There are parallel problems for the role of demonstration in another important Galenic area, that of fundamental physical theory. Galen wishes to present his view as having been “demonstrated”, especially by the text of Elements According to Hippocrates (Hipp. Elem.), and indeed the first part of that work is an attempt to establish a rigorous logical method for the foundation of the theory (see Leith 2014; Kupreeva 2014; Singer 2021a). The problem is that this form of clear logical argumentation takes us only as far as the refutation of Atomism (as Galen understands it); that is, it is a proof of the plurality of types of fundamental component of the universe. When he moves from that argument against Atomism/Monism, or for pluralism in general, to the argument for the specific number and nature of the elements of his own theory, however, the argument is much less straightforward. Again, it seems clear that he takes his theory, at least in its essentials, to be not only true but deducible from evident facts and/or common conceptions; but the precise nature and status of the arguments—and indeed of Galen’s claims for them (see further §3.4, paragraph 2)—seem much less clear.