The set of all \(T\)-sentences \(T\ulcorner \phi \urcorner \leftrightarrow \phi\), where \(\phi\) is any sentence of the language \(\mathcal{L}_T\), that is, where \(\phi\) may contain \(T\), is inconsistent with PA (or any theory that proves the diagonal lemma) because of the Liar paradox. Therefore one might try to drop from the set of all \(T\)-sentences only those that lead to an inconsistency. In other words, one may consider maximal consistent sets of \(T\)-sentences. McGee (1992) showed that there are uncountably many maximal sets of \(T\)-sentences that are consistent with PA. So the strategy does not lead to a single theory. Even worse, given an arithmetical sentence (i.e., a sentence not containing \(T)\) that can neither be proved nor disproved in PA, one can find a consistent \(T\)-sentence that decides this sentence (McGee 1992). This implies that many consistent sets of \(T\)-sentences prove false arithmetical statements. Thus the strategy to drop just the \(T\)-sentences that yield an inconsistency is doomed. 