Comment by burrows

> I had two points in these posts. One is that none of this pertains to whether or not space is continuous.

To me, “space is continuous” seems like a proposition that must be demonstrated a posteriori and I wouldn’t expect properties of formal systems to serve as evidence for the claim. So I agree.

> The other is that the statement “arithmetic is consistent” is provable in some contexts.

Agreed.

> If the universe “contains” a model of PA then is that model consistent or not? How does one know? (I doubt it’s meaningful to say that the universe contains PA though.)

Okay, yes, how can we interact with or measure PA as implemented by the universe? How do we (or can we) meaningfully talk about the universe implementing PA?

Yes those questions seem interesting to me, but I don’t have anything intelligible to say about them.