Addendum to “Sloman's view of Gödel's sentence”

摘要

The mapping between arithmetical expressions and meta-arithmetical statements, based on Gödel's numbering, cannot go awry in any “non-standard” model, as Sloman suggested. Gödel's numbering itself cannot go awry, because it involves only the standard model, and the extra elements in “non-standard” models, in so far as they are involved in meta-theoretical interpretation at all, cannot affect the mapping, because they have no independent meta-theoretical meaning.