Nuts and Bolts 009: Validity and Soundness

nuts and bolts Philosophy

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“You make a valid point.” Have you ever heard anyone say this? When people say this they probably mean something like “you make a good point,” but when you enter the world of philosophy, you realise that the word “valid” is reserved for a different purpose. Similarly, in everyday speech when someone says “He has convinced me, because he made a valid argument,” they probably mean that someone has made a convincing argument. But in logic, the fact that an argument is valid certainly doesn’t indicate that it’s persuasive – or even good.

Logical Validity

To say that an argument is logically valid is not to say anything at all about the truth of the claims made in an argument. Validity has to do with the form of an argument, rather than its content. A valid argument is one in which the conclusion logically follows from its premises. In other words, in a valid argument the conclusion of an argument would be true if the premises are true, because the conclusion gets its truth from the premises. Another way of putting this is to say that the conclusion is somehow “contained in” the premises. An example would be:

  1. If something is square, then it has four sides.
  2. Q is a square.
  3. Therefore Q has four sides.

The conclusion that Q has four sides clearly follows from the two premises. It is contained in the premises in the sense that Q and the property of having four sides are in the premises, and the fact that Q meets a condition for having four sides can be seen by reflecting on the premises. To understand them clearly is to grant the conclusion. Another way of referring to validity in this sense is deductive validity, since we are deducing the conclusion from the premises.

Notice that validity doesn’t establish anything in regard to truth. An argument can be valid even if its conclusion is obviously incorrect. For example:

  1. If the sky is blue, then Donald Duck is the president of the USA.
  2. The sky is blue.
  3. Therefore Donald Duck is the president of the USA.

The argument is perfectly valid, since the conclusion does follow from the premises in the sense described earlier. But since the first premise is absurd, the conclusion is not true.

Soundness

Validity is necessary for a good deductive argument, but as seen in the Donald Duck example, it’s not enough. What an argument really needs is to be sound. A sound argument is a valid argument where all the premises are actually true, and so the conclusion doesn’t just follow from the premises, it’s also true.

Take a fairly uncontroversial example:

  1. If a substance is composed of H2O then it is water.
  2. The substance in lake Taupo is composed of H2O.
  3. Therefore the substance in lake Taupo is water.

Or a more controversial example, which I regard as equally sound:

  1. Whatever begins to exist has a cause of its existence.
  2. The universe began to exist.
  3. Therefore the universe had a cause of its existence.

Of course, in a disagreement with another person, it’s not enough to just have a sound argument to persuade them. You’ve got to be able to show them that the argument really is sound by showing that the premises are true and that the conclusion follows. I can’t help you with that.

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