An argument is valid if it seems appropriate, well-grounded and can be defended. A contract is valid if it is enforceable in law. In other words, it applies legally to a particular situation. A bank-note is valid if it can be exchanged and used for purchase, and a passport is valid if it lets the holder come in and go out of a country. A will is valid if correctly made, and certified by an appropriate court. In all these cases, valid refers to the soundness in some situation. Logical uses of this idea are similar, but phrased much more exactly.
- All men are mortal.
- Socrates is a man.
- Therefore, Socrates is mortal.
- However, this is also a valid syllogism:
- All cups are green.
- Socrates is a cup.
- Therefore, Socrates is green.
And it is not true that Socrates was green.
- The following is valid but not sound:
- All animals live on Mars.
- All humans are animals.
- Therefore, all humans live on Mars.
The problem with the argument is that it is not sound. In order for a deductive argument to be sound, the deduction must be valid and all the premises true.
- Michael Frede, Essays in Ancient Philosophy (Minneapolis: University of Minnesota Press, 1987), p. 104
- Stephen Priest, The British Empiricists (Oxford; New York: Routledge, 2007), p. 193