) The President of the United States is a man.

is a sound argument. At the point at which Joe Biden ceases to be the President of the United States, it will cease to be a sound argument.

Some statements are obviously true. Some, although they are not controversial, you will need to look up, or do some sort of investigation to establish as true or false.

If you needed to look up the answer to the question, that is fine. You’re not expected to know everything already.

​Sometimes it seems difficult to assess the truth of a statement. Consider

It is raining.

Someone might claim this is true now, but false tomorrow, or true in Hamilton but not in Auckland.

The difficulty here is not created by truth, but by the way the statement is put. Generally, when someone says “it is raining” what they mean is “It is raining here, at the moment”. (It would be very strange to say “It is raining”, and then say “Oh, I meant it is raining in Thunder Bay, Ontario”. That would be to miscommunicate.) We could make such statements more specific (by always including reference to time and place). But it would be tedious to do so, so we don’t. It is still either true or false that it is raining here, at the moment.

Sometimes, it is not possible to establish the truth or falsity of a statement. Sometimes, even after research, it remains controversial. When that happens, you may need to suspend judgement on the truth of the statement, and so also on the soundness or cogency of the argument. ​It is important, however, to not give up too soon when it comes to assessing truth. You are giving up too soon if you find yourself saying “who really knows?” to just about everything.

There is a philosophical position which involves doubting the truth of nearly everything. It is known as ‘scepticism’. Note that even sceptics live their lives as if a whole lot of ordinary claims are true. You may adopt the position of scepticism if you choose, but for the purposes of assessing the soundness and cogency of everyday arguments it’s important to take a more everyday approach to truth.

​Some propositions are more difficult to assess than others. It is important to not simply give up and throw your hands in the air in horror. Pause, and think carefully.

Consider the statement

Most of the people reading this textbook are enrolled in a course.

Is this true?

When considering its truth value you might start by noting that most people in the world are not enrolled in any sort of course. So if it’s true, it needs to be something special about people who read this textbook.

We can also note that it is not the case that all people who read the textbook are enrolled in a course. I have read it, for instance, but I’m not enrolled in any course.

If you’re reading this textbook because it’s assigned for the course, then you know that it is true that at least some people reading it are enrolled in a course. But how do you work out if it is true that most people who read it are enrolled in a course?

The answer is that you should think carefully about whether it is likely to be true. It is possible that this textbook has secretly become some sort of bestseller, and that lots people are reading it for fun. But it’s not very likely. Generally speaking, people read textbooks to help them with some particular course. The number of people who read textbooks for recreational purposes is fairly small, and this textbook is less accessible than many, because you can’t walk into an ordinary bookshop and purchase it. So, having weighed all that up, it seems to me that the statement is likely to be true.

Determining truth is not always easy, but it is possible, and it is important.

Cogent arguments and false conclusions

With a deductively valid argument, the truth of the premises guarantees the truth of the conclusion. That means that a valid argument with true premises must have a true conclusion. This makes sound arguments particularly useful.

With non-deductive arguments, the relationship between the premises and the conclusion is different. In a strong argument, the truth of the premises makes the conclusion likely, but stops short of guaranteeing it. One consequence of this is that it is possible to have a cogent argument with a false conclusion.

Consider the following argument:

P1. Nearly all of the presidents of the United States have been white men.
                                                       
[Probably] C. The 44th president of the United States was a white man.

This is a strong argument: the truth of the premise does not guarantee the truth of the conclusion, but it does make it very likely. There is no problem with the form of the argument.

The premise is true. (There have been 46 US presidents, and 45 of them have been white men.)

Since we have a strong argument with true premises, this argument is cogent.

Note, however, that the 44th president of the United States was Barack Obama. He is not a white man. So this is a cogent argument with a false conclusion.

We can make this even more explicit:

​P1. 45 of the 46 presidents of the United States have been white men.
P2. Barack Obama was the 44th president of the United States.
                                                       
[Probably] C. Barack Obama was a white man.

This argument is still a cogent argument.

This is merely a consequence of the way cogency has been defined. Any strong argument with true premises will be a cogent argument even if the conclusion is false.

This means that there is an extra step when assessing cogent arguments than there is with sound arguments. With a sound argument, the truth of the conclusion is guaranteed, and does not need to be independently assessed. With a cogent argument, once the argument has been established as cogent it’s a good idea to consider whether you have any additional reason for thinking that the conclusion is false. It isn’t common, but sometimes there will be some additional information you possess which shows you that the conclusion is false. This won’t stop the argument from being cogent (because that is determined by the definition of cogency), but it does deserve to be commented on. It is a relevant piece of assessment for cogent arguments.