Semantic Regularity and the Liar Paradox
Nicholas J. J. Smith · The Monist · 2006
§ 1. introduction. There are two main tasks in which writers on the Liar paradox might see themselves as engaged. The first task is saying what is going on in a natural language such as English when we say things such as ‘This sentence is not true’. The second task is constructing consistent formal systems which have as much expressive power as possible, or which can express certain notions in which the author is particularly interested. Many authors attempt both tasks at once: they present a consistent formal system, and argue that it provides a model of natural languages such as English. My task here is the first one. I do present a consistent formal system and claim that it provides a perfect model of natural languages such as English, but this system involves no surprises. It is none other than the standard framework of classical logic and model theory. The real weight of the argument lies in the claim that the classical framework—without alteration or addition—contains the resources to model what happens when we say in