How Do We Know What's Real? Hermann Cohen's Strange Answer

The Puzzle of the “Given”

Imagine you’re sitting in science class, and your teacher says: “Scientists have discovered a new particle.” You nod along. But then a philosopher raises her hand and asks: “How do you know the particle is real?” The teacher might say: “Because we detected it with our instruments.” But the philosopher isn’t satisfied. “How do you know the instruments aren’t tricking you?” The teacher might say: “Because our theories predicted it.” And the philosopher asks: “And how do you know those theories are true?”

This can go on forever. Every answer seems to depend on some other assumption you haven’t proved yet.

Now here’s what’s strange: most people think that somewhere, at the bottom of this chain, there must be something that’s just given to us. Something we don’t have to prove. Basic facts. Sensations. Raw data. Something our minds just receive from the world, like a package thrown through an open window.

Hermann Cohen, a German philosopher who lived from 1842 to 1918, thought this was completely wrong. He thought nothing is ever just “given” to us. Not sensations. Not facts. Not raw data. And he thought that accepting something as “given” was the biggest mistake a philosopher could make.

But then he had a problem: if nothing is just given, where does our knowledge come from? How do we know anything at all?

The Man Who Didn’t Fit In

Hermann Cohen grew up in a small German town. His father was a synagogue cantor. Young Hermann was expected to become a rabbi. He went to a rabbinical school, studied hard—and then decided he didn’t want to be a rabbi. He went to university instead.

This was a big deal. In Germany at that time, it was almost impossible for a Jewish person to become a university professor in philosophy. Cohen managed it anyway, becoming a professor at the University of Marburg. But throughout his career, he was caught between two worlds. He was a German philosopher who wrote about Christianity and Western philosophy. He was also a Jewish thinker who wrote about Judaism and Hebrew scriptures. He was attacked by anti-Semites who said Jewish people didn’t belong in Germany. He argued back—sometimes in ways that make modern readers uncomfortable, like when he insisted that Germany was the best place for Jewish people to live.

He died in 1918, just before the rise of Nazism would prove him tragically wrong.

But what makes Cohen interesting isn’t just his biography. It’s his strange, stubborn idea about knowledge.

The Transcendental Method: A Different Way of Thinking

Cohen was obsessed with one question: What method should philosophy use?

Most people think philosophy starts with big questions: What is reality? What is good? What is beauty? But Cohen thought philosophy should start differently. It should start by looking at what humans actually do—especially what scientists actually do—and then figure out what must be true for that activity to work.

Here’s an example. Suppose you walk into a room and see that a chair has been knocked over. You think: “Someone must have bumped into it.” You didn’t see the bump. You didn’t hear the bump. But you know something caused the chair to fall. Why? Because you have a concept of causation—the idea that every event has a cause.

Where did you get that concept? Did you learn it from experience? Kant (the philosopher Cohen was obsessed with) said no. You couldn’t learn causation from experience, because you need the concept of causation in order to have the kind of experience where you notice causes at all. It’s like trying to use a ruler to measure itself.

Cohen took this idea and ran with it. He said: The task of philosophy is to figure out what concepts and laws we must already have in order to have the kind of experience we do have.

But here’s where it gets weird. Cohen didn’t think these concepts and laws were inside our heads. He didn’t think they were “mental structures” that our brains just happen to have. He thought they were… well, he thought they were the laws of mathematics and physics themselves.

The “Fact of Science”

Let me try to explain this more concretely.

Cohen said philosophy must begin with what he called the “fact of science.” This sounds fancy, but it just means: look at what scientists have actually figured out. Look at Newton’s laws. Look at calculus. Look at the equations that predict where a planet will be next year. These things work. They produce real knowledge. That’s a fact.

Then the philosopher’s job is to ask: What must be true for this kind of knowledge to be possible? What concepts and principles are hiding inside these successful theories, making them work?

For Cohen, this was a radical departure from how most people thought about philosophy. Most philosophers before him thought you started with the mind and then asked how the mind could know the world. Or you started with the world and then asked how the world got into the mind. Cohen said: start with the knowledge itself—with the actual theories scientists have written down in books—and work backward from there.

This is called the transcendental method. “Transcendental” here doesn’t mean mystical or spooky. It just means: looking for the conditions that make something possible. Like asking: What has to be true for a bird to fly? The answer involves air pressure, wing shape, muscle strength—conditions that make flight possible. Cohen was asking: What has to be true for scientific knowledge to be possible?

The Strange Idea of “Pure Thinking”

In his later work, Cohen pushed this idea even further. He started talking about something he called “pure thinking.”

Here’s the problem he was trying to solve. Remember how I said Cohen thought nothing is “given”? Well, if you take that seriously, you can’t even say “our minds are given sensations” or “our brains are given data.” Because those things—sensations, data, brains—would also be “given.” They’d be things we just accept without explanation.

Cohen wanted no part of that. He wanted everything explained. Every single part of knowledge had to be generated by thought itself, not just accepted from outside.

This is where “pure thinking” comes in. For Cohen, pure thinking is thinking that doesn’t depend on anything outside itself. It doesn’t rely on sensations coming in from the world. It doesn’t rely on a brain that just happens to work a certain way. It generates its own content.

What does that even mean? Let me give you an example Cohen actually used.

Infinitesimals: The Math That Makes Physics Possible

Have you ever learned about calculus? There’s a weird concept in calculus called the infinitesimal—a quantity that’s smaller than any finite number but not zero. Imagine dividing something into pieces, then dividing those pieces, then dividing those pieces again, forever. The infinitesimal is what you get at the “end” of that process, if there were an end.

For a long time, mathematicians were suspicious of infinitesimals. They seemed like nonsense. How can something be smaller than any number but not zero? That’s like saying something exists between “exists” and “doesn’t exist.”

But Cohen thought infinitesimals were actually the key to understanding reality. Here’s why.

Think about what it means for something to be a real object—a real thing in the world, like a table or a planet. For science to talk about real objects, it needs to be able to say where they are in space and time. It needs to give them unique locations. But to do that, science needs a way to talk about continuous motion—objects moving smoothly from one point to another, not jumping around.

And the mathematical tool for talking about continuous motion is… calculus. And calculus depends on infinitesimals. So, Cohen argued, infinitesimals are a necessary condition for science to represent reality. They aren’t just a handy math trick. They’re a condition that makes scientific knowledge possible.

This is a perfect example of the transcendental method in action. Cohen didn’t start by asking “What is reality?” He started with the fact that science works, and then asked: “What mathematical concepts must be true for science to work?” His answer: infinitesimals.

This Gets Complicated (Here’s What It Accomplishes)

I should be honest: the details of Cohen’s argument about infinitesimals are incredibly technical, and even professional philosophers and mathematicians found them hard to follow. A famous logician named Gottlob Frege said Cohen’s writing was too unclear to understand. Another famous philosopher, Bertrand Russell, argued that Cohen was just wrong about the math—that modern mathematicians had found better ways to do calculus without infinitesimals.

What matters is not whether Cohen got the math right. What matters is the bigger picture he was trying to paint.

Cohen was trying to show that the concepts we use to understand reality aren’t discovered in the world—they’re generated by thinking itself. Mathematics isn’t something we find lying around in nature. It’s something thought creates. And yet, this created thing—mathematics—is what lets us understand reality at all.

This is a radical view. It means the world doesn’t “give” us knowledge. We build the tools for knowledge, and then the world becomes knowable through those tools. The knowledge is real, but it’s real because of what we bring to it.

Ethics: Same Method, Different Subject

Cohen didn’t stop with science. He thought the same method could apply to ethics.

What’s the “fact” we start with when we think about how people should act? For Cohen, it wasn’t feelings of sympathy or religious commands. It was law.

Think about what law does. Law creates a system of rules that are supposed to apply to everyone. It’s supposed to be universal. It’s supposed to be rational—you can argue about what the law should be, and give reasons. And it’s supposed to reconcile the wills of different people, so that what you want and what I want can both exist together in a stable system.

Cohen said: start with the fact that we have legal systems. Then ask: What must be true for law to be possible? What concepts and principles must already be at work in law for it to function as a system of universal, rational rules?

His answer was something like: the concept of a pure will—a will that isn’t determined by causes outside itself, but freely gives itself laws. And the concept of humanity—not just individual humans, but all of humanity together, as beings who can be bound by universal laws.

From these concepts, Cohen argued for a surprising conclusion: democratic socialism. If law is supposed to reconcile everyone’s will, then everyone must have a say in making the laws. And if law is supposed to prevent exploitation, then workers should collectively own the means of production. Cohen was a Kantian socialist—someone who believed socialism followed from the same principles Kant used to argue for universal moral laws.

Religion: When Ethics Isn’t Enough

Near the end of his life, Cohen turned to religion. He wrote a book called Religion of Reason Out of the Sources of Judaism. This title tells you a lot: Cohen thought religion could be rational, and he thought Judaism was the original source of rational religion.

But here he faced a problem. He had already argued that ethics could give us everything we needed for a complete theory of humanity. Ethics gave us universal laws. Ethics gave us the ideal of a perfect society. Ethics gave us God—for Cohen, the idea of God just is the idea of those perfect ethical laws, combined with the faith that humanity is moving toward them.

So what does religion add?

Cohen’s answer is subtle. He said: Ethics treats all humans as alike. It cares about universal laws that apply to everyone equally. But every person is also unique—and specifically, every person is unique in their failures.

Think about it. You and your friend might both be “imperfect” in general, but your imperfections are different. You lie about small things to avoid conflict. Your friend brags too much. Your other friend is too shy to speak up. A universal ethical law says “don’t lie” or “be humble” or “be brave”—but it doesn’t capture the particular, messy, specific ways each person fails.

Religion, Cohen argued, is about that particularity. It’s about recognizing your own specific failures, confessing them, and trying to overcome them. It’s about the individual’s personal relationship with God—a relationship that’s different for every person.

This was a way for Cohen to say that religion matters without saying that ethics was incomplete. Ethics gives us the universal. Religion gives us the personal. Both are necessary.

What Does All This Mean?

I’ve thrown a lot at you. Let me try to pull it together.

Cohen’s central idea is: Nothing is given. Everything must be generated by thinking itself.

This means:

Science doesn’t discover reality—it constructs it. But the construction is real. Mathematics and physics create the conditions under which we can have knowledge at all.
Ethics doesn’t discover values—it constructs them. But the construction is real. Law and moral reasoning create the conditions under which we can be free, rational agents.
Religion doesn’t discover God—it constructs the relationship between God and the individual. But the construction is real. The personal struggle with failure and the attempt to become better—this is where religion lives.

Everything, for Cohen, is about method. Not about finding the right answers, but about asking the right questions—specifically, the question: What must be true for this kind of knowledge to be possible?

Why This Still Matters

Cohen’s philosophy is not popular today. Most philosophers think he was wrong about infinitesimals. Many think his ethical system is too abstract. Some think his defense of German nationalism was a mistake.

But his deeper insight—that knowledge isn’t about receiving a “given” world, but about constructing the conditions for knowledge—is still alive. It shows up in modern philosophy of science, where thinkers ask what “constitutive principles” make scientific theories possible. It shows up in debates about artificial intelligence, where we ask whether a machine can “know” anything without having a human-like body. It shows up in discussions about justice, where we ask what conditions must be true for a society to be fair.

Cohen’s method—start with what works, then ask what must be true for it to work—is a powerful tool. You can use it yourself. Next time you learn something in school, don’t just memorize it. Ask: What had to be true for this knowledge to be possible? What concepts, what laws, what assumptions are hiding inside it?

You might not end up agreeing with Cohen. Most people don’t. But you’ll start thinking like a philosopher.

Appendices

Key Terms

Term	What it does in this debate
Transcendental method	A way of doing philosophy that starts with some existing knowledge (like science or law) and asks what conditions must be true for it to be possible
Pure thinking	Thinking that generates its own content without depending on anything “given” from outside
Fact of science	The idea that philosophy should start by accepting that scientific theories actually work, and then figure out how
Infinitesimal	A mathematical concept smaller than any finite number but not zero; Cohen thought it was necessary for science to represent reality
Given	Something you accept without explanation; Cohen thought nothing should be treated this way
Correlation	Cohen’s term for the personal relationship between an individual and God in religion

Key People

Hermann Cohen (1842–1918) – German-Jewish philosopher who argued that nothing is “given” to us and that thinking itself generates the conditions for knowledge
Immanuel Kant (1724–1804) – The philosopher Cohen built his ideas on; Kant argued that our minds actively shape our experience rather than just receiving it
Gottlob Frege (1848–1925) – A logician who thought Cohen’s writing was too unclear to be understood
Bertrand Russell (1872–1970) – A philosopher and mathematician who argued Cohen was wrong about infinitesimals
Franz Rosenzweig (1886–1929) – Cohen’s friend who argued that Cohen’s later religious writings broke with his earlier philosophy

Things to Think About

Cohen says nothing is “given” to us—not sensations, not data, not facts. But doesn’t that mean we can never be wrong? If we construct all our knowledge ourselves, what stops us from just making stuff up?
Cohen thought the “transcendental method” could work for both science and ethics. But science deals with facts about what is, while ethics deals with rules about what ought to be. Are those really the same kind of thing? Can you use the same method for both?
Cohen said religion adds something ethics can’t: attention to the individual’s particular failures. But couldn’t a good friend or therapist do the same thing? Why does that require God?
Cohen argued that Jews should stay in Germany and that German culture was especially important for humanity. He died before the Holocaust. Was he wrong, or just unlucky? Can a philosophical argument be good even if history proves its practical conclusions disastrous?

Where This Shows Up

Philosophy of science today – Many philosophers still ask what “constitutive principles” make scientific theories possible, following Cohen’s method even if they reject his specific answers
Debates about artificial intelligence – When people ask whether AI can “know” anything or whether it’s just processing data without understanding, they’re grappling with Cohen’s question about what knowledge really requires
Legal arguments about justice – When lawyers argue about what rights people should have, they often use a version of Cohen’s method: start with what a just society requires, then work out what laws are necessary to make that possible
Religious debates about universalism vs. particularity – Cohen’s question about whether ethics can handle individual uniqueness is still alive in discussions about whether morality should be the same for everyone or tailored to each person’s situation