Systematic Philosophy

to know what can be known

What Is Soundness?

There are a few technical terms philosophers use to talk about the quality of an argument. One of these terms is “soundness”.

What soundness is

To say that an argument is “sound” is to say that that argument is valid and that all of its premises are true. That’s all. Is the argument valid? Are all of its premises true? If so, it is sound. If not, it is unsound.

Some examples

Let’s look at a few examples. First, consider this argument:

  1. All cats are animals.
  2. All animals are things.
  3. Therefore, all cats are things. [1,2]

First we check for validity. Is the argument valid? To be valid, all of the entailments the argument represents must actually hold. The argument represents the proposition <all cats are animals> and the proposition <all animals are things> as jointly entailing the conclusion <all cats are things>. This is the only entailment the argument represents, and those propositions actually do entail that conclusion. It follows that the argument is valid. Now we check for the truth of the premises. Are all cats animals? Yes. Are all animals things? Yes. So all of the premises are true. Thus the argument is valid and has only true premises. It follows that the argument is sound.

Now consider this argument:

  1. All cats are animals.
  2. All dogs are animals.
  3. Therefore, all cats are dogs. [1,2]

Again the first step is to check for validity. Is the argument valid? This argument represents the proposition <all cats are animals> and the proposition <all dogs are animals> as jointly entailing the conclusion <all cats are dogs>. But these propositions do not actually entail that conclusion. It follows that this argument is not valid. Because it is not valid, the argument is automatically unsound.

Lastly, consider this:

  1. All cows can fly.
  2. All things that can fly are triangular.
  3. Therefore, all cows are triangular. [1,2]

To check for soundness, we first check for validity. The argument is in fact valid, so we next check whether the premises are true. Can all cows fly? No. Are all things that can fly triangular? No. None of the premises of the argument are true. For it to be sound, all of the premises need to be true. It follows that while the argument is valid, it is unsound.

Why people care about soundness

If an argument is valid, then if its premises are true, its final conclusion must also be true. If an argument is sound, then it is valid and has only true premises. It follows that if an argument is sound, its final conclusion has to be true. In fact, if an argument is sound, then all of its steps have to be true.

If it is sound, all of its steps are true.

The fact that soundness guarantees truth has led many philosophers to conclude that a sound argument is the same thing as a good argument. This is not true. In fact, the relation between soundness and the quality of an argument is somewhat complex. It is true that in order to be flawless, an argument must be sound. But as we will discuss, it is also the case that some sound arguments are bad and some good arguments are unsound.

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Written by Geoff Anders

May 22, 2011 at 11:41 am

Posted in Uncategorized

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