[lmm]

How is that not a workaround? It's "just how consistency proofs are done" because it's a standard, popular workaround for the problem. We absolutely would prove consistency of ZFC and similar theories in ZFC if we could, we only work in stronger systems because we have to.

[randallholmes]

You don't work around what is impossible. A consistency proof for a theory T is usually a construction of a model of that theory in some context we have confidence in. Godel's theorem shows that that context has to be stronger than T. This isn't some kind of obstruction, it is reality. And there are strong systems we have confidence in.

[lmm]

> Godel's theorem shows that that context has to be stronger than T. This isn't some kind of obstruction, it is reality.

What distinction are you drawing? I see no contradiction between something being reality and something being an obstruction to be worked around.

[randallholmes]

I have the same objection when people talk about defining set theories in such a way as to avoid the paradoxes. We don't avoid or work around the paradoxes: they are mistakes. We simply do things correctly, we do what we can do.