‘ Means that ’ and the liar ∗

By means of ‘means that’ and propositional quantification, we can define a truth predicate. This also allows the construction of liar sentences, either by self-reference or by means of quantification. In order to avoid inconsistency, restrictions on expressive power must be imposed, and the question is how far such restrictions will limit our ability to say of what is intuitively described as ‘‘meaningful’’ that it is precisely meaningful. 1. ‘Means that’ and truth predicates We like to think of the sentences we use as meaningful. We like to think that for any wellformed sentence of our natural language, be it Swedish, English, Tagalog or any other of the terrestrial languages, a speaker can utter that sentence and in virtue of semantic properties already established, thereby express a proposition, something that is true or false depending on what the world is like. We would not like to be in the predicament of constructing a sentence that is well-formed, as far as we can tell, and for which we can even give argument that should lead us to accept it as intuitively correct, and yet at the same time have to judge it meaningless, in the sense of not expressing any proposition. Yet, there seem to be such sentences, or at least nearly enough. ∗An earlier version of this paper was presented at the LLS Colloquium at Ohio State University. I had extremely valuable comments from Neil Tennant, Kevin Sharp, Gabriel Uzquiano Cruz, Craige Roberts, and -especially -Stewart Shapiro. Before that I received helpful comments from Sten Lindstöm on a first draft. I'd also like to take the opportunity to thank Dag for uncountably many stimulating discussions over the years, for great cooperation and great friendship.