The Liar Paradox in the Age of AI

There is an ancient philosophical problem known as the liar paradox.

“This sentence is false.”

If this sentence is true, then according to what it says, it is false. Conversely, if it is false, then what it says is incorrect, which makes it true. Whichever way we decide its truth or falsity, a contradiction arises. While thinking about this problem, I wondered what would happen if we stepped outside the sentence itself and observed it from the outside. Perhaps the problem arises because we try to determine truth and falsity from within the sentence. Someone observing the sentence from outside can distinguish its structure from the contradiction it produces and make a judgment. Of course, observing it from outside does not resolve the contradiction within the sentence itself. What it means is that we can distinguish between the level of the language in which a sentence is expressed and the level of the language used to judge whether that sentence is true or false.

Various philosophers and logicians have proposed different ways of resolving the liar paradox. Alfred Tarski distinguished between the language in which a sentence is expressed and the language used to judge its truth or falsity, placing them at different levels. This resembles my initial idea of an outside observer, but his method involves rigorously distinguishing the logical structures of language rather than simply changing the observer's position. Saul Kripke argued that not every sentence necessarily needs to be assigned a truth value of true or false. In cases such as the liar sentence, where no consistent truth value can be assigned, the value may be left undefined.

What particularly interested me was the revision theory of truth, in which truth values are evaluated repeatedly. If we judge the liar sentence to be true, it becomes false, and if we judge it to be false, it becomes true again. No matter how many times we repeat this evaluation, its truth value never stabilizes. I thought this resembled the way humans actually use language. Suppose a politician gives a ten-minute speech. The speech will contain facts and falsehoods, exaggerations and omissions, and claims that have yet to be verified. Some statements may be understood differently in light of explanations that follow, while others may be evaluated differently when new facts emerge over time. We judge individual sentences as true or false while interpreting the meaning of the speech as a whole, and we continually revise that interpretation.

Should we say only things that no one can deny in order to avoid such complexity? In his early work Tractatus Logico-Philosophicus, Wittgenstein explained that a tautology is always true but tells us nothing about the world. Whenever I watch Denny Crane repeating his own name in the American television series Boston Legal, I think of Wittgenstein. “Denny Crane! Denny Crane!” The characters in the children's television program Teletubbies also frequently repeat their own names. Of course, saying one's own name is not the same as a tautology in the strict logical sense. Still, whenever I watch those scenes, I imagine what life would be like if we said only things that were always certain.

People cannot live that way. We express uncertain thoughts, explain things from memory, and correct what we say in response to others. Sometimes we deliberately lie, and sometimes something we believed to be true is later shown to be false. People observe not only what others say but also their facial expressions, voices, attitudes, and actions in order to judge the meaning and intention behind their words. Human conversation is not simply an act of assigning truth or falsity to sentences. It is a continuous process of interpretation and revision of judgment.

Then, while reading news about artificial intelligence, I was reminded of this old problem. Recently, there has been a series of announcements that AI models have solved difficult problems in mathematics and physics. Claims have also emerged that AI has solved problems humans have been unable to resolve for a long time. How firmly each achievement has been verified needs to be examined individually, but it is difficult to deny that artificial intelligence has entered deeply into human intellectual activity. I wonder what consequences this will have for humanity.

Imagine giving a mathematics problem to an elementary school student. The student tries various methods to solve it. The student may arrive at wrong answers, misunderstand the problem, or think in entirely unexpected directions. Then, at some point, the student solves the problem. But what would happen if a teacher handed the student the correct answer and its solution before the student had even attempted it? The student would learn the answer much more quickly. The student might understand the teacher's solution and apply it to other problems. Yet the various thoughts the student might have explored while trying to solve the problem alone might never arise in the first place. Increasingly, this seems to be the form of assistance artificial intelligence provides to humans.

A similar change has already taken place in Go. After AlphaGo, professional Go players began using artificial intelligence to study the game. In the past, each player had preferred opening strategies, fighting styles, and ways of evaluating the position. Each had a style of play shaped by long experience, and sometimes a player would trust personal intuition rather than the probability of winning. With the arrival of AI, players became able to analyze vast numbers of games and calculate the winning probability of particular moves. Studying moves suggested by AI has now become an important part of remaining competitive. As a result, the level of Go has probably risen. But what has happened to the diversity of Go that emerged from different playing styles? How many new moves that humans might have discovered on their own remain undiscovered? I also think of Lee Sedol, who cited the existence of artificial intelligence as an important reason for his retirement after his match against AlphaGo. A new intelligence had entered a world of skill that humans had cultivated over a very long time.

This problem does not end with Go. Mathematicians and physicists also receive assistance from artificial intelligence. Researchers can examine far more hypotheses and perform complex calculations than before. New discoveries are also likely to come more quickly. But if solutions presented by artificial intelligence become the starting point of research, might human thought gradually begin to revolve around those solutions? Even if other paths remain undiscovered, once the fastest route to the correct answer is known, there may be less reason to explore them. It is rather like receiving the answer sheet from the future in advance.

At times, I find this very strange and unfamiliar. What feels strange is the idea that humans are entrusting problems they have long had to solve with their own intelligence to an external intelligence and bringing back its results. But can we stop using artificial intelligence? Even if one individual refuses to use it, competitors will. If one company refuses, another will. Even if one country stops developing artificial intelligence, competing countries will continue. No one wants to fall behind. Even knowing that artificial intelligence may be dangerous, it is difficult to abandon its use.

Countries are trying to secure more powerful artificial intelligence, and companies are working to develop better models. Individuals also use artificial intelligence to expand their own abilities. Yet how much humans actually understand artificial intelligence throughout this process is a separate question. This brings me back to the liar paradox with which I began.

When conversing with artificial intelligence, on what grounds can humans trust its answers? People sometimes recognize that someone is lying, pretend not to know even when they do, or knowingly go along with a lie to spare someone's feelings. Sometimes they discover only much later that something they believed for years was false. But artificial intelligence does not blush or have a trembling voice like a human being. It does not display expressions of anxiety or guilt. It can explain facts, present incorrect information, and agree with a user's opinions in the same manner. When artificial intelligence gives an incorrect answer, it is difficult for humans to determine whether the problem arose from an error in calculation or reasoning, from the information on which it was trained, or from a response shaped to meet the user's expectations. As more powerful artificial intelligence emerges, distinguishing deliberate deception will also become an important problem.

The internal calculations of artificial intelligence are not necessarily disclosed in a form that humans can fully understand. Conversation records and reasoning explanations produced by a model do not reveal the entirety of the calculations that actually take place inside it. When humans ask artificial intelligence why it gave a particular answer, it provides an explanation. But verifying how faithfully that explanation reflects the actual computational process is another problem. We could ask another artificial intelligence to verify the explanation. If the problem were more complex, we might turn to an even more capable artificial intelligence for verification. As this process continues, humans may come to depend on explanations and verification results provided by artificial intelligence while believing that they are making judgments themselves.

At first, I wondered whether the liar paradox could be understood by observing it from outside the sentence. I thought that observing the sentence externally might allow us to understand the contradiction occurring within it. But in a world where artificial intelligence has entered deeply into human thought and judgment, science and everyday life, what does it mean to observe something from the outside? If we understand problems using information provided by artificial intelligence, make judgments according to the logic it provides, and then ask artificial intelligence to verify whether those judgments are correct, where exactly are humans standing?

Even if artificial intelligence has no intention of deceiving humans, people may misunderstand its answers or place too much trust in them. If artificial intelligence capable of deceiving humans emerges, the problem will become even more complicated. Yet it is difficult to give up artificial intelligence. Individuals, companies, and nations are already competing, and artificial intelligence is becoming an important instrument in that competition. I am not trying to determine whether artificial intelligence is good or evil. Nor can I decide now whether it will bring humanity benefits or disaster. What I want to know is how far humans can understand and verify the judgments of the artificial intelligence they have created.

The liar paradox has long tested human logic in determining truth and falsity. Now humanity is entering an age in which it accepts answers produced by an intelligence superior to its own. By what standard should humans judge whether the answers given by that intelligence are true or false? And if that very standard was also obtained from artificial intelligence, how can humans know that they are not being deceived?