it was meant to correct Silas, who seemed to think that I was reading some deep significance into our inability to know all the truths of arithmetic. My point was that there are lots of things we can't know all the truths about, and this was therefore not the feature of arithmetic I was pointing to.

Yes, it was. When I and several others pointed out that arithmetic isn't actually complex, you responded by saying that it is infinitely complex, because it can't be finitely described, because to do so ... you'd have to know all the truths.

Am I misreading that response? If so, how do you reconcile arithmetic's infinite complexity with the fact that scientists in fact use it to compress discriptions of the world? An infinitely complex entity can't help to compress your descriptions.