Intellectual curiosity is the true barometer; you either thirst to know more, or you're content with ignorance.
There is a third way!
You thirst to know more but have a soul crushing deficit of self esteem and truly believe you're incapable of anything more than menial labor. You remain with your thirst, not content with your ignorance, but unable to overcome the self image of "absolute moron with no place in the scientific community who must be narcissistic for even thinking he could be" and so you grow to hate yourself even more because of it!
...Err.... Or so my friend says.
I have come to realize a PhD just means you have spent a lot of time thinking about what you are doing.
Doesn't mean what you are doing is smart really. Just well thought about.
I think it's a general thing with highly capable persons in expert and highly intellectual domains that eventually you kinda figure out what Socrates actually meant with "All I know is that I know nothing"
I feel like that sentiment is easily reached by anyone who is curious and likes to learns, so a lot of people.
If one thinks a lot, likes to learn and, maybe more important, thinks about knowledge and learning things, that person will probably get there.
A certain educational background probably helps but is neither required nor sufficient, IMHO.
Everyone is just making it up as we go along.
Be skeptical of anyone who claims they have the answer.