Understanding the Difference Between Validity and Soundness in Deductive Reasoning

When it comes to logical arguments, terms like 'valid' and 'sound' are often used. But what exactly do they mean, and how do they differ? Let's break down the concept of validity and soundness using deductive reasoning and explore both valid and sound arguments, as well as an invalid one, for clarity.

What is a Valid Argument?

An argument is considered valid when the premises logically lead to the conclusion. In other words, the premises must be such that if they are true, then the conclusion must also be true. This is what we mean by 'necessary' - the premises must logically guarantee the conclusion. It is important to note that the premises themselves don’t have to be true, but as long as they are, the argument is valid.

A Famous Example of a Valid Argument

Consider the following example:

Premise 1: All humans are mortal.

Premise 2: Socrates is a human.

Conclusion: Therefore, Socrates is mortal.

This argument is valid because if it is true that all humans are mortal (Premise 1), then everyone who is a human must be mortal. Given that Socrates is a human (Premise 2), what is true of humans must also be true of Socrates, making the conclusion logically follow from the premises.

What is a Sound Argument?

A sound argument, similar to a valid one, also guarantees the conclusion. However, a sound argument has an additional requirement: its premises must actually be true. Therefore, not only does the argument guarantee the conclusion, but it also starts with true premises. The conclusion of a sound argument is therefore also true.

An Example of a Sound Argument

Here’s an example of a sound argument:

Premise 1: By definition, a premise is a proposition that serves as the foundation for a conclusion and is either true or false.

Premise 2: A sound argument by definition is one that is valid and ensures the conclusion is true.

Conclusion: Therefore, a sound argument guarantees a true conclusion supported by true premises.

In this example, both premises are true by definition, and therefore the conclusion logically follows, making the argument sound.

The Importance of True Premises

While a valid argument only requires the truth of the conclusion if the premises are true, a sound argument insists that the premises themselves are true. This distinction is crucial because the soundness of an argument is the result of a combination of both validity and the truth of its premises.

Let's delve into why this is important by examining a more complex argument:

The Difficulty in Claiming Soundness

A famous example based on inductive reasoning is the soundness of the first premise in the Socrates argument:

Premise 1: All humans are mortal (based on inductive reasoning).

Premise 2: Socrates is a human (an actual fact).

Even though the first premise is highly likely to be true, inductive reasoning does not provide necessary truth. This is where David Hume’s skeptical argument comes into play, emphasizing that what might be true based on observation or inductive reasoning does not equate to necessary truth.

Conclusion

In summary, while a valid argument only requires the logical connection between premises and conclusion, a sound argument demands that both the premises and the connection are true. This is essential for any argument to be considered strong and reliable. Understanding the difference between these concepts helps in constructing and evaluating logical arguments more effectively.

Bonus: An invalid argument occurs when the premises do not guarantee the conclusion. For instance, take the following:

Premise 1: All cats are mortal.

Premise 2: Socrates is a philosopher.

Conclusion: Therefore, Socrates is mortal.

Even if all premises and the conclusion are true, the argument is invalid because we cannot infer that Socrates is mortal from the fact that all cats are mortal or from the fact that Socrates is a philosopher.