How can I convince my supervisor that I have enough data to support my findings? I am a final-year Ph.D. candidate in a physics-oriented field. Over the course of my program, I have developed a postulate which leads to some contradictions with some of the tenets of my field, and I have obtained what I would consider a suitable amount of data which both supports my postulate, and conflicts with the (pre-)existing conclusions.
I am in the process of writing a paper on the matter with my supervisor. While initially supportive of my ideas/work, he has unfortunately seemed to change his mind recently, for a number of reasons which I find questionable. Of note, he has repeatedly stated in writing that the work is unsuitable, because I have failed to &quot;either prove that the postulate is correct, or disprove the existing work&quot; (according to further discussions, he believes that having conflicting data is not proof that the existing work is incorrect).
However, in my understanding of the scientific method, it is not possible to prove that my postulate is correct, or that the existing work is strictly incorrect. As I understand it, all I can do is provide data which agrees with what I am trying to say, and which contradicts with what other work has concluded. While I believe that I have done a sufficient amount of work necessary to support my thesis, he is of the opinion that I haven't, and is threatening to withhold granting my degree if I don't meet his expectations.
Perhaps related: he is an engineering professor and as far as I can tell has not published on a postulate before. However, to be fair, neither have I!
My questions are then:

Assuming I obtained the data in the best possible manner, is my supervisor correct in that I have not reached the required threshold for my work to have suitable academic merit necessary to receive a doctoral degree? (Generally speaking - I am aware that practices may vary depending on location).
If not, what must I do in order to reach this threshold?
If so, what can I tell/show him in order to convince his that my work is indeed suitable?
I don't think that anybody can possibly provide an answer without having access to many more details. The precise field matters, how well established the prevailing theories in your field are, how the quality of your data compares to previous work, how the rigor of your arguments compares to other work, etc.
Generally, making these sorts of judgements is what your advisor is for, because he/she has many years of experience in the field.
Now it can happen that your interests and those of your advisor are not perfectly aligned. Your advisor may be too conservative, because he/she does not want to make a mistake. You may be overly aggressive, because you want to get your thesis done.
The question is how to proceed. You could ask your advisor to let you finish a draft, and show it to a third person, an expert in the field (possibly a member of your thesis committee) with no direct interest in the outcome, and who you can trust to keep a confidence.