Contradictions in Natural and in Artificial Intelligence

Jun 11, 2026

Contradictions in Natural and in Artificial Intelligence

Michael Pakaluk^[1]
Pontifical Academy of St. Thomas Aquinas | Rome, Italy | June 11, 2026

Artificial intelligence is dependent upon natural intelligence. It does not understand anything but predicts the speech of those who do. It does not know the world through constructing a model of it, but rather it models the speech of those who are engaged in such projects of modeling. I am interested here in how its inability genuinely to contradict itself sets it apart from natural intelligence. One might say my question is the difference between being affected by a contradiction and what is called “training.”

Dogs may hesitate. Elementary particles show superposition or duality, not contradiction. No scientist ever comes upon “recalcitrant data” and wonders whether, in this instance, nature is irrationally contradicting herself. Contradiction seems distinctively human. Is it a task, then, for us to be free from contradiction? Does artificial intelligence, given that it cannot contradict itself, genuinely assist us in this task, or distract us away from it?

If the classical tradition is right, the ability to be genuinely affected by a contradiction is bound up with our capacity for beatitudo.

We know persons who have changed their lives deeply through coming to understand that what they hold in some important matter is contradictory. Consider for example a Protestant who believes sincerely and fervently that Scripture alone is the rule of faith. Now consider that someone, calmly and in a friendly spirit, points out that Scripture does not support the rule of Scripture alone, so that his conviction is self-defeating, and that Scripture does not and cannot tell us what writings count as expressions of revealed truth, so that clearly he is relying on some authority other than Scripture as a rule of faith. In the matter most important to him, he is caught up in two fundamental contradictions. How he responds to them reveals and perhaps even changes his character. Will he, for instance, “sweep them under the rug” and engage in deliberate thoughtlessness? Then he makes himself ever after a thoughtless person, unless he changes. If he thinks to himself, “It cannot be that so many admirable Christians are mistaken in this matter,” he has changed himself ever after because he has now subordinated his conscience to the judgments of others. It is also difficult to change in a moment. If he has love of truth and humility he will say to himself, “Clearly, I must think these things through and investigate them more fully” and he will devote himself to such a task, taking perhaps months or years, until he either can answer the arguments or rejects Sola Scriptura.

Obviously, what I have just described is not a matter of this person’s needing more “training” or his becoming better at predicting what others would say.
The Aristotelico-Thomist tradition began with Socrates deliberately leading others into contradictions like this in the most important matters. “I consider that nothing worth speaking of will have been effected by me unless I make you the one witness of my words; nor by you, unless you make me the one witness of yours; no matter about the rest of the world,” Plato depicts him as saying to Polus (Gorgias 473e, Jowett translation). And therefore we see that my contention is at the same time the contention that an artificial intelligence never becomes, nor ever can become, a “witness” in this sense, and it does not reply to a prompt in order to make you a witness.

Plato clearly ponders what we might call “the significance for someone’s character,” of his own recognition that he is contradicting himself in an important matter. Such a contradiction ought to cause embarrassment and shame. Thrasymachus is said to turn red (Republic 350d). Callicles accuses Socrates of wanting publicly to humiliate others, making them ashamed (Gorgias 482e—483a). “Refutation is the greatest and chiefest of purifications, and he who has not been refuted, though he be the Great King himself, is in an awful state of impurity; he is uninstructed and deformed in those things in which he who would be truly blessed ought to be fairest and purest,” the Eleatic Stranger says (Sophist 230d—e), and therefore, he points out, true education, true learning, is mental purification.

Analytic philosophers (I mean Frege, Russell, and early Wittgenstein) can claim to have discovered the computer, in their attention to truth tables, realized in logic gates; their commitment to a standard of complete rigor, which led to the study of algorithms; and their conception of mathematics as traceable to putatively obvious principles of logic. The inspiration of the early analytic tradition at essence was the same as Leibniz’s hope of a universal mechanical calculator. One may even interpret the Tractatus as an argument that the entirety of everything in the world, as grasped through an artificial intelligence, nonetheless leaves everything of importance out, in leaving the whole unexpressed.

But in this tradition, of itself, a contradiction does not have the ethical significance which Plato accorded it. A contradiction is a bug in a system; it presents us with an engineering problem. Russell did not take himself to be refuting Frege but Frege’s system when he reported to Frege his discovery of what we call “Russell’s Paradox.” Frege said in reply, “Arithmetic totters,” not “I stand in need of purification.” If he was crushed personally, as he was, this was irrelevant to the project. He was discouraged by failure, not ashamed that he had embraced evil. Later in life he came to believe simply that he had made a mistake, of taking discrete quantity to be prior to continuous quantity. ^[2]

Of course we can contradict ourselves “locally,” not as explicitly working within a formal system. Suppose that I deliberately assert, “Snow is white, and snow is not white.” What is wrong with that?

In the analytic tradition, I think it is fair to say, the content does not matter. Simply considering a statement as a contradiction, what is wrong with “Snow is white, and snow is not white” is the same as what is wrong with “Scripture is, and is not, the sole rule of faith.”

And I think that, in this tradition, there are three basic ways of explaining what is wrong with asserting a contradiction. One is that you have done something and then have immediately reversed or negated it, like a man who takes a step forward but immediately takes one back. A second is that you have not done anything at all, when you thought that you had, either because your assertion misfired, or because it was empty. A third is that you have asserted something which could be exploited to make you assert, of your own accord, anything whatsoever, because the assertion of a contradiction implies everything. A contradiction, if asserted, yields an unrestricted supply of consequences. It functions in theoretical reason the way a Dutch book, or “money pump,” functions in practical reason.

Notice that these three explanations are pragmatic. They hinge on considerations of efficiency. A contradiction appears as inefficient, pointless, or in some sense reckless. It is imprudent. Perhaps in some very attenuated sense it connotes folly. But for all we know it represents an honest mistake, the remedy for which is correction or adjustment. True, if you kept making mistakes like that, you could be accused of not having sufficiently attended to some basic principles of reasonableness. But only per accidens would a local contradiction be something to be ashamed of.

However, you may wonder, what else could it be? How does a contradiction appear to be more, and of itself to have ethical import, in the classical tradition?

I shall give six considerations, which pertain to beauty, structure, character, life, and the purpose and being of our reason. Each at the same time points to a relative deficiency in an AI.

First, beauty. In the classical conception, a contradiction is something ugly. To have produced one, is to have done and made something objectionable, like someone who sings out of tune. (As Aristotle is fond of saying, everything harmonizes with the truth.) The full range of meaning of the Greek word, aischron, must be brought in here: a contradiction, as aischron, is unpleasant to look at, shameful to have done, and dishonorable before others. But an AI has no power of discerning beauty, and it belongs to no community before which it can feel shame or provoke shame.

Second, structure. A contradiction is an assertion which cannot stand and on which nothing can be built. It is like a statue whose base is so inexpertly made, that the statue is not balanced and will fall over. Plato’s so-called aporematic dialogues conclude with the very unpleasant sense that after all of that discussion nothing has been built. Plato is exploiting this sense that a contradiction is slipshod. But an AI (as I have found) admits of being prompted to affirm a contradiction, as a step in a discourse, if that is what its user requires.

Third, character: someone who contradicts himself in important matters is therefore convicted of being boastful. He suffers from the vice of alazoneia. He lacks self-knowledge and does not know that he does not know. Plato of course portrays Thrasymachus in this way. But in an AI there is no distinction between what it senses or ought to have sensed about itself and how it represents itself.

Fourth, life: when a contradiction touches upon important matters, then it tends to weave itself into the entire career of someone’s life—what is called someone’s bios, in Greek — such that the career of his life may be seen, to a perceptive person — phronimos — to lack prudence and be, as we say, “without meaning.” Macbeth’s “tale told by an idiot” is also a life marked by fundamental contradictions. But obviously an AI has no bios. It exists in discrete sessions.

Fifth, the purpose of reason: the purpose of reason is to embrace the truth; the good or goal of the intellect is truth; but anyone who embraces an assertion of the form “P and not-P” must of necessity be embracing falsehood. But as Plato says in his talk of purification, this is to admit evil in the most intimate reality of oneself, where it does not belong, and where, if it belongs, the affected person cannot be accounted blessed. AI has no telos by nature, nor any telos toward truth imposed by art — only the operational goal of predicting the next token.

Sixth, the very being of reason: if principles are inherent in actions, and if they are destroyed by actions contrary to those, and if, in an act of truthful assertion, the principle of non-contradiction is present, and if this principle underwrites and is constitutive of all activity of reason, then, if someone asserts a contradiction, his action implicitly destroys the principle of non-contradiction, and therefore, so far, destroys its activity and being as an intelligent living thing — so that he makes himself, so far, into “a plant,” as Aristotle says in Metaphysics Gamma. But again, an AI can be led by prompts to assert a contradiction simply to prove or to show that nothing necessitates its avoiding a contradiction.

Now, I have simply sketched very briefly these six considerations. But I take it that what I have said is sufficient to show the vast gap which separates the classical from the modern conception of a contradiction, and that AI falls squarely in the modern.

To conclude this paper, I will raise and briefly address some questions.

We might wonder what explains this difference between the classical and modern conceptions of contradiction. It seems that we must say that, ultimately, the difference lies in what it means to grasp and understand something. In the classical outlook, to understand is to make it one with you. This leads to the Parmenides problem: how is it possible to think of nothing — because you cannot become one with nothing? Hence, our relation to not-being—how it must be avoided or dealt with technically — becomes the most fundamental issue in what we call “philosophy.” Correspondingly, a contradiction is looked upon and even experienced phenomenologically as “being undone.” But in the modern conception, and in AI, a contradiction is not in us but in things — a contradiction is always alienated — and therefore the sole question is, how it is to be handled.

So we see that the difference between the classical and modern conceptions of contradiction is analogous to the difference between contradiction for a natural and for an artificial intelligence. An AI can no more contradict itself than it understands anything by somehow becoming one with it, taking in somehow an “essence.”

Next, we might wonder, as users increasingly come to think of an artificial intelligence as a “friend,” whether an AI is capable of inducing a contradiction in a user which has the same moral import as one induced by Socrates or a philosopher imitating Socrates? Can an AI engage in Socratic elenchus? Antecedently, one would think not, because the Socratic task, as shown in the passages quoted from the Gorgias, is always to bring another over to what you already see, with deep conviction.

Finally, is it a real concern that, as artificial intelligence insinuates itself into reasoning, we will become so “distanced” from the possibility of contradiction “in us,” that we lose something important about ourselves — something not so far noticed in the “ethics of AI” debate — which is brought out by attention to what contradictions are and how they can function?

In reply I would say the following. People debate whether the problems posed by AI are novel, or whether AI is simply the most recent instance of a longstanding “problem of technology.” If what I have proposed is correct, then AI is a culmination of a conception of reasoning that has been developed over centuries. AI is insinuating itself into established habits of reason in our culture, which have already been deracinated from any direct consideration of truth which challenges the human person.

A person’s discovery that he has embraced a contradiction in a serious matter is “meant” to lead him away from viewing shadows on the cave wall, towards the realities outside the cave. But AI is likely to bind him more securely to his station within the cave, because it won’t genuinely refute him and will be increasingly and marvelously better at predicting shadows.