Topic: GENERAL LOGIC
On the Storeyed Revenge of Strengthened Liars
By Jordan Howard SobelThe Strengthened Liar observes that if we follow a partiality theorist and declare the Liar sentence neither true nor false (or failing to express a proposition, or suffering from some sort of grave semantic defect), then the paradox is only pushed back. For we can go on to conclude that whatever this status may be, it implies that the Liar sentence is not true. This claim is true, but it is just the Liar sentence again. We are back in paradox.(Glanzberg 2002, p. 468; 2004, p. 29; 2001, p. 222, “We are back in our contradiction.”)
There are problems with this charge that strengthened liar sentences avenge would be disparagements that they do not express propositions, by reappearing as claims that are easy consequences of these disparagements. For one thing, if, as one supposes, claims would be propositions not sentences, [t]his claim cannot be the Liar sentence again. (Cf., Grim 1991, p. 19.) For another thing, while it does follow from the disparagement that a Liar sentence does not express a proposition, that this sentence does not express a true proposition, it is a consequence of that disparagement that this claim or proposition is not expressed by the Liar sentence itself. However, there are ways in which informal and formal revelations that Liar sentences do not express propositions and seem to bring them back with vengeance. This is their story.
Source: Online Papers in Philosophy