 According to Priest the strengthened Liars show that a single feature of the semantic paradox underlies its different formulations. The totality of sentences is divided into two subsets: the true ones, and their ‘bona fide complement’—call it the Rest. Now the essence of the liar is “a particular twisted construction which forces a sentence, if it is in the bona fide truths, to be in the Rest (too); conversely, if it is in the Rest, it is in the bona fide truths” (Priest 1987, p. 23). The standard Liar, ‘This sentence is false’, is just a particular instance of this, producing a contradiction within the bivalent framework, in which the Rest is identified with the set of the false sentences. We can try to resolve the problem by admitting sentences that are neither true nor false, so that the false ones become a proper subset of the Rest. However, the strengthened Liars show that we can use the notions introduced to solve the previous paradox to re-describe the Rest. Once the set of sentences is partitioned into a trichotomy (true, false, and neither true nor false), the disjunctive ‘This sentence is false or neither true nor false’ embraces the whole Rest, i.e. the new(ly described) complement of the set of the true sentences. What about adding more values? If there is some fourth thing that a sentence can be, besides true, false, and neither true nor false, we can always take the notion fourth thing and produce another strengthened Liar: