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. Q.E.D.*

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.

Start the proof!

MouseOver the
sign to pause the demonstration.