No. Words don't mean whatever you want them to mean. PhDs generally require:
- getting admitted
- taking classes
- doing research under the supervision of an advisor
- writing that into a dissertation
- defending the dissertation
In principle you could drop out of grad school and do the other steps on your own. While this might be a worthwhile endeavor for you, there is no quality control. A "crackpot" might convince himself and like-minded people (even those with PhDs) that his ideas are right, whereas they will not convince a reputable university to endorse their ideas.
In my office, some of the most experienced and smartest people never got the PhD. They certainly deserve it -- 30 years of research, conferences, grants etc. is a much better qualification than 5 years in grad school (and everyone who matters knows this). But a PhD is an academic qualification, not (only) an award for merit. If you award yourself a PhD and someone calls you on it, they are absolutely not going to buy your explanation about how a bunch of arXiv papers are equivalent to a PhD from a university.