What makes someone deserving of a Ph.D.?
For a Ph.D., my favorite explanation is this cartoon by Matt Might.

In short: a Ph.D. is a measurable contribution to a sum of human knowledge.

To be able to answer this question, all you need is an idea of how to describe what you have discovered, and how it fits into the context of work by others that has come before.  This is often not easy to answer, but an important thing to think about as one is writing one's thesis in any case.