 One way of dealing with this worry is to employ external means, such as proof theory, in support of the model-theoretic definition. This is done by Georg Kreisel in his “squeezing argument”, which we present in section 3.3. Kreisel’s argument crucially depends on the language in question having a sound and complete proof system. Another option is to use set-theoretic reflection principles. Generally speaking, reflection principles state that whatever is true of the universe of sets, is already true in an initial segment thereof (which is always a set). If reflection principles are accepted, then at least as concerns the relevant language, one can argue that an argument is valid if and only if there is no counter set-model (see Kreisel 1967, Shapiro 1987, Kennedy &amp; Väänänen 2017).