[FOM] consistency and completeness in natural language

[Torkel Franzen]

Neil says:

  >> After all, whether or not we know that S is consistent, we
  >> know that B(_n) is true if and only if n is a proof in S of (x)A(x).

  >This is incorrect. Suppose we don't know that S is consistent. I take 
  >it, then, that you are countenancing the possibility that S is
  >inconsistent. But if S is inconsistent, the "if" part of your claim fails.

  How do you arrive at this conclusion?

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Torkel Franzen