A Liar’s Paradox Solution

We’ve probably come across many forms of the paradox before. The most amusing one I’ve ever seen was the two door dilemma from Labyrinth. Is the following statement true?

This statement is false.

If it’s true, it’s false. If it’s false, it’s true. What to make of this?

There’s been many convoluted solutions to get around the apparent contradiction, but I have my own, simpler explanation, which is a bit of Alfred Tarski’s solution fused with Arthur Prior’s solution, with some amateur philosophical ideas thrown.

Like every other paradox you can find, this one has its roots in language in an extreme degree. The problem with bothering to eke out a paradox from “this sentence is false” is that it has the form of being meaningful without delivering any meaning. There’s a possibility that this sensible-seeming sentence would have meaning (we’ll come back to this) but it’s never evaluated in that regard. It’s always isolated and examined on its own merits.

The sentence appears to make a truth claim, namely, that it is false, but it doesn’t propose anything about itself that we can negate. Is the sentence not off-white? Not underneath a layer of topsoil? Not a rough draft of Star Trek fanfiction? Claims to truth need two targets, the subject of the sentence and the category, a “state of being” expressed in sentence predicates. “Jay didn’t make peanut butter pie last weekend,” very roughly reworded, is the same as “It’s false that Jay can be categorized as a enjoying the state of being a maker of peanut butter pie last weekend.” All sentences can be reformulated this way. It’s true, by the way, that I didn’t make peanut butter pie last weekend. I made it two weekends ago.

Rewording the liar’s paradox sentence in such a way, we can’t say anything about it’s not-truthfulness: “It’s false that the sentence can be categorized as enjoying the state of being truthful.” There’s no category, even an implicit one, that we can point to to evaluate the proposition. If you try to use “truthful” as a category, which it is, you end up with with circularity, not necessarily a paradox.

I’ll offer another angle using this explanation. The sentence’s opposite, “This sentence is true,” is also meaningless and nonsensical, because we don’t know what about it is true. I am imagining a Intro to Philosophy freshman saying, “It’s true about itself!” and I am also imagining my hands wringing his neck (it’s definitely a guy, since women have enough sense to avoid philosophy classes). Despite the sentence’s form, we can’t even say it’s a tautological statement (“if it’s true, it’s true”), because we don’t know the category.

Here’s a context where the sentence can actually be evaluative for truth. “Jay made peanut butter pie last weekend. This sentence is false.” Here, the subject of “this” refers to the preceding sentence, not the sentence itself. This takes it out of the liar’s paradox but it makes the sentence meaningful by giving it context. A syntax fascist might this doesn’t work because I am using the wrong determiner subject to make it meaningful, and it should be “that sentence is false,” which is not the paradox’s sentence in question. This criticism fails what I call the punch test, whereby you go up to a stranger and try to explain your linguistic nitpicking, and if your explanation sounds too ridiculous to a sensible everyman on the street, he’ll justifiably punch you in the face for time-wasting pedantry. Common-use language doesn’t need that level of detail.

tl;dr—”This sentence is false.” is not a paradox but a meaningless utterance without context, and can’t be logically evaluated for truth.