In Scott Aaronson's answer to my question about the Extended Church-Turing Thesis, he says
I don't see how talking about "proofs" of the CT or ECT adds much light to this discussion. Such "proofs" tend to be exactly as good as the assumptions they rest on---in other words, as what they take words like "computation" or "efficient computation" to mean. So then why not proceed right away to a discussion of the assumptions, and dispense with the word "proof"?
I would like to start a "discussion of the assumptions," or a question like, "What are the right axioms for the notion of computation and algorithm." I would probably seed it with the list of axioms Dershowitz and co-authors use to prove Church-Turing Thesis, or Extended Church-Turing Thesis.
So my meta-question is this: where would the best venue be for this? It seems as though it would be a natural candidate for a blog entry, but perhaps it would be better as a community wiki on the main site, so people could vote up and down axioms/intuitions that resonated, or didn't. Any preferences/suggestions?
EDIT: thanks everyone for your input. I will ask a question, but probably next week. I don't have time to shepherd a question for the next several days.