What Were Arabic Philosophers Doing with Logic?

Imagine you’re sitting in a classroom, and someone says: “Every human is an animal.” That seems obviously true. But then someone else asks: “Does that mean every human who has ever existed or ever will exist is an animal? Or does it mean that every human who is alive right now is an animal? Or does it mean something else entirely?” Suddenly a simple sentence starts to look complicated.

Now imagine that you’re a philosopher living in Baghdad around the year 1000, and you’re trying to figure out the exact rules for how to reason correctly—not just in Arabic, but in any language, in any time, about anything at all. You’re trying to build a system so precise that if you follow its rules, you’ll never make a mistake in your thinking. This is what the philosophers we’ll talk about were doing, and their work is still surprising.

A Strange Debate About Grammar and Logic

Around the year 932, two scholars faced off in a debate before a powerful government official. One was a Christian logician named Abû Bishr Mattâ (think “Matt”). He believed that logic—the rules for correct thinking—was universal, the same for everyone everywhere. The other was a Muslim grammarian named Sîrâfî, who thought this was nonsense. Sîrâfî argued that you couldn’t separate thinking from the language you think in. Arabic has its own structure, he said, and Greek logic (which was based on Greek language) doesn’t necessarily apply.

Abû Bishr responded: “Logic enquires into the meaning, whereas grammar enquires into the expression. The meaning is more exalted than the expression.”

But Sîrâfî wasn’t convinced. He kept pushing back with examples from Arabic that didn’t fit the Greek logical rules. The debate apparently didn’t go well for Abû Bishr—he came across as clumsy and outmatched.

This debate wasn’t just a classroom squabble. It raised a real question: Is logic about the structure of language, or is it about the structure of thought itself? And if it’s about thought, can we study thought without studying language?

What Is Logic Actually About?

The greatest philosopher to take up this question was a man named Avicenna (who lived from about 980 to 1037). He was from what is now Iran, and he wrote an enormous amount—philosophy, medicine, astronomy, poetry. He was so famous that people called him “the leading scholar.”

Avicenna’s answer to the question “what is logic about?” went like this.

Think about the concept “horse.” When you think “horse,” you’re thinking about something that exists out in the world (or could exist). That’s a first concept—a thought about a real thing. But now think about what happens when you put “horse” together with “animal” in your mind to form “every horse is an animal.” The concepts “subject” and “predicate” aren’t things you find out in the world. Horses don’t have little labels saying “I am a subject.” These are properties that concepts acquire when the mind works with them. Avicenna called these secondary intelligibles—properties that belong to concepts as concepts, not to the things the concepts represent.

For Avicenna, logic is the study of these secondary intelligibles. Specifically, it’s the study of how to use them to move from what you already know to what you don’t know yet. This made logic a real science in its own right, with its own subject matter, just like geometry has triangles and physics has motion.

But not everyone agreed with Avicenna. A later philosopher named Khûnajî (who lived in the 1200s) pointed out: “Wait—when logicians study things like ‘genus’ and ‘species,’ they’re not just studying properties of concepts. They’re also studying the concepts themselves—like what it means for something to be a category or a type of thing.” So Khûnajî argued that logic’s real subject matter was something broader: conceptions and assents—that is, the basic mental acts of forming ideas and agreeing or disagreeing with statements.

This might sound like a nerdy technical dispute, but it mattered. If logic is about secondary intelligibles, then it can be a pure formal science, just about the structure of thought. If it’s about conceptions and assents, then logic has to deal with the messy reality of how actual human minds think—including how we use language, how we’re persuaded, and how we make mistakes.

A Very Complicated Thing About “Every J is B”

Let’s look at one specific problem that obsessed these philosophers for centuries.

Take the statement: “Every human is laughing.” Is that true? Obviously not—not every human is laughing right now. But now think about: “Every human is an animal.” That seems true even when you’re not thinking about humans. So what makes one “every” statement work differently from another?

Avicenna noticed that when you say “every J is B,” you need to specify what you mean by “every.” Do you mean every J that exists right now in the external world? Do you mean every J that has ever existed or will ever exist? Or do you mean every J that could possibly exist—even if it doesn’t? Philosophers call this the problem of the subject term—what exactly are you talking about when you say “every J”?

Avicenna thought the subject term should be “ampliated” to include possible things. When you say “every triangle has three sides,” you don’t mean just the triangles that happen to exist right now. You mean all possible triangles. So the subject means, roughly, “everything that could be a J.”

But Avicenna also introduced another distinction, which later philosophers found crucial. He said a proposition like “every human is necessarily a rational body” can be understood in two ways:

The dhâtî reading (essentialist): “As long as something exists as a human, it is a rational body.” This is true for each human during their whole life.
The wasfî reading (descriptive): “As long as something is moving, it is changing.” This isn’t about the thing’s essence—it’s about a temporary description.

Later philosophers realized that these two readings give you different logical results. If you think about “every J is B” in the essentialist way, you get one set of rules for how statements can be converted and combined. If you think about it in the descriptive way, you get a different set.

A later philosopher named Râzî (who died in 1210) made this even more explicit. He distinguished between what he called externalist and essentialist readings.

Think about this: “Every triangle is a figure.” On the externalist reading, this means every triangle that actually exists in the world is a figure. But what if no triangles exist at all? Then the statement would be false—or maybe meaningless. On the essentialist reading, the statement means: “Everything that would be a triangle, were it to exist, would be a figure.” This works even if no triangles exist.

Râzî showed that most of Avicenna’s logical rules worked perfectly on the essentialist reading. But Khûnajî came along and said: “Wait—the essentialist reading, as Râzî understands it, still only talks about possible things. But what about impossible things? If I say ‘no square is a triangle,’ I’m not just talking about possible squares—I’m also saying that even if you tried to imagine a square that was a triangle, it wouldn’t work.” So Khûnajî stretched the essentialist reading to include impossible cases as well.

This led to truly weird results. Remember the counter-example Avicenna used to show that “no horse is sleeping” doesn’t convert to “no sleeping thing is a horse”? (Because some sleeping things could be horses.) Under Khûnajî’s reading, that conversion does work—because you can imagine a “sleeping thing that is not a horse,” even if that’s impossible in reality. The statement “some sleeping thing is not a horse” comes out true, because in the world of all possible (and impossible) things, there are sleeping non-horses.

This sounds bizarre, but it reveals something deep: when you’re building a system of logic, you have to decide what your domain of discourse is. Are you talking about the actual world? All possible worlds? All conceivable worlds, including impossible ones? Each choice gives you different rules.

The Classroom of the World

Over several centuries, this tradition of logic was refined, debated, and eventually taught in schools across the Islamic world. By the 1300s, standard textbooks had been written that summarized the main positions. Students would memorize these and then argue about them.

What’s remarkable is how long this tradition lasted and how seriously it took the project of getting logic exactly right. These philosophers weren’t just repeating Aristotle—they were modifying, criticizing, and rebuilding his system. They introduced new concepts (like the essentialist/externalist distinction), new problems (like what to do with impossible subjects), and new solutions (like Khûnajî’s radical expansion of the domain).

And they never fully agreed. Tûsî (who lived in the 1200s and helped build one of the great observatories of the medieval world) defended Avicenna against both Râzî and Khûnajî. Kâtibî (another 1200s logician) tried to find a middle path. The debates continued for centuries, with philosophers in Persia, Egypt, North Africa, and India all contributing.

Why This Matters

You might wonder: why spend centuries arguing about whether “every J is B” should be read one way or another? What difference does it make?

One answer is that getting logic right matters for everything else. If you’re going to reason about God, about justice, about what exists, about how to interpret the Qur’an—you want your reasoning to be sound. A small mistake in your logical rules could lead to massive errors in your conclusions.

Another answer is that these debates reveal something about how human thinking works. The question “what does ‘every’ mean?” isn’t a trivial one. It’s connected to how we understand possibility, necessity, existence, and the relationship between our minds and the world.

These Arabic philosophers were doing something that still feels modern. They were trying to build formal systems that could capture the structure of correct reasoning, and they were willing to follow their rules wherever they led—even into impossible objects and strange domains. They were, in their own way, doing what mathematicians and logicians still do today: asking what it means for something to follow from something else, and trying to make the answer precise enough to check.

Appendices

Key Terms

Term	What it does in this debate
Secondary intelligibles	Properties that concepts acquire when the mind works with them (like “subject,” “predicate,” “genus”)—the subject matter of logic according to Avicenna
Conception and assent	The two basic kinds of mental acts: forming an idea (conception) and agreeing or disagreeing with a statement (assent)
Subject term	The thing you’re talking about in a statement like “every J is B”—philosophers disagreed about whether this means actual Js, possible Js, or both
Essentialist reading	Reading “every J is B” to mean “everything that would be a J (if it existed) is B”—works even if no Js exist
Externalist reading	Reading “every J is B” to mean “everything that actually exists as a J is B”—depends on what’s real
Conversion	The logical rule that lets you swap the subject and predicate of a statement (like turning “every J is B” into “some B is J”)
Modal proposition	A statement that includes words like “necessarily,” “possibly,” or “at least once” (as opposed to simple “is”)

Key People

Avicenna (c. 980–1037): A Persian philosopher and physician so famous he was called “the leading scholar.” He rebuilt Aristotle’s logic from scratch and argued that logic’s subject matter is secondary intelligibles.
Abû Bishr Mattâ (d. 940): A Christian logician in Baghdad who debated a grammarian about whether logic is universal or depends on language. He lost the debate but raised important questions.
Râzî (d. 1210): A philosopher who introduced the essentialist/externalist distinction for reading subject terms. He was critical of Avicenna but worked within his framework.
Khûnajî (d. 1249): A logician who pushed the essentialist reading to include impossible things, leading to very different logical rules. His work was hugely influential.
Tûsî (d. 1274): A philosopher and astronomer who defended Avicenna’s original system against Râzî and Khûnajî. He helped build a famous observatory.

Things to Think About

If you say “every triangle has three sides,” what exactly are you talking about? Triangles that exist right now? Triangles that have ever existed? All possible triangles? Does your answer change what you think “every” means?
Khûnajî thought we should include impossible things in our logical domain. That means we can talk about “a square circle” or “a sleeping thing that isn’t an animal” as items in our system. Does that make sense? What would be the point of including things that can’t possibly exist?
The debate between Abû Bishr and Sîrâfî was about whether logic is universal or depends on language. Do you think different languages might have different logics? Or is there one set of rules for thinking that works no matter what language you’re thinking in?
Avicenna thought of logic as its own science with its own subject matter (secondary intelligibles). But his critics said this made logic too narrow. What would be lost if logic only studied the properties of concepts and didn’t also study how actual people think, argue, and make mistakes?

Where This Shows Up

In math class: When your math teacher says “every even number is divisible by two,” they’re using the essentialist reading—they mean every possible even number, not just the ones that exist.
In video games: Game designers have to decide what counts as “every” object when writing game logic. Does “every enemy” mean enemies currently on screen, or all enemies that could spawn?
In computer programming: When programmers write “for every item in this list,” they have to decide exactly what counts as an item—and this can get surprisingly tricky.
In everyday arguments: When someone says “everybody knows that” or “that’s always true,” they’re making a claim about universals—and the same questions about what “every” means apply in real life.