Wednesday, 18 April 2012

Soundness, validity, and life on Mars

In philosophy, an argument is valid if it is not possible that all the premises be true and the conclusion false. The following is the paradigm (often repeated) of a valid argument:
  1. All men are mortal
  2. Socrates is a man
  3. Therefore, Socrates is mortal.
(1) and (2) are the premises, and (3) is the conclusion. In this argument, it is not possible that both premises be true, and the conclusion false. Therefore, the argument is valid. However, validity has nothing to do with the actual truth of the premises or the conclusion - it is to do with how the conclusion (whatever it is) relates to the premises.
Validity by itself is not enough for an argument to be convincing. An argument also has to be sound. To be sound, an argument has to be valid, and in addition all its premises must be true. Whilst the above argument is valid, it is debatable whether it is also sound. Maybe we’d trivially disagree with premise (2), for example, and say that Socrates was a man, rather than is. If we disagree with a premise, we needn’t be committed to the argument’s conclusion. Soundness is therefore often a matter of judgment, whereas validity is not.
So to be convincing (i.e. a good argument), an argument must be valid, and it must also be sound. However, if an argument is valid, then that doesn’t mean that it has the potential to be sound. Consider:
  1. I have a black cat
  2. I don’t have a black cat
  3. Therefore, there is life on Mars.
This is a valid argument (believe it or not). Remember that to be valid, it must be impossible that both premises are true and the conclusion false. This argument satisfies that definition, since it is impossible that both premises be true full stop, as they are contradictory. This yields what is sometimes called 'the principle of explosion' - the fact that (in classical logic at least), a contradiction logically entails every proposition. Needless to say though, only a complete nutcase would take this as proof that there exists life on Mars!
Philosophers are understandably wary of contradictions. By thinking about such cases, we can be more careful about using words like ‘valid’ as a means of persuasion in everyday conversation. Hooray!


  1. This seems to be an arbitrary, and insufficient, definition of validity. Your definition of validity lacks any requirement for the conclusion to be a logical consequence of the premises.

    A more precise definition could require that, a) the truth of the premises entail the truth of the conclusion, and b) the premises be logically consistent. With this definition, your black cat - mars example is rendered invalid, which is more intuitively satisfying.

    Indeed this is the definition of validity endorsed by wikipedia.

  2. Wikipedia's definition is consistent with what I have said, Martin. A contradiction entails every proposition: .

    So the conclusions of the second argument do entail the premise.

    I have not come up with this definition of validity myself - its the one commonly used. I should say that 'valid' used here is a technical term, used in logic. It is used to mean something more like 'generally persuasive argument' in everyday talk, but as I have suggested, this is misleading.

  3. My bad. Don't be silly - wrap your willy.

  4. "So the conclusions of the second argument do entail the premise."

    Obviously I meant the other way around. Premises entail the conclusion.

    And wise words, Amis, wise words.

  5. That is absurd. I enjoy philosophy but logic has never been my thing.

    Thanks so much for correcting the mistake on my blog. I have updated the Oriel post. Sorry to be slow to respond; I've been offline.


Blog Directory
BLOG DIRECTORY, Submit blog free, Promote Blog, Best directory