> No, you haven't. You've merely failed to locate any. You've said "I'm not going to prove that this works. I'm going to assume that it does and act as if it did, and place the burden on you to prove otherwise."
Excellent point. It's not even known if we can get any inconsistencies without making this definition; and it's known that, if it's true that we can't get any inconsistencies without it, then we can't prove that it's true. Building on such possibly shaky foundations can't make them stronger.
(That's not mathematical maundering, by the way; it is a correct if informal statement of part of the incompleteness theorems. I appreciated excalibur (https://news.ycombinator.com/item?id=17736486 )'s point, and wanted to underline the significant, and mathematically precise, difference between "one apparent inconsistency is not present" and "there is no inconsistency.")
Excellent point. It's not even known if we can get any inconsistencies without making this definition; and it's known that, if it's true that we can't get any inconsistencies without it, then we can't prove that it's true. Building on such possibly shaky foundations can't make them stronger.