Truth Value

Consider the following perfectly valid argument: 

  1. Premise One: All books are made of concrete. 
  2. Premise Two: All concrete items are used to make food. 
  3. Conclusion: Therefore, books are food. 

Something fishy here? Obviously, it would be quite difficult to imagine that the premises are true. It is not hard, though, to see that IF they were true, the conclusion would be true by necessity. Not all good arguments, therefore, are true then. 

So what do you mean by "valid" and what is "soundness"? Validity refers to the argument's structure, how it was built. Validity encompasses the entire argument. Therefore, premises cannot be valid or invalid. They can only be measured for their relative soundness. Soundness can either refer to the premise or the argument as a whole. If an argument or premise is generally free from defect, that is, essentially true, then it is sound. 


An invalid argument can never be sound, whereas, in the example above, an unsound argument can be valid. Validity only guarantees that, if all the premises are indeed true, then the conclusion must be true. 

An argument can be valid in any of the following situations: 

  • All the premises are true and the conclusion is itself true. 
  • Some or all premises are false and the conclusion is true.
  • Some or all premises are false and the conclusion is false. 

If, on the other hand, all of an argument's premises are true then we must accept that the conclusion is, indeed, true; we have good alternative to accepting the truth of this claim. Validity then is not enough to make a good argument because validity does not guarantee that the premises are true, it only guarantees that the argument is true IF, and only IF, the premises are, in fact, true. Validity only concerns itself with the connection between the premises and the conclusion. 


If an argument is valid, its structure is essentially unflawed, and its premises are all true, then the argument is deemed to be sound. That is, one is forced to accept the conclusion of the argument as the truth. Let us end with an example of a valid and sound argument: 

  1. Premise One: All men are mortal. 
  2. Premise Two: Socrates is a man. 
  3. Conclusion: Therefore Socrates is mortal. 

Ahh that's more like it.  Happiness is a sound argument.