What is a sound argument example?

I used the following example as a sound argument but was marked incorrect. I can't determine where I went wrong.

Table of Contents Show

What is an Argument?
What is a Sound Argument?
What is an Unsound Argument?
Examples of Sound and Unsound Arguments
What is the Difference Between Sound and Unsound Argument?
Sound Arguments
Sound Argument Example

All criminal actions are illegal
All murder trials are criminal actions Therefore
All murder trials are illegal

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The key difference between sound and unsound argument is that a sound argument is valid and has true premises whereas an unsound argument is invalid and/or has at least one false premises.

Soundness is a technical feature of an argument. It helps us to determine whether the conclusion of an argument is true. Although many people assume that soundness refers to the validity of an argument, this is not so. A valid argument is not necessarily a sound argument. In fact, soundness of an argument is determined by two factors: validity and truth of the premises.

CONTENT

1. Overview and Key Difference
2. What is an Argument
3. What is a Sound Argument
4. What is an Unsound Argument
5. Side by Side Comparison – Sound vs Unsound Argument in Tabular Form
6. Summary

What is an Argument?

In the field of logic and philosophy, an argument is a series of statements intended to determine the degree of truth of another statement. Premises and conclusions are the building blocks of an argument. Premises are a series of statements that provide reasons or evidence to determine the truth of a conclusion. Therefore, an argument can have more than one premise. A conclusion in an argument is the main point the arguer is trying to prove. Thus, an argument has only one conclusion and one or more premises. Let’s look at an example:

Premise 1: No one under eighteen-years-old can vote. Premise 2: Rogan is under eighteen.

Conclusion: Therefore, Rogan cannot vote.

What is a Sound Argument?

An argument must fulfill two requirements in order to be considered as sound. One requirement is that the argument must be valid. An argument is valid when its conclusion follows logically from the premises. In other words, it is impossible for the premises of an argument to be true while the conclusion is false. The second requirement is that all its premises should be true. Thus, a sound argument is a valid argument that has true premises.

Figure 01: A Sound Argument

The following is a sound argument as it contains true premises and is valid.

All men are mortal. Socrates is a man.

Therefore, Socrates is mortal.

What is an Unsound Argument?

An unsound argument is the opposite of a sound argument. Thus, an unsound argument can be either valid or invalid. However, if the argument is valid, it has at least one false premise in order to consider it as an unsound argument.

Figure 02: An Unsound Argument

Examples of Sound and Unsound Arguments

Let’s look at some examples of sound and sound arguments now.

Example 1:

All multiples of 10 are multiples of 5. 20 is a multiple of 10.

Therefore, 20 is a multiple of 5.

It is a valid argument since the conclusion logically follows from the premises. Moreover, it has true premises. Therefore, this is a sound argument.

Example 2:

All cats are pink. Toffee is a cat.

Therefore, Toffee is pink.

The above is a valid argument too since the conclusion logically follows from the premises. However, the first premise is not true. Therefore, this is an unsound argument.

Example 3:

All cows are mammals. All dogs are mammals.

Therefore, dogs are cows.

The above argument contains true premises, but it is invalid since the conclusion doesn’t logically follow from the premises. Therefore, it is also an unsound argument.

What is the Difference Between Sound and Unsound Argument?

A sound argument is an argument that is valid and has true premises while an unsound argument is an argument that is invalid or has at least one false premises. Hence, this is the key difference between sound and unsound argument. Therefore, a sound argument always has true premises and true conclusions whereas an unsound argument may have both false and true premises and conclusions. Thus, this leads to another difference between sound and unsound argument.

The following infographic presents the difference between sound and unsound argument in brief.

Validity and the truth of the premises are the two factors that determine the soundness of an argument. A sound argument is an argument that is valid and has true premises while an unsound argument is an argument that is invalid or has at least one false premises. Thus, this is the key difference between sound and unsound argument.

Reference:

1. Wiki.lesswrong.com. (2019). Sound argument – Lesswrongwiki. [online] Available here.
2. En.wikipedia.org. (2019). Soundness. [online] Available here.
3. YouTube. (2019). What are ‘Valid and Sound?’ – Gentleman Thinker Available here.

Hasa is a BA graduate in the field of Humanities and is currently pursuing a Master's degree in the field of English language and literature. Her areas of interests include language, literature, linguistics and culture.

Validity and strength of arguments do not on their own tell us whether arguments are good or bad. We’ve actually seen rubbish arguments that were valid. That’s why we need to introduce two further concepts for arguments: being sound and being cogent.

So far we have talked about the kind of support that can be given for conclusions: deductive and non-deductive.

We defined an argument as being valid if it’s a deductive argument for which the premises succeed in providing conclusive support for the conclusion.

And we defined an argument as being strong if it’s a non-deductive argument in which the premises succeed in providing strong support for the conclusion.

By that, we mean that, if the premises are true, then the conclusion would be given the appropriate support for also being true.

But we haven’t said anything yet about whether the premises are true or not. This is what we do when we evaluate whether arguments are sound or cogent.

Sound Arguments

Definition: A sound argument is a valid argument that has true premises.

Firstly, a sound argument is a deductive argument. It’s trying to establish conclusive support for its conclusion. Secondly, the argument is valid: the premises, if true, would guarantee that the conclusion is also true. And on top of all that, the premises are actually true. Therefore, a sound argument guarantees that its conclusion is true.

We say that a sound argument is a good argument. It is a good argument because it guarantees that the conclusion is true. It would be irrational for you not to believe the conclusion of a sound argument.

Of course, sound arguments are very rare, because they’re very hard to establish. But, some arguments are sound.

Sound Argument Example

The province of Québec is part of Canada. Patrick was born in Québec. Therefore, Patrick was born in Canada.

This is a valid argument. Can you see why?

Furthermore, the premises are true: Québec is indeed part of Canada, and Patrick was indeed born in Québec. Hence, you can be absolutely certain that Patrick was born in Canada, and you ought to believe that Patrick was born in Canada. There’s no way around it.

I drank coffee this morning; therefore, I drank something this morning.

Patrick got married on January 4, 2014. Patrick has not been divorced and Patrick is not a widower. Therefore, Patrick is not a bachelor.

It is true that Patrick got married on January 4, 2014, that he has not divorced and that he is not a widower. So Patrick is not a bachelor because a bachelor is an unmarried male, by definition.

Now, what about non-deductive arguments? For non-deductive arguments, we introduce the notion of a cogent argument.

Definition: A cogent argument is a strong non-deductive argument that has true premises.

And again, we say that cogent arguments are good. A cogent argument is by definition non-deductive, which means that the premises are intended to establish probable (but not conclusive) support for the conclusion.

Furthermore, a cogent argument is strong, so the premises, if they were true, would succeed in providing probable support for the conclusion. And finally, the premises are actually true. So the conclusion indeed receives probable support.

Patrick was born in North America and Patrick wasn’t born in Mexico. It’s thus quite probable that Patrick was born in the USA.

That is a cogent argument. If all you know about Patrick is what’s contained in the premises, and those premises are true (they are!), then that’s a fairly strong argument, because the population of the USA is over 300 000 000, whereas that of Canada is under 40 000 000. This means that the odds that Patrick was born in the USA are roughly 88%, which makes the support for the conclusion quite strong. Furthermore, the premises are true. Therefore, the argument is cogent, and so it is a good argument.

This means that we can have good arguments that have false conclusions!

I had coffee this morning. Therefore, it’s quite likely that I drank something this morning.

This is a strong argument with true premises, so it is cogent and therefore, good. But the conclusion is not guaranteed. It may be that I had coffee this morning by eating it, or by some other means. But of course, this is very unlikely, so the argument is strong, though it’s still possible that the conclusion is false. Still, this is cogent and therefore, a good argument.