Semantic Regularity and the Liar Paradox

Abstract

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 English 'This sentence is not true'.Apart from the fact that it is one hundred percent classical, the solution to the Liar to be presented here has two other notable features. First, it does not generate a strengthened Liar paradox or revenge problem. Second, the entrenched belief which the solution asks us to relinquish-and of course it must ask us to give up some such belief, for the Liar would not be a paradox if it could be solved without giving up anything-(a) is a belief whose proper home is philosophy of language, not logic; (b) is a quite general belief about the operation of language, rather than a particular belief about a certain class of words-in particular it is not a belief specifically about 'is true'; and (c) is also the key to a host of other deep philosophical problems such as Quine's problem of the indeterminacy of meaning, Kripkenstein's sceptical puzzle, Putnam's paradox, the problem of empty names, and a recalcitrant problem about the semantics of vague language-the problem of false precision. § 2. the classical framework. I have said that my solution stays entirely within the bounds of classical logic and model theory. To begin, I

Higher-order free logic and the Prior-Kaplan paradox

“…Bradwardine 2010; Dorr 2012; Slater 1986). Or one might insist that while Kaplan didn’t say what he seemed to say, he succeeded in saying something else (Bacon 2014; Smith 2006). The challenge for these kinds of responses is to offer some guidance as to what the additional or alternative contents are.…”