But that wouldn't be proving creationism via negative argumentation, since one of the underpinnings of creationism is a young earth and proving the earth is 6000 years is different from proving the earth is not billions.
"Evolution relies on the assumption x while creationism relies upon the assumption y. The two assumptions are diametrically opposed to each other, therefore proving one right disproves the other. Therefore proving y right (positive argumentation) proves x wrong."
Let's break this down into it's basic logic:
If X then not Y.
If Y then not X.
In this case, If we prove X is true then Y is not true, and if we prove Y is true then X is not true. However, and this is the crux of it: If X is proven NOT true, this does not mean Y is true, and if Y is proven NOT true, then X is not necessarily true. So, if we prove the earth is not over 4 billion years old, this does not mean it's 6000 years old (it could be 600,000 or 6 million or 6 years old), and if we prove that the earth is not 6000 years old, this does not mean it's over 4 billion (same is true, it could be 6, 60, 6000, 6 million, 6 quintillion years old).
Does that explain it?
The problem with this whole "If X is wrong then Y is true" philosophy is that it completely discounts the potential of the unknown. We cannot know everything, therefore we cannot know if there are more than two possibilities. If there are potential unknown possibilities then negative argumentation cannot make effective claims since they can only negate possibilities rather than support possibilities whereas positive argumentation will make effective claims by advancing the likelihood of possibilities over others. Given this, negative argumentation will never build a theory to be more likely than the unkown, only make them less likely than the unkonwn while positive argumentation will never make a theory less likely than the unknown but will make them more likely than the unknown. In this way we can say that yes, evolution may be wrong, creationism may be right, but <place holder for infinite number of unthought of hypothesis> may be right as well.