The Liar Paradox and the Meaning Paradox

On the nature of meaninglessness

What is meaning? And how do we know when a certain arrangement of figures has it? Clearly, a series of random characters like “dasjfewna” is meaningless. It’s not even a word, which is defined as “a single distinct meaningful element of speech or writing.”

And sentences like “Book table the the on is,” are similarly meaningless. Although the individual words in this sentence each have an ascribed meaning, they are structured ungrammatically so that the sentence lacks meaning. For now, we can define “having meaning” as conveying a thought, which the above word and sentence fail to do.

Yet meaninglessness also extends to grammatically correct sentences composed of meaningful words. Take the sentence, “Colorless green ideas sleep furiously.” The words and syntax both make sense, but the proposition about how colorless green ideas sleep is nonsense—the sentence might as well be gibberish.

Importantly for us, certain propositions in philosophy, despite being a source of rigorous scholarship and lively debate, are meaningless.

Yet how do we know? What makes a sentence like “Colorless green ideas sleep furiously” meaningless? What properties do these types of sentences possess (or fail to possess) that meaningful ones lack or have? I argued in my previous article that meaningless sentences include expressions understood as nonsensical, irrelevant, or invalid. By the standards of ordinary speech, propositions like these are neither true nor false—they don’t even have a chance to be one or the other—but are an error in discourse.

The Liar Paradox

Hopefully, this article will clarify the ideas sketched in my previous article, as I’ll try to make my (non) answer to the liar paradox straightforward. The statement, “This sentence is false,” is neither true nor false; it lacks meaning as a contradiction. No thought is expressed since a contradiction, quite literally, violates the laws of thought. What thought could you otherwise express by saying, “Both A and not A”?¹

If we were to hear someone say, “This sentence is false,” in regular discourse, we wouldn’t think they are referring to anything whose truth or falsehood could be examined. Rather, we’d just say they’re speaking nonsense. A heuristic for determining whether a statement is meaningless is whether a reasonable listener could respond by saying, “What the hell are you talking about?”

Yet this doesn’t mean that the liar paradox hasn’t been helpful for our understanding of logic, mathematics, and philosophy—as paradoxes can help us generate new insights, whether or not they are resolved. As argued, understanding the nature of “meaninglessness” reveals the issues with our conceptions of free will, knowledge, and morality—and its consequences for discourse.

And no, I don’t put myself above the many others who have tried to input meaning to the liar paradox. Attributing meaninglessness to the liar paradox is a fairly common interpretation, especially for ordinary listeners of the statement. I only intend for this article to explain this inherent intuition.

So why is the liar paradox nonsense? Let’s examine it. First, per the redundancy account of truth, we should recognize that descriptions of the truth of a proposition are irrelevant. So adding “It is true that . . . ” to the beginning of a proposition is redundant, as an assertion of truth is already baked into every proposition.

All statements of judgments carry an underlying (+) sign of truth that doesn’t need to be stated explicitly. The propositions “Snow is white” and “It is true that snow is white” are identical propositions—with the “It is true that . . . ,” used in the second sentence not operating. The statement just has two (+) signs.

The liar paradox must be assumed as true. Otherwise, the word “false” doesn’t do any work if “false” isn’t considered a true description of the sentence. You can’t get the “false” description to function unless the statement is initially assumed to say something true. The liar paradox, therefore, has both a truth operator and a falsity operator.

Let’s add “It is true that . . . ,” to the liar paradox to make this clear: “It is true that this statement is false.” Notice that we haven’t made any substantive changes to the proposition; it's substantively still the same as “This statement is false.”

We can now see that the liar paradox is asserting two separate claims:

1. This statement is true (implicitly, since it is a proposition).

2. This statement is false (as stated explicitly in the statement itself).

I hope you can see why the liar paradox is a straightforward contradiction (an assertion of both A and not A). The statement states that it is both true and false, two contradictory properties that can’t be held simultaneously, a plain violation of the law of non-contradiction (LNC).

These qualities of the sentence that the liar paradox ascribes are mutually exclusive. You can’t say that a sentence is both true and false any more than you can say that an equation equals both 1 and 2 or that a shape is both a square and a triangle. You wouldn’t just be wrong, but you wouldn’t have a chance to be wrong, since a contradiction conveys no thought that can carry a truth value. It does not compute.

Statements whose referent is something logically impossible (like statements about “colorless green” things or a “true sentence that is false”) lack “sense”—the thought to be understood by a listener. Since there is no way we could understand statements that refer to these inconceivable objects, no concept is conveyed. Statements that refer to them lack sense or are “non”-sensical. As the liar paradox fails to convey a thought, it might as well be gibberish.

Maybe one day, we will have reason to discard the LNC. But we shouldn’t discard it solely in response to a meaningless utterance like the liar paradox, as we can understand the sentence without throwing away basic logic and common sense. As for now, accepting a contradiction would be to accept anything as nothing definite could ever be expressed. So while my argument relies on accepting the LNC, without the LNC, you would have to accept everything.

For those still skeptical about the laws of thought and may tend towards something accommodating to contradictions like dialetheism, you should be prepared to explain what thought the liar paradox (or any contradiction) conveys when used in ordinary discourse. For instance, if someone were to state the liar sentence as he is pointing to an actually false sentence (for example: “The moon is made of cheese.”) then the liar paradox, when uttered in that context, conveys the thought: The statement ascribing a cheesiness property to the moon is not actually the case.

Yet when the statement “This sentence is false,” refers to a true sentence (the sentence itself, as it already has a truth operator), what thought is being conveyed?

If none, the statement can’t bear the properties of truth or falsehood (let alone both), as only expressions of judgments can be true or false. If a judgment is not expressed, the true/false property is inapplicable. And we’d recognize the statement to be meaningless.

In conversation, saying, “This sentence is false,” would create the same reaction that 1 equals two 2, or that a thing is both red all over and blue all over. We may be receptive to certain contradictions that do manage to convey a distinct thought: "Less is more,” “We have nothing to fear but fear itself,” “The more things change, the more they stay the same."

Yet we find those types of statements impactful because we understand that a thought is still being conveyed despite that thought being uncaptured by the statement’s words alone—which would be nonsense if understood only literally.

Moreover, if the liar paradox was meaningful, where do we draw the line for sentences that we should be capable of making sense of? Are semantics and grammar the only requirements for sentences to have meaning? I argue not, in view of that fact that we should understand the “meaning” of statements—the thought being conveyed—as more than just the internal structure of the statement, but how the statement relates to context.

Whether the liar paradox is true or false isn’t any more of a mystery than of 4-sided triangles or how furiously colorless green ideas sleep. It’s all nonsensical—you can’t make sense of a thought if there is no thought to make sense of.

When is Something Nonsense? (rather than true or false)

“The current Prime Minister of France is bald.” is a false statement. France’s Prime Minister, Gabriel Attal, appears to have a fine head of hair. But a statement like, “The current King of France is bald,” lacks the ability to be false, as argued above. There is no current King of France, so how could he possibly be bald?

Importantly, we’d process the two statements very differently. The judgment about the French Prime Minister is a judgment of a fact and can be understood as either true or false in relation to that fact. But that regarding the current French King is confused—it fails to denote anything; no judgment is conveyed.

If I were to make a claim about the current King of France, we wouldn’t just say that I was wrong but would respond with, “What the hell are you talking about?” Describing the sentence as only false would fail to capture the sentence’s nonsense, as it is not clear what thought the speaker tried to express. Was the speaker trying to refer to the Prime Minister? Or was the speaker trying to describe a previous King of France who was bald? Who knows. The listener is left trying to guess at the speaker’s meaning, as the words alone fail to express it.

Admittedly, this interpretation of meaninglessness is siding with Peter Strawson’s critique of Bertrand Russell’s theory of descriptions, where Strawson argued that statements that fail to refer like, “The Present King of France is Bald,” should be understood as meaningless rather than false. I won’t go over the logical issues of this debate, as I only argue here that Strawson’s view aligns more closely with our ordinary use of language.

To simplify, we can define “false” as “not being the case” and “meaninglessness” as “not capable of ever being the case.”

For instance, how could we understand the statement, “Colorless green ideas sleep furiously,” to be false? Does the speaker think it’s possible for colorless green ideas to sleep? Or is the speaker referring to something that could actually sleep? We don’t even know what thought is being conveyed, if any. So, we can’t judge a proposition as true or false if we don’t even know what that proposition is.

Rather the statement is a set of contradictions, asserting both A and not A. Like how the liar paradox can’t be both true and false:

1. A green thing can’t be colorless.

2. An idea cannot sleep.

3. You cannot sleep furiously.

Antithetical descriptions are not capable of ever being the case.

Meaningless statements also include statements that appear to be true but are only “vacuous truths.” These sorts of truths, although perfectly intelligible, fail to say anything and instead contradict beliefs already provided in context. For instance, if we say, “It is not true that colorless green ideas sleep furiously,” the statement would be true in only a vacuous sense. The speaker’s statement contradicts the understanding that what is being described could never be the case.

Also take the sentence, “All the cellphones in the room are off,” when it is understood by both the speaker and listener that there are no cellphones in the room. The sentence might have said something logically true, but you haven’t conveyed a meaningful thought to the listener. What is being referred to when you say, “are off”? The statement itself contradicts the understanding that there are no cellphones.

We can define “true” as “being the case,” and “meaningless” as “not capable of NOT being the case.” As vacuous truths are not capable of not being the case, they are meaningless.

This is the inconceivability objection—statements about inconceivable ideas (like colorless green things) have no meaning.

As I had argued previosly, certain views can create an inconceivable picture of a particular philosophical idea. The determinist’s idea of free will is a physical being not subject to the laws of physical causation. The skeptic’s idea of knowledge is justification for a belief that can’t ever be justified. The moral anti-realists’s idea of morality is inherent restrictions on free agents.

These concepts are meaningless. In no possible world can there be physical things entirely free from physical causation, unjustifiable beliefs that are justified, or free people who are inherently restricted to act morally. These are plain contradictions. So why do we give them so much attention? Why do people view these concepts as inherent riddles to be solved? It’s like trying to make a circle out of four straight lines. Its not possible to do in any world, because they’re nonsense ideas.

Now that we have a sense of concepts that are meaningless because of their inconceivability, we run into a problem of how these supposedly unintelligible concepts are so well understood in ordinary discourse. We can call this issue the “meaning paradox.”

The Meaning Paradox

Gilbert Ryle uses the below illustration to explain the idea of “Category Mistakes.”

A visitor is taking a tour of the University and is shown the University’s dormitories, administrative offices, laboratories, and all the other sites of the school. At the end of his tour, the visitor acknowledges these landmarks, yet still asks:

But where is the University? I have seen where the members of the Colleges live, where the Registrar works, where the scientists experiment and the rest. But I have not yet seen the University in which reside and work the members of your University.

What can the visitor be referring to? Maybe “the University” doesn’t exist? However, the visitor only mistakenly believes that the University is a separate physical structure rather than a collection of certain structures. Not only that, but the visitor’s own concept of the University does not make sense. What would the University even look like to the visitor? Some sort of physical structure separate from all of the other structures associated with the University? It is not a thing that could ever be the case.

This is what I discussed as the “inconceivability objection.” If the visitor cannot describe a conception of the University independent of the buildings and spaces, then the visitor’s concept of the university is meaningless.

But you can imagine the visitor being a “University anti-realist,” who argues that because all the physical structures in the university neighborhood have their own existence as dorms, offices, classrooms, and the like, then the University doesn’t exist, as we can understand the neighborhood in terms of those separate structures.

However, our issue isn’t with anything physical in the world. It's just our concept of “the University.” The visitor has the wrong one, as clearly we mean something when we describe the neighborhood as “the University.” I am referring to this as the “meaning paradox”: using meaningless words in a meaningful way. This can’t ever be the case. Either the word has no meaning, where it fails to convey a thought, or it has a particular meaning that the “meaningless” label fails to capture. One has to give.

Those who don’t understand the existence of free will, knowledge, and morality are like the visitor asking where the University is. They have the wrong framework to grasp these ideas and instead expect them in some ethereal form.

But if they’re meaningless, how do we understand statements like, “Abby chose to go to the store,” “Bobby knows that his car is parked outside,” or “Chad acted immorally by lying.” These types of statements are perfectly intelligible and convey a coherent thought to listener.

Yet if we hold a meaningless idea of free will, knowledge, and morality, then such sense-making would be impossible. “Choice,” “knowledge,” and “immorality” might as well be colorless green ideas or four-sided triangles. So which one has to give? Are these concepts truly nonsense, and would our discourse track reality better if we abandoned them, as some have argued? Or is there an actual referent that skeptics of these conceptions are missing?

This is a paradox for determinists, skeptics, and moral anti-realists. Senseless statements can’t be understood. Saying something along the lines of, “This tea is hoddey,” where hoddey is a word I had just made up, should give the listener pause. The listener couldn’t only say the statement was false, but failed to express anything meaningful.

However, what if we could have meaningful discussions on whether particular tea is or is not hoddey? Then, the word wouldn’t be meaningless. It has to refer to something if it expresses an intelligible thought that others can comprehend. If the listener can make sense out of a supposedly nonsense idea, then the idea isn’t nonsense.

Just because we can’t point to a physical “University-like” thing doesn’t mean the University doesn’t exist. And just because we can’t point to a physical manifestation of free will, knowledge, or morality doesn’t mean that these don’t exist as well. Rather, these concepts should be understood in a way that makes sense and aligns with their use in discourse. There is a thought being expressed when we use the word “University” like there is when we use “choice,” “knowledge,” or “moral.” Defining them precisely may be difficult (although feel free to review my attempts), but we can’t excuse ourselves from this necessary work by defining them out of existence.

Let me state the premises of the “meaning paradox.”

1. If a concept is inconceivable so that it lacks content, then it’s a meaningless concept.

2. Meaningless concepts cannot be used pragmatically in discourse.

3. Some concepts express a thought that can be used pragmatically in discourse.

4. Concepts that express a thought that can be used pragmatically in discourse cannot be meaningless.

5. If these concepts are not meaningless, they have a meaning that is conceivable.

6. However, if the meaning is conceivable, then it cannot be inconceivable.

In essence, you can’t use a supposedly meaningless concept in a supposedly meaningful way. Either the concept is meaningful, or it hasn’t been expressed meaningfully. The former would include certain foundational concepts in philosophy. The latter would include the liar paradox.

Conclusion

I have argued why meaning requires more than just defined words or obedience to grammatical rules; it also must convey a thought, which contradictions like the liar paradox fail to do.

Statements that are not capable of being the case (or not being the case) are contradictions that fail to convey a coherent thought. Therefore, statements that fit this description like the liar paradox, rather than being true or false (as only propositions about facts can be) are meaningless.

Yet if a statement is truly meaningless, it can’t be used in a way that would convey a thought—which would be a “meaning paradox.” One or the other has to give. The fact that we understand the thought conveyed when terms like “choose,” “know,” and “should” show that these terms do contain a certain meaning that fails to be captured by a method of understanding of these words (that of the determinist’s, skeptic’s, and moral anti-realist’s respectively). These concepts should, therefore, be understood in a different sense that aligns with how we use and comprehend them, so as to give them the meaning they are already recognized to have.

Side Note: I apologize for the hiatus; studying for finals and the holidays have dominated my weekends (or writing time). However, while I initially began this substack to argue for a conception of morality and law that I believe has gone overlooked in ethical and legal discourse, I realized only recently that these theories of morality and law rely on a certain theory of meaning. I hope to explain this theory of meaning in the next few articles. As a summary of what's to come of this project, I hope to first explain what I mean by “meaning,” then “morality,” then “law.” God bless those who are still reading as I work these thoughts out, but I hope my excitement of explaining these ideas translates into enlightening reading for you.

1. By which I mean, a thought that can be understood in a way that retains the contradiction. For example, if I were to say, “My day was both good and bad,” you wouldn’t necessarily understand the statement as a contradiction. Rather, you would likely interpret it as saying that my day was good in some respects and bad in others. This makes sense and is not a contradiction. However, if the statement were instead, “My day was both purely good and purely bad,” that interpretation would be closed-off. We may interpret the statement as nonsense unless we can extract some coherent thought from the statement, like meaning “good,” “bad,” or “purely” in a non-standard sense based on context so that they’re not mutually incompatible.