Nonsense, Irrelevance, and Invalidity

On the liar's paradox, free will, knowledge, morality, and the is-ought gap

When you hear certain paradoxes or puzzles in philosophy, an initial thought may be “challenge accepted.” An intellectual quandary is like a sword in the stone, where discovering an answer that past geniuses have failed to decipher would vest a thinker with prestige and praise for their analytical abilities. This may be why many philosophy articles and videos have titles like “Free Will Debunked” or “The Is-Ought Problem Solved.”

But what do these alleged answers to impossible problems really mean? What is the meaning of what is being asked, and how can we tell whether a response to them is meaningful?

This article will discuss concepts and philosophical arguments that are nonsense, irrelevant, and invalid, which can be broadly classified as meaningless statements—allowing us to safely ignore them. Moving past them, meanwhile, would be meaningful. You wouldn’t have to resolve a problem when you can show that it’s not a problem at all.

What Makes a Statement Nonsense

“This sentence is false.” What does this sentence mean? If it’s true, as the sentence declares, then it must be false. And if it’s false, as the sentence declares, then it must be true.

Known as the "liar's paradox,” this sentence is one of the most famous philosophical paradoxes and has been the subject of centuries of debate, implicating some of our greatest minds. Philosophers have proposed all sorts of theories to avoid the paradox, to make sense of a paradox, or to explain what the sentence is even stating.

But many still haven’t come to terms with the fact that the sentence is simply nonsense, unable to convey any information. As a self-contradiction, it lacks what is known as “truth-value” since it is unable to be either true or false. The speaker conveys no information, and the listener can’t respond, making the statement unintelligible gibberish. If you disagree, you must be able to provide some response if someone were to say, “This sentence is false” (not counting the request for clarification).

The liar’s paradox is similar to statements like “This circle has four sides,” “That bachelor is married,” or “1=2.” These statements are incomprehensible self-contradictions that no reasonable person could interpret—not at least without bending our conventions of ordinary language interpretation beyond recognition. If someone were to say these statements, we’d ask about the mental well-being of the speaker rather than try to make sense of their literal words.

Because no ordinary meaning can be derived from the statement “This sentence is false” by a reasonable person (either through the speaker’s intention, listener’s perception, reference to an objective state of the world, or any other possible definition of meaning), the liar’s paradox can be dismissed as meaningless nonsense.

We don’t need overly complex semantics of meaning that butcher our ordinary understanding of language to make sense of a nonsense statement. By having a standard of which propositions are capable of meaning and which are not, we can live with ignoring the meaningless ones and directing our attention to more interesting matters. At the very least, for a proposition to be meaningful, it can’t be self-contradictory in a way that fails to convey information.

But there’s a deep-rooted urge not to accept this answer. Some believe that Gordian knots require a method by which they can be untied. Dismissing a famous paradox as nonsense isn’t very satisfying. We like to think of paradoxes as mysterious and intriguing, stumbling even the wisest among us—not straightforward nonsense that we’ve all been wasting time with.

What if there is a deep philosophical truth resting in a more satisfying answer to the liar’s paradox? Maybe the secrets of the universe lay in untangled the meaning of the liar’s paradox, which we can discover if we only try harder.

Yet some puzzles, by their very nature, are not subject to a resolution. And one of the tasks of philosophy should be to distinguish those paradoxes that are subject to a solution and those that aren’t. There are plenty of statements that may appear to be mysterious paradoxes at first glance but, upon closer examination, are nothing more than incoherent babble or tautologous deepities to be ignored.

There’s also the prudence that should be recognized in classifying problems as having no solution. The fact that you can’t divide by 0 isn’t a challenge posed for some math hero to solve, but a logical fact that should be accepted and incorporated into our model of mathematics.

And it’s not like nothing is gained from dismissing the liar’s paradox. Confirming that certain quandaries have no answer can also be constructive. An accurate description of the world shouldn’t require personally gratifying answers, only reasonably acceptable explanations that can guide us through other topics.

We also don’t need an agreed-upon definition of meaning to dismiss a statement as meaningless. If a proposition isn’t capable of providing information, conveys the speaker's intent, or refers to something in the world—like the liar’s paradox—then it lacks meaning.

This classification of meaninglessness doesn’t just help us understand the liar’s paradoxes but can shed light on other hotly debated issues in philosophy.

What Makes a Statement Irrelevant?

A proposition doesn’t have to be a paradox to be meaningless. If it fails to convey any information so that it’s only a tautology, then it’s also meaningless on account of irrelevance.

Take a basic contradiction; this sentence, “This circle has four equal sides and four right angles,” is meaningless for failure to convey anything.

However, it’s opposite: “This circle does not have four equal sides and right angles” is also meaningless, as it’s only true in a trivial sense. To someone who already knows what a circle is, the truth is totally vacuous and meaningless—but due to lack of relevance rather than contradiction like the liar’s paradox.

The idea of a circle already implies that it doesn’t have equal sides and angles. So, if both speakers know what a circle is, then the statement can be discarded without consequence (see the maxim of relevance in language).

This is similar to our deflationist understanding of truth, where the concept of “truth” adds nothing to our discourse. The statements “snow is white” and “it is true that snow is white” are understood to be the same propositions, with the phrase “it is true” being redundant. Accordingly, the extra phrase is meaningless on account of irrelevance.

And just because a proposition is true doesn’t mean it can’t be meaningless. If I were to say, “The Big Bang caused me to write this article,” I may be saying something true. Had the Big Bang not occurred, I wouldn’t be writing this article. But it provides no information about the relevant causes of my writing this article. With this understanding of meaningless truths on hand, we can understand why popular criticisms of knowledge and free will can be ignored.

A relevant statement can’t be a mere tautology but should convey an intention by the speaker to convey information to the listener.

I’ll have more to say about meaning in a later article. Still, for now, we can settle on the condition that a proposition must (at least) intend to convey information to the listener for it to be relevant—and, hence, be meaningful.

Knowledge

Skeptics argue that to have knowledge, we must first disprove the possibility that reality is an illusion (e.g., we’re brains in vats, we’re in a simulation, we’re being controlled by an evil demon—which I will call “illusion theories”). Yet because we can’t disprove illusion theories, we can never say that we have knowledge about reality.

But this is self-defeating. Because there is no way to disprove illusion theories (given their logical possibility and correspondence with all of our evidence), skeptics, therefore, cannot present a conception of knowledge. No set of factual circumstances would allow one to have knowledge. More to the point, there is no possible world where knowledge could ever be obtainable, according to the skeptics. But then, what does knowledge mean under this standard that skeptics establish?

According to skeptics, statements about knowledge would be either irrelevant or nonsense — unless you say that knowledge doesn’t exist, then all your other statements on knowledge couldn’t ever be true—and therefore meaningless in either case. What would having knowledge even look like for the skeptic?

It would be like having a word for information that we couldn’t ever have, called schmowledge. The only correct way to describe schmowledge would be to state that it doesn’t exist. However, what would then be the point of talking about schmowledge? You couldn’t ever have a meaningful discussion on schmowledge, and there would be no consequences to removing it from our vocabulary as a senseless term. If knowledge is like schmowledge, where by definition it would be impossible to have—like how the skeptic understands it to be—then you couldn’t have any meaningful discussion on knowledge. But we do use “knowledge” in a meaningful way.

Statements like “I know that I’m sitting on a chair” or “I don’t know how many hairs I have on my head” have a certain meaning that listeners can comprehend. Therefore, we need to choose between the skeptic’s understanding of knowledge, which is meaningless, and our own, which can be.

I will call this the “inconceivability objection”: if X is inconceivable (not capable of existing in any possible world), then all true propositions about X can only refer to X’s non-existence. As a result, X itself may be classified as meaningless since no proposition about X could convey any information.

For example, if we defined a “womble” as a four-sided circle, then stating “Wombles don’t exist” would be a tautology, and saying “I have a womble” (or anything else about wombles) would otherwise be false. Therefore, the concept of a “womble” can be dismissed as meaningless under the inconceivability objection.

Claims about “wombles” isn’t the same as claims about leprechauns or unicorns. We can at least imagine tiny Irish men or winged, magical horses. Meanwhile, four-sided circles are entirely unimaginable.

The skeptic’s idea of knowledge is similarly meaningless. Because the skeptic cannot present any set of circumstances where one can have knowledge (as you cannot disprove illusion theories), then the skeptic’s idea of knowledge is inconceivable. Therefore, the skeptic’s sense of knowledge is meaningless under the inconceivability objection since knowledge can only be described through either tautologous or false propositions.

But we don’t need to get rid of knowledge entirely. We only need a better conception of it, which I had (very tentatively) defined as justified belief connected to a truth using a “reasonably certain” standard or proof.

I’ll call this the “relevance requirement”: If we understand a concept as having relevancy in discourse, then it should be given a meaningful definition that would give it such relevancy corresponding to its use in discourse.

For example, say we were to have a meaningful discussion on the “meaning of life” but recognized that there is no objective meaning of life. But this doesn’t mean we are speaking nonsense when discussing the meaning of life. This isn’t the liar’s paradox, where what is assumed to be true (as all propositions assume truth—per the redundancy theory of truth) is also recognized as false. Rather, there is a conception of the term that we are using that is meaningful and should be recognized as such, as opposed to the meaningless conception of the term. For instance, we may be talking about the “meaning of life” in a subjective sense.

The “relevance requirement” is a canon of interpretation stating that we shouldn’t attribute nonsense to a discussion we consider to be relevant. Suppose there is a concept of a term that is meaningless but is still used in a relevant way in discourse. In that case, that speech should be interpreted using the relevant, meaningful sense of the concept rather than the meaningless one.

As applied to knowledge, the skeptic’s concept of knowledge (requiring that one disproves the possibility of illusion theories) is subject to the inconceivability objection and is, therefore, meaningless. But we still use knowledge in a meaningful way, so we should give “knowledge” a definition that is meaningful under the relevance requirement.

Some may want to retain their skeptical theory by arguing that we should abandon the idea of knowledge entirely if skepticism shows that it’s meaningless. Yet this isn’t possible.

The idea of knowledge is hard-wired into our shared understanding of the world. Abandoning the idea altogether requires life to be impractical and our statements to be tedious since all of our propositions would have to have some qualifier for illusion theories (ex: “To the extent reality isn’t an illusion, I know that . . .”). Between either abandoning our understanding of knowledge entirely or skepticism, we can do fine without the latter.

Free Will

The above application of the inconceivability objection and relevance requirement apply to the determinist’s idea of “free will” as they do to the skeptic’s idea of knowledge. But I’ll make this explicit.

If you’re a physicalist, then you believe that everything that exists can be reduced to physical matter. And since physical matter is subject to the laws of causation, then free will isn’t even conceivable in a physical being. What would a physical being with true free will even look like? How can a thing not be subject to causation?

Free will couldn’t just be incompatible with our evidence on the brain, but incompatible with the laws of the universe. Under the determinist’s conception of free will, free will couldn’t exist in any possible world. It would be a meaningless idea, and saying “free will doesn’t exist” would only be a tautology. Therefore, the determinist’s concept of free will is subject to the inconceivability objection and can be dismissed as meaningless.

Some people argue that despite determinism, a certain idea of free will is still “useful.” Yet they don’t take the extra step and conclude that the determinist’s understanding of free will is “useless.”

However, there is an issue with dismissing the term as meaningless. We don’t have nonsensical or tautological discussions on free will. Our conversations about free will can be meaningful and informative, as those interested in the topic can attest to. Therefore, while the determinist’s idea of free will can be disregarded under the inconceivability objection, because of the relevance requirement, we should understand free will in a meaningful way that is compatible with how it’s used.

It wouldn’t make sense to have the term “free will” in our vocabulary if it wasn’t meaningful. We are left with either abandoning the concept altogether or understanding free will differently. And free will has good reasons to exist.

The distinction between a man killing his wife while he’s still asleep and a man killing his wife deliberately and in cold blood is a meaningful one that any reasonable person could recognize. The idea of free will helps us understand the intentionality of subjects in certain situations that convey information.

We should view free will as an experience, as I argue. This aligns more closely with our shared understanding of free will.

Responding to the question “Why did you forget to take the trash out?” with, “because electro-chemical processes in my brain had affected my body in such a way that did not cause me to take the trash out” is meaningless. While the response is literally true, it is effectively a tautology that fails to convey information. It can apply to all actions and inactions. Yet the inquiry is requesting a meaningful response. We wouldn’t blame the inquirer for asking the question that led to the empty response, but would blame the respondent who missed the point of the question.

Knowledge and free will are far from the only philosophical concepts that are meaningless in one sense, which their opponents argue them to be, but can be attributed a relevant definition. “Truth,” “Luck,” “Mind,” and “Desert” are similarly claimed to be subject to interpretations that would make their existence inconceivable, which is incompatible with their meaningful use in discourse.

Defining our terms is important, and if we’re going to be using concepts, then they should be understood in a meaningful way. Otherwise, our discussions can get stuck on terms that make as much sense as the liar’s paradox.

Is Ethics Meaningless?

In this article, I’ve targeted what some define as knowledge and free will to show that inconceivable ideas are meaningless and don’t belong in meaningful discussion. But couldn’t the same analysis be applied to morality?

Moral anti-realists argue that moral statements are similarly meaningless nonsense. Simply, if there are no genuine moral facts, then any descriptive statements posting their existence couldn’t be true or false but meaningless and would only reveal something about the speaker’s mindset.

Statements on morals are like Willie Sutton’s response when asked why he robs banks: “Because that’s where the money is.” The statement reveals no new information about banks (what the statement is referring to) that the listener didn’t already know, but is only meaningful by revealing something about the speaker himself and his state of mind.

But I will argue that it’s not moral statements that are meaningless. Rather, it’s the conception of morality that anti-realists hold, which is meaningless and is subject to the inconceivability objection.

Moral anti-realists have the standard of what I’ll call the “magic words” theory of ethics. When they ask, “Why should I be moral?” they are actually asking for a certain combination of words that could transform an otherwise cold-hearted criminal who couldn’t care less for his fellow man into a bleeding-heart saint who would sacrifice himself for it.

Maybe the magic words are a deductive proof establishing universal moral laws. Or perhaps they provide evidence for certain “moral stuff” in our universe. I’m not sure what anti-realists are asking for, but because these “magic words” don’t exist, they therefore conclude that morality doesn’t exist.

However, it is because we are free, with the ability to impose our own values onto the world, that we can’t be subject to “magic words,” and no such proof or thing is capable of binding anyone. There isn’t even any possible world that could contain moral facts binding over free people under the “magic words” theory of ethics. No statement or deductive proof or announcement could be actually binding on free people. Again, what could these magic words possibly be? What are the moral anti-realists even asking for?

Freedom is the foundation of morality, but it is also what makes the moral anti-realist’s understanding of morality inconceivable. Even if moral facts were carved by our creator in stone or etched into the stars of the universe, those physical facts couldn’t create moral demands on conscious beings—not at least independent of the will and values of those conscious beings.

The inconceivability objection applies to the conception of ethics held by moral skeptics. If they can’t provide a conception of morality, then they can’t explain how we can have meaningful discussions on morality. This is showcased by the Frege-Geach problem, where the non-existence of morality cannot explain the fact that moral arguments can be valid without these moral claims having truth-value (as the moral anti-realist argue they lack).

Moral skeptics should be able to offer some standards that would otherwise prove morality exists. Something has to satisfy them. But if they can’t have any standard, then they need a meaningful conception of morality that tracks meaningful discussions on the topic.

The fact that we understand terms like “moral” and “immoral” shows that there is a shared meaning to these terms that has some conception and is not entirely inconceivable. We aren’t making nonsense “liar’s paradox”-type statements when we say things like “stealing is immoral,” “it’s ethical to help the less fortunate,” or “whether or not abortion is immoral is a complicated issue.” We understand what these statements mean—making the “magic words” theory of morality incompatible with a sense of morality that is comprehensible.

Since moral anti-realists can’t offer any conception of what ethics could be, they should allow for a concept of ethics that makes sense. This is the account of ethics that I argue for: ethics by agreement.

Logical Invalidity and the Is-Ought Gap

Let’s discuss two people, Sam and Greg. Both Sam and Greg have their own set of facts that describe each of them: Greg is an electrical, Sam enjoys true crime podcasts, Greg lives in San Diego, Sam was born in August, etc.

However, no fact that solely references Sam can even state a fact about Greg. You can know everything you can about Sam: his childhood memories, his likes and dislikes, and his innermost thoughts. But none of that will tell you anything about Greg unless Greg is explicitly referenced—since Sam and Greg are two separate beings. While Sam and Greg may be related in some respects (say Sam and Greg have some relationship with each other), their separateness prevents facts solely about one conveying anything about the other—at least until the other is named.

No matter how many propositions you make about Sam, none of them will say anything about Greg without explicitly referencing Greg. There are Sam-facts and Greg-facts, which alone are as separate from one another as parallel lines. This is the heart of the is-ought gap.

Just like how the facts about Sam and Greg are separate, descriptive and normative facts are also logically separate. There are no empirical facts that necessarily imply normative or “should” claims—not until a “should” claim is explicitly premised. I can give you all the facts possible about health and human nutrition, but those couldn’t, on their own, conclude that you should diet and exercise.

And all the facts about human history, psychology, biology, and physics couldn’t get you a theory of morality. Rather, morality derives from valuing reason and freedom, which would endorse that one should abide by those principles that free people would reasonably agree to, as I argue here.

This also seems a bit counterintuitive. All the facts of the world should count for something about morals. But if you think about it, how could they? Facts don’t have any values laden within them. And we can only get should claims from values.

Take an example. If we have a super-computer, no amount of information we put into the computer would make it grow legs and give it certain passions or recognize ethical duties (not, at least, without that computer first becoming conscious and gaining the ability to impose its own values on the world). The computer can contain all the information in the universe, but none of those facts alone can give the computer a value-based agenda. If you think that descriptive claims can imply normative claims, do you really believe that pure information processing can lead the information processor to have values?

Descriptive facts alone are orthogonal, or unconnected, to values. Descriptions may exist in our mind-independent model of the world, but values are purely mind-dependent and exist only as far as conscious beings create them. If the world suddenly depopulated all its conscious beings, then values would similarly be depopulated from the world—although the descriptive facts would be the same. Values are things that are imposed onto the world, not things that exist in the world.

Attempts to bridge the is-ought gap are effectively exercises in sophistry. They should be viewed like a magician’s performance. You should know that the magician didn’t really do the impossible by violating the laws of physics—rather, there was only some trick they performed to make it appear so. The same guard we put up when we hear claims of magic or miracles should also be repurposed to claims of deriving values from facts.

It is unfortunate that the “is-ought gap” is described as the “is-ought problem.” It isn’t any more of a problem than 50 being greater than 30. You may not wish that 50 be greater than 30, but in every possible world, 50 will be greater than 30. And in every possible world, descriptive statements will never lead to normative conclusions.

The “is-ought” gap isn’t a matter to be “solved” but recognized in our model of the universe. Any possible “answer” would likely serve to confuse our concept of descriptive or normative statements, like how trying to force a round peg into a square hole would only do damage to the peg or to the hole. Supposed bridges to the is-ought gap are inherently invalid.

Any answers to the is-ought gap are therefore subject to the inconceivability objection. There is a logical divide between “is” and “ought” claims, where any sort of unity would be logically impossible, and therefore meaningless—giving us license to ignore them.

However, any answers are also not subject to the relevance requirement. Our ordinary discourse doesn’t suffer from a divide between “is” and “ought” claims. Normative claims can be value-determined, and descriptive claims can be objectively determined. There is no need to alter this distinction to give our speech meaning.

So, alleged answers to the is-ought gap can be disregarded as meaningless without the need to give them a meaningful interpretation.

Conclusion

Some propositions are self-contradictory nonsense. Some propositions are irrelevant. And some propositions are invalid. All of them are meaningless. And we can tell if an idea itself is meaningless if that idea is inconceivable—not being possible in any world— allowing us to ignore that idea as propositions used to describe it serve no purpose in discourse. However, the meaningless understanding of these ideas would be incompatible with the fact that these ideas are used in meaningful ways.

Therefore, we can use the relevance requirement to give them a meaning that is compatible with their use in public discourse. This can be applied to our understanding of knowledge, free will, morality, and many more issues where our dialogue is muddled. Going forward, we can do better in disregarding meaningless concepts, imposing meaning on confused concepts, and understanding the distinction between the two.