 Evidently we have two spaces of possibilities, S1 and S2, and the question now arises whether a sentence interpreted over one of these spaces expresses the very same thing as any sentence interpreted over the other. Does \(h \amp r \amp w\) express the same thing as \(h \amp m \amp a\)? \(h \amp r \amp w\) expresses (the singleton of) \(u_1\) (which is the entity \(\langle 1,1,1\rangle\) in S1 or \(\langle 1,1,1\rangle_{S1})\) and \(h \amp m \amp a\) expresses \(v_1\) (the entity \(\langle 1,1,1\rangle_{S2}). {\sim}h \amp r \amp w\) expresses \(u_2 (\langle 0,1,1\rangle_{S1})\), a point adjacent to that expressed by \(h \amp r \amp w\). However \({\sim}h \amp{\sim}m \amp{\sim}a\) expresses \(v_8 (\langle 0,0,0\rangle_{S2})\), which is not adjacent to \(v_1 (\langle 1,1,1\rangle_{S2})\). So now we can construct a simple proof that the two sentences do not express the same thing.