To begin thinking about this "indirect" method of proof, consider a different proposition to prove.
(****) Any unsound but valid argument has at least one false premise
sign to pause
the demonstration. As usual, we begin by supposing that we have an arbitrary member of the subject group.
But for this one we will make an additional assumption...
1. So, suppose that A
is any unsound but valid argument.
Now, assume that (****) is wrong and that argument A has no false premises.
2. This assumption (if true) would mean that A only has true premises.
But A is supposed to be valid, so would (if the assumption were true) fit the definition of sound!
3. This proves that the assumption in red is wrong. Even though A is unsound, this assumption leads to the conclusion that it's sound.
Thus, A must have at least one false premise.
Q.E.D. (because we've proven (****)'s claim true of A.)