Two Senses of Ontology
It will be useful for us to get clear on the notion of "positive ontology". "Ontology" when it's used as a mass term usually means the study of being as such. But this cannot be what one means when one says "provide a positive ontology for x". For, it wouldn't make sense to say "provide a 'the study of being as such' for x".
So what does one mean by "positive ontology"? Well, to answer that question it's important to note that "ontology" can be used -- and is often used by philosophers -- as a count-noun rather than a mass term. For example, when philosophers say "my ontology includes 4-dimensional spacetime worms," they're using "ontology" as a count-noun. When we use "ontology" in this sense, we're referring to our commitments about what exists, our ontological commitments.
We can think of "ontology" as a count-noun picturesquely by imagining ourselves writing out a list of everything that we think exists. If we were to carry out this project by writing down specific things on the list like that baseball, that butter knife, Joe's 32nd birthday, the millitary ... the list would be too long to finish in our lifetime. So we would be better off to speak at the most fundamental or general level we can. That is, we would write down general categories like physical objects, times, sets, events, or whatever. When we have completed our list, we have produced our positive ontology -- the things that we think exist. If later on under the influence of some clever Berkeleyan idealist, say, you decide that there aren't any physical objects, you would erase that category from our list. You would then say something like, "my ontology doesn't include physical objects." Again, a great many contemporary philosophers use ontology in this sense.
Thus, if a philosopher were to say "provide a positive ontology for x", what she means is "show that x exists". This is uncontroversial. What nearly all philosophers have realized is that you don't need to show that something exists in order to explain what that thing must be like if it were to exist. Go back to our Berkeleyan idealist. She can write pages and pages for you on what the concept of a physical object is. She will even (depending on the nuances of her view) cheerfully admit that the concept of physical object is coherent. But note that in doing so she never once will attempt to show that these things exist -- she doesn't include them in her ontology. She doesn't have a positive ontology for physical objects, but she knows perfectly well what the concept is, and that it is coherent. This is because it's not necessary to provide a positive ontology for x in order to explain why the concept of x is coherent.
Sometimes philosophers who do have positive ontologies for x decide to put aside the reasons for why they think that x exists, in order to focus purely on what the fundamental nature of x is like. The positive ontology they have for x will not shed much light, in this context, on what x is like. For example, if you want to know what the concept of a baseball most fundamentally involves, and a philosopher replied, "Well, that's easy. Look, they are part of my positive ontology! They are included among the set of things that exist!" you would think it a very annoying joke indeed. This is because providing a positive ontology for x is not sufficient to explain what the concept of x amounts to.
In short, conceptually analyzing x and providing a positive ontology for x are two different projects. Anyone who conflates these -- for example, one who says that you must provide the latter to provide the former -- is making an elementary philosophical mistake.
Rude, offensive, irrational jackass.