Why expect that we have a canonical model when we talk about sets or predicates if we're entertaining skepticism that we have a canonical model for integer-talk?
We don't. Skepticism of sets, predicates, and canonical integers are all the same position in the debate.
And so is skepticism of canonical Turing machines, as far as I can tell. Specifically, skepticism that there is always a fact of the matter as to whether a given TM halts.
I think you might be able to make the skeptical position precise by constructing nonstandard variants of TMs where the time steps and tape squares are numbered with nonstandard naturals, and the number of symbols and states are also nonstandard, and you would be able to relate these back to the nonstandard models that produced them by using a recursive description of N to regenerate the ...
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!"