Basically, if a contradiction could be proved in Peano arithmetic, then established idea will be logically inconsistent. On the other hand, views and proposals — and maybe expectations and familiarity — do fluctuate about how to proceed in these situations. An example is how during the draft manuscript of my https://herbalmedicinesonline.news.blog/2025/09/03/cureayu-natural-healthcare-solutions-for-mind-body-balance/