Chapter One, Tutorial Five

Proofs

** [**Gold

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 By definition of sound, A must be be
valid 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.

MouseOver
the

sign to*pause*
the demonstration.

sign to

We need to think about *any* argument A
that

- is valid,
*and* - has no false premises.

So, *suppose* that A
is any valid argument with no false premises.

Then because A has no false premises,
it follows that *all* its premises are true.

Finally, then, A is valid and has only true premises. So, A is "sound" by our definition of that term.

Q.E.D. (because we've gotten to the "*then*" clause.)

Click **here
to replay****.
Next... **