 Instead of considering two sentences “A cat is on a mat” and “A cat* is on a mat*” now consider only the one “A cat is on a mat”, allowing its interpretation to change by first adopting the standard interpretation for it and then adopting the non-standard interpretation in which the set of cats* are assigned to ‘cat’ in every possible world and the set of mats* are assigned to ‘mat’ in every possible world. The result will be the truth-value of “A cat is on a mat” will not change and will be exactly the same as before in every possible world. Similar non-standard reference assignments could be constructed for all the predicates of a language. [See Putnam 1985, 1994b.] However, unlike the GCT argument, the Permutation Argument is susceptible to the Lewis-styled reply above.