 This debate thus concerns whether there is one and only one set of logical constants for a system of representations, and if so, which ones are the logical ones. We will not get into this debate here, but there is quite a large literature on what logical constants are, and how logic can be demarcated. For a general discussion and further references, see for example (Engel 1991). Some of the classic papers in this debate include (Hacking 1979), who defends a proof-theoretic way of distinguishing logical constants from other expressions. The leading idea here is that logical constants are those whose meaning can be given by proof-theoretic introduction and elimination rules. On the other hand, (Mauthner 1946), (van Benthem 1986), (van Benthem 1989), and (Tarski 1986) defend semantic ways to mark that difference. The leading idea here is that logical notions are ‘permutation invariant’. Since logic is supposed to be completely general and neutral with respect to what the representations are about, it should not matter to logic if we switch around the objects that these representations are about. So, logical notions are those that are invariant under permutations of the domain. (van Benthem 1989) gives a general formulation to this idea. See the entry on  logical constants  for more.