The quantification over T is still kind of weird, though. In a formulation like `for all T, (T and P consistent and T and neg P consistent)` is trivially false, just take `T = {neg P}` and now `{P, neg P}` is inconsistent.
We're never trying to show P is independent of all theories, just some specific one.
The quantification over T is still kind of weird, though. In a formulation like `for all T, (T and P consistent and T and neg P consistent)` is trivially false, just take `T = {neg P}` and now `{P, neg P}` is inconsistent.
We're never trying to show P is independent of all theories, just some specific one.