Semantic guardian angels

01/11/2024

The liar paradox starts with a simple sentence that appears to say of itself that it is false. If the sentence is true, then it must be false and if it is false, then it must be true! One way to escape the paradox is to insist that what these sorts of sentences seemingly mean is not what they really mean. But how do we sort these defective sentences from ordinary ones? What explains why the meanings of the former kind are not what they appear? In this post, Dr Will Gamester suggests that we can answer these questions by appealing to a theory of why our words and sentences have the meanings they do in general.

The first sentence of this blog post is false.

Is the above sentence true? That depends on whether what it says is really the case. Now, what it appears to say is that the first sentence of this blog post is false – so it is true if and only if the first sentence of the blog post is false.

The problem is that the sentence is itself the first sentence of the blog post. It follows that the sentence is true if and only if it is false. But that is a contradiction!

This is a paradox and a famous one, usually known as the “liar” paradox. These days, most proposed solutions take for granted that the sentence above really does say what it appears to say and try to show how to resist the apparently innocuous reasoning that takes us from this assumption to contradiction and disaster.

But perhaps the most natural response to the paradox is to say that the opening sentence of this blog post is somehow defective, and that it doesn’t really say anything at all. The sentence appears to say that the first sentence of this blog post is false – but that is a kind of illusion.

This would certainly help to avoid the paradox if it were true. The fundamental problem with this thought, however, is that it’s hard to see why this should be the case. The sentence above has all the hallmarks of a meaningful English sentence. If you wanted to write a sentence that said that the first sentence of this blog post is false, you would probably write: “The first sentence of this blog post is false.” That is, you would probably produce something that looks exactly like the first sentence of this blog post. So why should that sentence fail to say what it appears to say? It’s hard to come up with a convincing answer.

Worse, if the words we produce regularly failed to mean what they appear to mean, that would rapidly undermine language as a useful medium in which to communicate and reason. So ideally, we need our explanation to imply that semantic illusions arise when and only when the alternative is contradiction. But what mechanism could possibly guarantee that illusions appear in all and only the right cases? To believe in this, it seems, is to put your faith in a kind of semantic guardian angel, who intervenes whenever needed to protect our words from paradox. Surely this is absurd. Isn’t it?

I think it’s helpful to see our question here – why does the first sentence of this blog post fail to mean what it appears to mean? – as an instance of a more general question – why, in general, do our words mean what they do? Spoken words are just noises, written words are just shapes. Why do certain noises and shapes have meanings when others don’t, and why do they have the particular meanings they have? Why does “snow is cold” say that snow is cold, rather than saying that grass is green, or nothing at all?

There’s a kind of answer to this question that I like, known as interpretationism. The (very!) rough idea is this: among the many possible interpretations of the words we produce is the correct interpretation; and which interpretation is correct is determined by which interpretation is best. The best interpretation is the one that does the best job of portraying us as reasonable creatures – as saying things we believe to be true and taking others at their word – while remaining relatively simple and elegant. This is a controversial view, but also an independently well-developed and reasonably popular one.

How is this relevant to the liar paradox? There are two key thoughts. First, contradictions entail everything, so any interpretation on which the first sentence of this blog post says what it appears to say will be trivialising: it will imply that every sentence we speak is trivially true. Second, any interpretation on which the language we speak is trivial is a terrible interpretation. It follows that the best interpretation, and so the correct interpretation, will not be one on which the first sentence of this blog post says what it appears to. And the same will go for any other putatively contradictory sentence.

Far from a being of mysterious power, our semantic guardian angel is found built into the very mechanism through which language gets to be meaningful.

Will Gamester is a Teaching Fellow in the School of Philosophy, Religion and History of Scienc at the University of Leeds, where he was previously a British Academy Postdoctoral Fellow and before that a PhD student. As well as paradoxes and the foundations of meaning, Will has an array of interests in metaphysics, metaethics, and the philosophy of language, particularly in realism and anti-realism, moral vagueness, and the nature of human kinds.