Then the universe doesn't use that arithmetic in implementing physics,
How do you know?
Mainly from the computability of the laws of physics.
Like I said just above, it uses the kind of arithmetic that can be captured in a small set of axioms.
What kind of arithmetic is that? It would have to be a kind of arithmetic to which Godel's and Tarski's theorems don't apply, so it must be very different indeed from any arithmetic I've ever heard of.
Right -- meaning the universe doesn't use arithmetic (as you've defined it). You're getting tripped up on the symbol "arithmetic", for which you keep shifting meanings. Just focus on the substance of what you mean by arithmetic: Does the universe need that to work? No, it does not. Do computers need to completely specify that arithmetic to work? No, they do not.
By the way:
1) To quote someone here, use the greater-than symbol before the quoted paragraph, as described in the help link below the entry field for a comment.
2) One should be cautious about modding down someone one is a direct argument with, as that tends to compromise one's judgment. I have not voted you down, though if I were a bystander to this, I would.
Silas:
First---I have never shifted meanings on the definition of arithmetic. Arithmetic means the standard model of the natural numbers. I believe I've been quite consistent about this.
Second---as I've said many times, I believe that the most plausible candidates for the "fabric of the Universe" are mathematical structures like arithmetic. And as I've said many times, obviously I can't prove this. The best I can do is explain why I find it so plausible, which I've tried to do in my book. If those arguments don't move you, well, so be it....
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!"