> the former should be construed as expressing the same thing as the latter. If it's just a linguistic disagreement, then I think we can set that aside
No, this is not just a linguistic disagreement. This is the crux of the matter. By saying that "the earth is round" and "the proposition 'the earth is round' is true" mean the same thing you are conflating two different ontological categories. When you do that, your reasoning is no longer sound.
Consider this:
P1: The U.S.S. Enterprise can travel faster than light.
Is P1 true? If yes, then how can that be when we know from relativity theory that nothing can travel faster than light? And if no, then what about these:
P2: The U.S.S. Enterprise is powered by a matter-anti-matter reaction controlled by dilithium crystals.
P3: The U.S.S. Enterprise is powered by squirrels running on treadmills.
---
P.S. It occurred to me that there is a TL;DR answer to the question of what Turing did that was so important: he invented general-purpose software.
No, this is not just a linguistic disagreement. This is the crux of the matter. By saying that "the earth is round" and "the proposition 'the earth is round' is true" mean the same thing you are conflating two different ontological categories. When you do that, your reasoning is no longer sound.
Consider this:
P1: The U.S.S. Enterprise can travel faster than light.
Is P1 true? If yes, then how can that be when we know from relativity theory that nothing can travel faster than light? And if no, then what about these:
P2: The U.S.S. Enterprise is powered by a matter-anti-matter reaction controlled by dilithium crystals.
P3: The U.S.S. Enterprise is powered by squirrels running on treadmills.
---
P.S. It occurred to me that there is a TL;DR answer to the question of what Turing did that was so important: he invented general-purpose software.