> A PhD is just a certification that you have depth and breadth around a topic at an expert level.
I have a PhD (in pure mathematics), and I disagree with this statement. It does not explicitly include the words "knowledge" or "learning" but I they're implied by "depth and breadth". But a masters is sufficient to show that you are capable of learning a lot of existing knowledge (and have actually done so).
The key distinction about a PhD, in my mind at least, is that it is a certification that you are capable of inventing new knowledge.
Generally, yes, you need to have learnt a lot of existing knowledge to do that but it is not strictly required and in any case certainly not the point.
I disagree with both of you: having "learnt a lot of existing knowledge" is explicitly required; and the PhD does not just certify "depth and breadth" of knowledge - it also certifies that you have made an original contribution to knowledge.
The General Regulations for the Degree of Doctor of Philosophy [1] at the University of Oxford require the examiner's report to confirm that:
"1. the student possesses a good general knowledge of the particular field of learning within which the subject of the thesis falls;
2. the student has made a significant and substantial contribution in the particular field of learning within which the subject of the thesis falls;
3. the thesis is presented in a lucid and scholarly manner;
4. in their opinion the thesis merits the Degree of Doctor of Philosophy;
5. the student has presented a satisfactory abstract of the thesis."
Similarly, the regulations from the University of Cambridge [2] require both that "a candidate wishing to proceed to the Ph.D. Degree under these regulations shall be required to give proof of a significant contribution to scholarship" and that their oral examination will cover "the general field of knowledge within which it falls" (not just the thesis itself).
In a way I agree with what you are saying, that the differential new skills that a PhD provides over a Masters is the ability to invent new knowledge and/or assess the claimed new knowledge of others. But, to get a PhD, you have to get a Masters first (or do Masters equivalent work in the first 2 years of your PhD program).
In effect, once someone has a PhD certificate, they can throw away their Masters certificate, since the PhD certificate guarantees that they also have sufficient breadth of knowledge + new-knowledge-invention skills.
I have a PhD (in pure mathematics), and I disagree with this statement. It does not explicitly include the words "knowledge" or "learning" but I they're implied by "depth and breadth". But a masters is sufficient to show that you are capable of learning a lot of existing knowledge (and have actually done so).
The key distinction about a PhD, in my mind at least, is that it is a certification that you are capable of inventing new knowledge.
Generally, yes, you need to have learnt a lot of existing knowledge to do that but it is not strictly required and in any case certainly not the point.