T1.3: 4 of 8
Mostly we learn logic so we can better reason about the world. But sometimes we reason about logic too.
Let's begin with a very easy example. We can show just by going through the definition of 'sound' that
(*) Every sound argument has no false premises.
How do we prove this? It may seem too obvious for words (once you understand the definition). But bear with this thinking...
(*) is about ALL sound arguments. So, first we consider any sound argument; suppose A is any such argument.
By definition of sound, A must be be valid and have all true premises.
Finally, because A's premises are true, it cannot have a false premise.
That's it: we just suppose that we have a sound argument, call it "A", and chase through the definition of "sound".
Let's look at a demonstration to underscore the step-by-step proof process.
We will show that
(**) If an argument is valid and has no false premises, then it is sound.