It is in fact provably impossible to construct a computable nonstandard model (where, say, S and +, or S and × are both computable relations) in a standard model of computation.
Would you give a reference? I found it easy to find assertions such as "the completeness theorem is not constructively provable," but this statement is a little stronger.
A monthly thread for posting rationality-related quotes you've seen recently (or had stored in your quotesfile for ages).
ETA: It would seem that rationality quotes are no longer desired. After several days this thread stands voted into the negatives. Wolud whoever chose to to downvote this below 0 would care to express their disapproval of the regular quotes tradition more explicitly? Or perhaps they may like to browse around for some alternative posts that they could downvote instead of this one? Or, since we're in the business of quotation, they could "come on if they think they're hard enough!"