Then, we can close F in order to get a proposition in two manners : (1) “∀_x F_x” (for every x , Fx) ; (2) “∃_x F_x” (for at least one x Fx). In (1) is false and (2) is true. In Σ1 with only integers from 1 to 7, (1) and (2) are both true ; in Σ2 as {8 ; 14 ; 20 }, (1) and (2) are both false. So the semantic as developed in model-theoretical point of view takes care of the objects you are working with, and the domain you consider. This leads to consider pragmatic as defined below.