The inadequacy of formal demonstrations

Because a certain person once confidently told me that they're going "rescue logicism from Gödel's incompleteness theorem" by bypassing it entirely, it might behoove this person to learn about what they're trying to bypass. A good place to start would be this wonderful article in Slate today called "Does Gödel Matter?"

My favorite part:

What is it about Gödel's theorem that so captures the imagination? Probably that its oversimplified plain-English form—"There are true things which cannot be proved"—is naturally appealing to anyone with a remotely romantic sensibility. Call it "the curse of the slogan": Any scientific result that can be approximated by an aphorism is ripe for misappropriation. The precise mathematical formulation that is Gödel's theorem doesn't really say "there are true things which cannot be proved" any more than Einstein's theory means "everything is relative, dude, it just depends on your point of view." And it certainly doesn't say anything directly about the world outside mathematics, though the physicist Roger Penrose does use the incompleteness theorem in making his controversial case for the role of quantum mechanics in human consciousness. Yet, Gödel is routinely deployed by people with antirationalist agendas as a stick to whack any offending piece of science that happens by. A typical recent article, "Why Evolutionary Theories Are Unbelievable," claims, "Basically, Gödel's theorems prove the Doctrine of Original Sin, the need for the sacrament of penance, and that there is a future eternity." If Gödel's theorems could prove that, he'd be even more important than Einstein and Heisenberg!

As for the anonymous philosopher I mentioned above, good luck on constructing your "tenable framework".