The Philosopher Who Trapped His Teacher

A Boy, a Command, and a Puzzle

Imagine a little boy, hungry, standing in front of his mother. He tugs on her sleeve and says, “Give me bread!” He doesn’t say, “I want to have bread.” He doesn’t say, “It would be good if you gave me bread.” He just commands: give me bread. Does the boy think the thought “I want to have bread”? Or does he just feel the want and shout the command, without ever turning it into a thought in his head?

A group of philosophers in twelfth-century Paris thought the answer was clear: no, the boy does not have that thought. He just feels the hunger and shouts. His command is a sign of his feeling, not of a thought. When you hear him, you might form the thought “He wants bread”—but that’s your thought, not his. And this matters because it raises a deeper question: what is the relationship between the words we speak and the thoughts in our minds? Are they the same thing, just in different forms? Or is something more complicated going on?

This was one of many puzzles debated by a philosopher known as Alberic of Paris, who taught on a hill called Mont Sainte-Geneviève (where the Panthéon now stands) around the 1130s and 1140s. He had been a student of the famous Peter Abelard—and then became his fiercest opponent. The fight between Alberic and Abelard was not just a personal rivalry. It was a battle over some of the deepest questions in logic and philosophy.

What Is Logic Really About?

Let’s start with something that sounds simple but turns out to be surprisingly tricky.

When I say “Socrates is a human,” what am I doing? Abelard and his followers said I am predicating the word “human” of the word “Socrates.” Logic, for them, was about how words relate to other words. But Alberic disagreed. He thought logic was about things—real things in the world. When I say “Socrates is a human,” I am saying that the thing Humanity is predicated of the thing Socrates. The word “human” is just the sound we make to point to this real relationship between things.

This might sound like a nerdy technical disagreement. But it had huge consequences. If logic is about words, then you can change the words and the logic changes. If logic is about things, then the way things actually are in the world determines what’s true—and you can’t wiggle out of it by playing with words.

The Embarrassing Arguments

Alberic’s most famous achievement was to find a logical trap that Abelard couldn’t escape. Here’s roughly how it works—though fair warning: this part gets a bit twisty. I’ll explain the core idea and what it accomplishes.

Abelard believed that for a conditional (an “if-then” statement) to be true, the antecedent had to contain the consequent. Think of it like this: “If Socrates is a human, then Socrates is an animal” is true because being human contains being an animal. The definition of human includes animal. But “If Socrates is a human, then Socrates is not a stone” is trickier. Being human doesn’t contain not-being-a-stone in the same way. Not-being-a-stone is just something that happens to be true of humans, not something that’s part of what “human” means.

Fair enough. But then Alberic constructed a chain of reasoning that used only conditionals that Abelard himself accepted—and arrived at a conclusion that Abelard was forced to call both true and impossible. The conclusion was something like: “If Socrates is a human and not an animal, then Socrates is not a human and not an animal.” Abelard had to admit that the reasoning was valid, but the conclusion violated one of his core principles (the principle that no statement can imply its own opposite).

This was a disaster for Abelard—what philosophers call a reductio ad absurdum, a reduction to absurdity. It showed that his system of logic was inconsistent. You could start with premises he accepted, follow his own rules, and end up with nonsense.

The story goes that Abelard was forced to grant the argument’s necessity. He couldn’t find a way out. And this moment—this “embarrassing argument”—changed the course of medieval logic. Other schools of philosophy had to scramble to find their own solutions. Some abandoned Abelard’s containment requirement. Others (like Alberic’s own followers) said the problem didn’t arise for them because they had a different understanding of what predication means.

What Are Universals, Anyway?

Here’s another puzzle that divided Alberic and Abelard. Think about the word “human.” It applies to billions of different people—you, your friend, a stranger in another country. But what makes all these different individuals count as the same kind of thing? What is it that they share?

Abelard thought universals (like “human” or “animal”) were just words. They’re names we give to groups of things that are similar, but there’s no actual thing that is Humanity floating around in the world. There are just individual humans.

Alberic thought this was wrong. He believed universals are real things. But he wasn’t saying they exist separately from individuals, like floating Platonic forms in some other dimension. He said universals are “sorts of things” (maneriae rerum). When you say “Human is a species,” you’re talking about a real kind of thing that really exists in each individual human. The whole nature of Animal is in each animal; it’s just that we can think about it separately from the individual animal.

This led to a strange but interesting consequence. What if there were only one of something? Could it still be a universal? Abelard said no—a universal has to be predicated of many things. But Alberic said yes. His followers used the example of the phoenix, a mythical bird that only ever has one living individual at a time. Even though there’s only one phoenix at any given moment, Alberic argued, “phoenix” is still a universal. It’s naturally apt to be predicated of many, even if it happens that there’s only one around.

Time and How Things Exist

This might seem like an odd thing for philosophers to argue about, but they also disagreed about what it means for something to exist across time.

Abelard was a strict presentist: only the present moment exists. The past is gone (nothing anymore), and the future isn’t here yet (nothing yet). And since things can only be made up of parts that exist, Abelard concluded that there are no such things as wholes that stretch across time. A day doesn’t really exist as a thing—it’s just something we conceive of.

Alberic found this deeply unsatisfying. He said, look, there are two different kinds of wholes. Some wholes have all their parts at once—like a stone or a table. But other wholes exist through the succession of their parts—like time, or a speech, or a running race. A day exists as long as some part of it exists. The past hours and the future hours are parts of the present day even though they don’t exist. The day is a “successive whole.”

This might sound like a technical quibble, but it had a surprising connection to Alberic’s argument against Abelard about thought. Remember how Abelard thought that understanding a sentence is like looking at stones one after another? Alberic pointed out that if Abelard was right that only the present exists, then those successive acts of looking—and the thoughts that come from them—couldn’t exist either. Abelard was caught in his own trap.

Does God’s Knowledge Change?

The final puzzle we’ll look at is about God and the future.

You’ve probably heard that the future is uncertain. Maybe tomorrow there will be a sea battle, maybe not. But if God knows everything, then God knows whether there will be a sea battle tomorrow. And if God knows it, then it has to happen—otherwise God would be wrong. But then it’s not really uncertain, is it?

Philosophers have argued about this for centuries. Alberic’s solution was bold and simple: God’s knowledge changes. As things happen, God finds out about them. Just like you learned that the boy wanted bread by hearing him shout, God learns about the world as it unfolds.

But wait—doesn’t that mean God is changing? And if God is perfect and changeless, how can that be?

Alberic’s followers offered two clever defenses. The first: the changes are like swapping coins in your pocket. If you have ten coins and you swap one for another, you still have ten coins. God’s knowledge gets swapped out as things happen, but the total amount of knowledge doesn’t change.

The second defense is even more interesting: God’s knowledge is infinite. And if something is infinite, you can add to it without making it bigger. Think of a hotel with an infinite number of rooms. If a new guest arrives, you just move everyone one room down—guest 1 to room 2, guest 2 to room 3, and so on forever—and suddenly room 1 is free. The hotel is just as full as it was before. Similarly, new knowledge can be added to God’s infinite knowledge without changing how much God knows.

You might think this is cheating. Many philosophers have thought so. But it shows how creative Alberic and his followers were willing to be.

Why This Still Matters

None of these debates are just historical curiosities. The question about what universals are—whether categories like “human” or “animal” exist in the world or are just names we invent—is still alive in philosophy today. The puzzle about conditionals and logical consequence that Alberic used to trap Abelard is a problem that logicians still work on. And questions about divine foreknowledge and the nature of time continue to be debated by philosophers and theologians.

What Alberic showed was that philosophy is not just about having opinions. It’s about working out the consequences of your views, even when those consequences lead to embarrassment. And it’s about being willing to say, “My teacher was wrong, and here’s exactly why.”

Alberic’s own writings have been lost. We only know his ideas through the notes of his students and the arguments of his opponents. But that’s enough to see that he was one of the sharpest thinkers of his time—a philosopher who wasn’t afraid to trap his own teacher in a contradiction and watch him squirm.

Appendices

Key Terms

Term	What it does in the debate
Universal	A category or kind (like “human” or “animal”) that can be said of many individual things; philosophers argued about whether universals are real things or just names
Predication	The relationship between what you’re talking about and what you say about it (like saying “Socrates is human”); Alberic thought this was primarily a relationship between real things
Conditional	An “if-then” statement; the core of Alberic’s attack on Abelard involved what makes conditionals true
Successive whole	Something that exists through time, with parts that come one after another (like a day, a speech, or a race); Alberic used this idea to explain how things can exist even when their past parts are gone
Containment	Abelard’s idea that for a conditional to be true, the meaning of the “if” part must contain the meaning of the “then” part; Alberic showed this led to problems

Key People

Alberic of Paris (taught c. 1130s–1150s) — A philosopher who taught on Mont Sainte-Geneviève, known for his fierce opposition to his former teacher Abelard and for constructing logical arguments that trapped Abelard in contradictions.
Peter Abelard (1079–1142) — One of the most famous philosophers of the Middle Ages, known for his brilliant and sometimes controversial ideas; Alberic was his student and then his critic.
John of Salisbury (c. 1115–1180) — A philosopher who studied under both Abelard and Alberic; his writings are one of our main sources of information about what Alberic taught.

Things to Think About

The boy demanding bread doesn’t consciously think “I want bread”—he just feels hungry and shouts. What does this say about the relationship between feeling, thinking, and speaking? Are there things you do or say that don’t correspond to any conscious thought?
If universals are real things, what exactly is the thing that you and your best friend share when you’re both human? Is it something you can point to? Is it in both of you, or somewhere else?
Alberic said that if you add something to an infinite amount, it doesn’t get bigger. Does that make sense? Can you think of cases where it does—or doesn’t—work? (Hint: think about the hotel with infinite rooms.)
If God knows everything that will happen, can the future really be uncertain? And if God doesn’t know everything, is God still God? Can you find a way out of this puzzle that doesn’t involve God’s knowledge changing?

Where This Shows Up

School debates about categories: When you argue about whether something “counts as” a mammal or a tool or a sport, you’re having a version of the debate about universals.
Computer logic and programming: The question about conditional statements (if-then) is central to how computers make decisions; different programming languages handle this differently.
Discussions about time and existence: When people talk about whether the past “really exists” or whether time travel could work, they’re dealing with questions about the nature of time that Alberic and Abelard argued about.
Arguments with friends: If you’ve ever tried to show someone that their own beliefs lead to a contradiction (like “you say you trust me, but if you really trusted me you wouldn’t check my phone”), you’ve done exactly what Alberic did to Abelard.