[frostburg]

No, there is no reason to think that the human brain is capable of computing anything that isn't Church-Turing computable. Luckily no translation actually requires a "general solution" of the problem formally.

[yters]

How do you know this is true?

[frostburg]

Texts have finite length.

[yters]

Can you expand the missing premise?

  1. Texts have finite length.
  2. ____
  3. Therefore, the halting problem does not impact machine translation.

[frostburg]

Sorry, missed this. I'll try to explain. A real computer doesn't actually have an infinite tape (memory) like a canonical Turing Machine, it's actually a finite state machine with a vast amount of possible states that we conveniently think about as analogous to a Turing machine, hence the the halting problem is actually solvable (just not in practice) for real hardware.

Given content that can be expressed in two languages in a text of finite length, you could in theory enumerate all the possible translated texts.

[yters]

If it is not solvable in practice, I don't see how finiteness addresses my objection...