The various types of Cosmological arguments (like the first, second and third way of T. Aquinas, the Kalam cosmological argument, the Leibnizian argument and the Platonic argument from composite entities) all start from considerations of the Universe.
The universe can be defined as the physical object made of all physical objects.
Such broad definition encompasses even the possible existence of multiverses.

Hume in his writings “Dialogues concerning Natural Religion” and “Inquiry concerning Human Understanding” tries to dismiss the force of these cosmological argument by saying that we cannot make epistemically justified assertions on the universe as a whole. Clearly all cosmological arguments have to claim at least some knowledge of the universe as a whole (like is origin, nature etc) and therefore, in Hume’s opinion, such arguments are flawed.

Hume defends his position by saying that we are not in a sufficiently good epistemic position to make claims on the universe because the universe as an object of study is unique in its type.

Hume claims that to have knowledge of things, or at least to be able to infer things from observation, the object of study has to belong to a broader category or kind.
To give him some (very modest) credit, nobody denies that belonging to a class of things empowers predictive ability in an inferential process (for example, we know how a specific peace of paper will react when lit on fire given the fact that we have lots of paper from which we can see how paper in general behaves when put on fire).

Clearly the universe, by his own definition, cannot be studied by studying other universes. Therefore the cosmological arguments fails. That’s it. Thank you Hume, you prevented me and lots of other people from losing so much time in studying all of these boring abstract arguments!
Just kidding. Hume’s argument is clearly flawed. Let’s see why.

a) First of all, as we can usually do with Hume’s arguments, we can use a “reductio ad absurdum” approach. If in fact Hume’s necessary condition for justified knowledge were true we couldn’t reach any conclusion of any thing that has a general and encompassing status!

For example, as Richard Swinburne says in his book The Existence of God: “physical anthropology could not reach conclusions about the origin and development of the human race (because, as far as our knowledge goes, it is the only one of its kind). The implausibility of these consequences leads us to doubt the original objection, which is indeed totally misguided [emphasis added]” (page 134, Second Edition).
Hume set a bar for justified knowledge which is simply unnecessarily high. A bar which is contradicted a posteriori, that is, contradicted by reasonable knowledge we have reached regarding unique and broadly encompassing entities or concepts.

b) Second, the argument fails to show a real distinction between the universe and any other object. As Swinburne points out in his book previously mentioned, the uniqueness of an object of inquiry is relative to it’s description. In fact every object can be seen as unique.

Every particular and distinct object is unique and different from everything else (otherwise, given the principle of identity, it wouldn’t by either particular or distinct). A particular book is different from any other book (even different from the other copies of the same book) and such unique status doesn’t impede the inferential process of knowledge. Under this perspective every object is unique to itself and a kind of its own and there is no true difference between the universe as an entities and the other objects.

If somebody points out that the entities which compose the universe have common properties even the universe itself shares properties with the objects it contains. As Swinburne writes: “[the universe] is, for example, like objects within it such as the solar system, a system of material bodies distributed in empty space. It is a physical object and like other objects, has density and mass.”

For this reason Hume’s objection doesn’t succeed in showing why the universe would have a uniqueness different and superior from the one of other objects, therefore failing to show why our epistemic position towards the universe as a whole would be different from the one we have with singular objects.

c) Third, if the universe is defined as the sum of objects within it, there is no reason whatsoever to doubt why a principle that seems to hold for every object within the universe would not hold to the universe itself. The premises of the Cosmological arguments like the principle of causality (or more precisely the “ex nihilo nihil fit” principle), the principle of sufficient reason, or the one of motion as defined as a passage from potency to act, or the one regarding the contingency of composed entities (utilized by the Platonic Cosmological argument) all have a status of universality (that is, this principles, when defined correctly, apply transversally, without exceptions). This means that they claim to apply in every case. And if they really do apply in every case of objects within the universe, these principles apply by necessity to the universe, which is nothing but the objects in which such principles apply (see my article  https://apologeticaecreazione.wordpress.com/2017/08/22/largomento-cosmologico-di-leibniz-e-la-difesa-del-principio-di-ragion-sufficiente/  for a longer treatment of the issue and the falsely claimed fallacy of composition.)

Therefore Hume’s objections fails because the claim of weak epistemic position is answered by the fact that the universe is reduced to the things (i.e. the specific objects within the universe) with which we have a good epistemic position. The good epistemic position towards particular objects permits us to identify transversal and universal principles that permit us to make statements on the universe as a whole.
The transversality of these principles can put the universe as a whole in a certain category, that is the category of entities in which theses principles apply (these principles would apply to all objects plus the object which encompasses all objects, i.e. the universe). Hence the universe, as already shown in point b), is not a complete separate entity, and we can therefore make considerations about it to then develop cosmological arguments.

Amedeo Da Pra