Key Concepts: Validity And Soundness

Validity and soundness are features of inferences, or derivatively, arguments. So, for example, we say that the following inference is valid:

1. All men are mortal;

2. Socrates is a man;

3. Therefore Socrates is mortal

The first two lines are premises. They are the claims that we are reasoning from. The word `therefore' signals that we are making an inference. The final line is the conclusion. This is arrived at via the inference.

An inference is valid if and only if the conclusion cannot be false if the premises are true.

Alternatively, you might like to think of the truth of the premises guaranteeing the truth of the conclusion.

The important thing to note about this definition is that it does not require that the premises are true. So, for example, the following is a valid inference.

1. All men are donkeys;

2. Socrates is a man;

3. Therefore Socrates is a donkey.

It is valid despite the fact that the first premise is false.

An inference is sound when it is valid and the premises are true. So, we see, our first inference was not only valid but also sound. Our second inference was valid only.

Quick Exercises:

a) Formulate a valid argument that is not sound.

b) Formulate an argument that is valid and sound.

c) Formulate an argument that is neither valid nor sound.