Okay, I don' t have to speculate or argue. I'm an alien, and I don't consider it a "fact," unless fact is defined to include the consequences of language. I.e, as an alien, I can see your process, and, within your process, I see that "1 + 1 = 2" is generally useful to your survival. That I'll accept as a fact. However, if you believe that 1 + 1 = 2 is a "fact," such that 1 + 1 <> 2 is necessarily "false," I think you might be unnecessarily limited, harming long-term survival.

It's also useful to my survival, normally. Sometimes not. Sometimes 1 + 1 = 1, or 1 + 1 = 0, work better. I'm not kidding.

The AI worth thinking about is one which is greater than human, so that a human can recognize the limitation of fixed arithmetic indicates to me that a super-human AI would be able to do that or more.