If you’re interested in solutions to the Liar, I assume you know what it is, so I’ll be quick with the explanation. “This sentence is false” – is that sentence true or false? If it’s true, then it’s false, and if it’s false, then it’s true. Whoa!
The Liar is a serious problem for logicians and philosophers because it calls classical logic into question. The Liar does not go away unless we make some changes, either to the way that we refer to things, the way we understand truth, or to some laws of classical logic, such as the law of excluded middle or the law of non-contradiction.
There have been many proposed solutions to the problem, and I’ll be doing a survey of them. I’ll begin with the most tempting and popular solution: the argument that the Liar is (or should be considered) meaningless.
The solution comes in a few basic flavors, but they all hinge on the idea that the Liar is only a problem if it is in fact saying something. If it isn’t – in other words, if it doesn’t express a proposition (philosophy talk for “statement”) – then it’s just a bunch of words put together, like “mafpol govohav,” or “the dog.” In order for a sentence to be meaningful, it must have a subject – a thing it is about – and a predicate – something being said of that subject. The Liar, so the argument goes, has no subject.…