Pretty sure the incompleteness theorem doesn't enable one to study things one cannot study. (eg imagine a logic for which one could not write down the axioms but was nonetheless 'consistent' by some external measure)
I suppose an easy way out is to show that such a thing cannot exist in the way that other mathematical structures exist, trivially showing that you have studied all of it that there is(n't) to study.
I'm aware of death penalty abolitionists who argue that innocents have been executed. I'm not aware of persuasive evidence. If it were trivial to find some, surely you would have just posted a link instead of an insult.
It takes only a small amount of induction to conclude that given the number of death row exonerations pre-execution, there almost certainly have been innocent persons executed.
If you hold out for conclusive proof, you will probably not find it, as it's a bit of a fool's errand to attempt to exonerate a dead man when you could devote that effort to exonerating one who the state has not yet committed manslaughter upon.
Your response is a non sequitur, which could explain the downvoting (though certainly not by me). My comment was a reference to this: https://www.youtube.com/watch?v=ANPsHKpti48
