I'm not redefining anything. I'm asking whether you accept it to be possible that one day a flaw will be found in arithmetic, leading to a contradiction. An e

I'm not redefining anything. I'm asking whether you accept it to be possible that one day a flaw will be found in arithmetic, leading to a contradiction. An example might be proving that 17 is prime on the one hand, and then finding a factorization of it on the other. The fact that arithmetic is widely used throughout the world without contradiction does provide some evidence that it's consistent, but other famous theories (e.g. Newtonian physics) have been found to be not quite right. Maybe the flaws in arithmetic only show up when really huge numbers are involved. Stated another way, how do you know that arithmetic is "internally consistent"? Why do you judge it to not be among the "potentially inconsistent axioms" of stronger systems? If it's just due to our empirical success with numbers to date, then you should admit there to be some small chance that we've just not discovered the problems, to date. Or, you can prove arithmetic correct in some stronger system, but then how do you check the consistency of that system? At some point, you have to rely on your intuition about what the axioms are supposed to be about.