Capital P proof is great if you want to know whether a topological space is separable, but if you want to know if you should stop paying your taxes because mayb

Capital P proof is great if you want to know whether a topological space is separable, but if you want to know if you should stop paying your taxes because maybe they're causing more harm than good then you're going to have to rely on something besides capital P proof. You're going to have to rely on induction and probability. More vs less data matters quite a bit in such places. Sources can include people you've never met, have no reason to lie, and happened to be in an opportune position to contribute to the sort of lowercase p proofs that you need. If we can fix social media there can be many such people. If not, there will be necessarily fewer, and they'll have to be replaced by people for whom addressing the public with new information is their job. The latter sort are high value targets for corruption. As long as they're worried about keeping that job, they have to also worry about who they upset with their information. You're necessarily going to get weaker lowercase-p proofs from such people. That's not to say that we'll have no tools for keeping power in check, but we will have fewer, which means their abuses will be more frequent and more severe.