A monthly thread for posting rationality-related quotes you've seen recently (or had stored in your quotesfile for ages).
- Please post all quotes separately, so that they can be voted up/down separately. (If they are strongly related, reply to your own comments. If strongly ordered, then go ahead and post them together.)
- Do not quote yourself.
- Do not quote comments/posts on LW/OB.
- No more than 5 quotes per person per monthly thread, please.
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!"
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. What I was referring to was a nonstandard model that was computable according to an equally nonstandard definition of computation, one that makes explicit the definitional dependence of Turing Machines on the standard natural numbers and replaces them with nonstandard ones.
The question I'm wondering about is whether such a definition leads to a sensible theory of computation (at least on its own terms) or whether it turns out to just be nonsense. This may have been addressed in the literature but if so it's beyond the level to which I've read so far.
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.