When Relations Go Wrong: Bradley's Regress

Suppose you have a lump of sugar. It’s white, sweet, and hard. You can see the whiteness, taste the sweetness, and feel the hardness. But here’s a strange question: what is the thing that holds all those qualities together? What makes them one lump of sugar, instead of just a pile of unrelated properties floating around?

You might say: “Well, there’s a relation between them. The whiteness is connected to the sweetness, and they’re both in the sugar.” That seems simple enough. But a British philosopher named F. H. Bradley noticed something troubling about this idea. He thought that if you look closely at what relations are supposed to be, they start to multiply endlessly—like mirrors reflecting each other, with no end in sight. And that, he argued, means something has gone very wrong with our whole way of thinking about how things are put together.

The Puzzle: What Do Relations Actually Do?

Imagine you have two things—let’s call them A and B—and you want them to be connected by a relation, R. Maybe A is a red ball and B is a blue ball, and R is “being to the left of.” So A is to the left of B. Fine.

Now, Bradley asks: what is R? Is it something separate from A and B? If it is, then we have three things: A, B, and R. And now we need a new relation—call it R1—to connect R to A and to B. After all, if R is just floating around on its own, how does it actually do the connecting? But then R1 itself needs connecting to A, B, and R, so we need R2, and then R3, and so on forever.

Bradley thought this was a disaster. He wrote: “The links are united by a link, and this bond of union is a link which also has two ends; and these require each a fresh link to connect them with the old.” We end up with an infinite chain of relations, trying to connect things with more things that also need connecting. Nothing ever actually gets related.

This endless chain is what philosophers call “Bradley’s regress.” It’s like trying to glue two pieces of paper together, but every time you add a drop of glue, you need another drop of glue to stick the first drop to the paper, and then another to stick that drop to the first drop, and so on. You never just get two things stuck together.

How Did We Get Here? A Very Old Problem

Bradley wasn’t the first person to notice this kind of problem. About 2,300 years earlier, Plato ran into something similar. Plato believed that when we say two things are both “large,” there must be something—a Form of Largeness—that they both participate in. That Form is what makes them large. But then Plato noticed: that Form of Largeness is itself large (since it’s the source of largeness). So now we have three large things: the two original things and the Form. What explains their shared largeness? We need another Form of Largeness. And then another. And so on forever.

This is called the “Third Man Argument,” and it haunted philosophy for centuries. Philosophers kept finding versions of it popping up in different places. Medieval thinkers discussed it. Muslim theologians argued about it. And in the 1600s, Leibniz—who was both a philosopher and a mathematician—wrote a short note saying that if you try to treat relations as real things, you start an infinite process that never stops.

But Bradley made the problem famous. He published his arguments in 1893, in a book called Appearance and Reality. He wasn’t just playing with logic puzzles—he really thought the whole relational way of thinking about the world was fundamentally broken.

What Would It Take for a Relation to Work?

Bradley considered several possibilities for what relations could be like. None of them satisfied him.

First, maybe a relation is just an attribute of the things it connects—like whiteness is an attribute of sugar. But Bradley thought this doesn’t work either. If you say “the sugar is white,” you’re either saying something different from the sugar (in which case, how are they connected?) or you’re saying something identical to the sugar (in which case, you haven’t said anything new). He saw a basic problem with how we talk about things and their properties.

Second, maybe a relation is completely independent from the things it relates. It’s its own thing, just sitting between A and B. But Bradley thought this made the relation into just another object—something that itself needs relating. That’s where the infinite regress starts.

Third, maybe relations are internal to their relata—that is, they’re somehow built into the nature of the things they connect. For example, being taller than you is a relation that depends on your height and my height. Nothing extra is needed. But Bradley had a very particular understanding of how this would work. He thought that if a relation is internal, it must be grounded in parts of the qualities it relates. And those parts would themselves need relations to connect them. And those parts would have their own parts, and so on forever, like an endless splitting of things into smaller and smaller pieces.

So every option seemed to lead to an infinite regress. Bradley concluded that the whole idea of relations—of things being connected by something separate—was an illusion. Real reality, he thought, must be one single, seamless whole where nothing is really separate from anything else. This view is called “monism”: the idea that everything is ultimately one thing.

The Great Debate: Bradley vs. Russell

Bradley’s arguments caused a huge stir. The most famous response came from Bertrand Russell, another British philosopher who thought very differently. Russell believed in “external relations”—relations that are perfectly real and don’t depend on the nature of the things they connect. For Russell, “being to the left of” is a genuine relation that holds between two objects regardless of what those objects are like inside.

In 1910 and 1911, Bradley and Russell had a public debate in a philosophy journal. Russell wrote that there’s a difference between a “mere aggregate” of things—like a pile of Legos—and a “unity” where things are actually connected—like a Lego castle. The relation in a unity relates; in an aggregate, it doesn’t. And that’s just a basic fact about how the world works. No further explanation is needed.

Bradley wasn’t satisfied. He kept pressing Russell: what makes a relation able to relate? If you can’t say anything about how it does its job, aren’t you just hiding the problem?

Some philosophers sided with Bradley, others with Russell. But the debate raised a deeper question that nobody has fully settled: can we ever really explain how things are connected, or do we just have to accept connection as a basic feature of reality?

Why This Matters Today

You might think this is just an old, dusty debate that nobody cares about anymore. But actually, Bradley’s regress keeps showing up in modern philosophy. Here are some places where it matters right now:

How do properties and objects fit together? If you think there are objects (like chairs and tables) and properties (like being brown and being wooden), you need some way to connect them. What makes this particular brownness belong to this particular chair? Some philosophers say there’s a special relation called “instantiation” or “exemplification.” But then Bradley’s regress threatens: what connects the instantiation relation to the object and the property?

What makes a sentence more than just a list of words? The sentence “Alice is wise” means something different from the list “wise, Alice, is.” The sentence has a kind of unity—the words are put together in a meaningful way. Linguists and philosophers of language worry about whether relations between words can explain this unity, or whether they fall into Bradley’s regress.

How do our minds combine different sensations into one experience? When you see a red square, you’re experiencing redness and squareness together. What makes them one unified experience instead of two separate sensations? Some philosophers think this is a version of Bradley’s problem too.

What Philosophers Still Argue About

Nobody has found a solution that everyone agrees on. Here are the main positions people take:

Some philosophers say Bradley was just confused. Relations don’t need to be connected to their relata by further relations—they just do their job. Asking “how do relations relate?” is like asking “how do triangles have three sides?” It’s built into what they are.

Others try to invent special kinds of relations that can’t lead to regress. Maybe there are “self-relating” relations that connect themselves to their relata. Or maybe relations are “relata-specific”—meaning they’re unique to the particular things they connect, like a custom-made bridge that only fits between two specific buildings.

Some philosophers say the mistake is thinking that relations are separate things at all. Instead, the connection between a property and an object is just the fact that the object has the property. The fact itself is basic—it doesn’t need a relation to hold it together. This is called the “brute fact” approach: you just accept that some things are connected, and you stop trying to explain why.

And some say the infinite regress isn’t actually a problem. Maybe it’s okay for explanations to go on forever, like an endless series of mirrors. Each step explains something, even if you never reach a final answer. This is called “benign infinitism.”

The Deeper Question

Underneath all this technical arguing, Bradley’s regress points to something really puzzling. We talk about things being connected all the time—friends, ideas, objects, experiences. Connection seems like the most basic thing in the world. But when you try to analyze it, to say exactly what a connection is, it starts to slip through your fingers. Every attempt to pin it down seems to create more things that need connecting.

Maybe that means our everyday way of thinking about the world—as made up of separate things that get connected by relations—is just a useful fiction. Or maybe it means we need completely new concepts that don’t work the way “relation” does. Or maybe it just shows that some things are too basic to explain, and we have to learn to live with the mystery.

Even after more than a hundred years, philosophers still haven’t agreed. And that might be the most honest thing to say about Bradley’s regress: it revealed a real puzzle about how the world is put together, and the puzzle is still waiting for someone to solve it.

Key Terms

Term	What it does in this debate
Regress	An infinite chain where each step requires another step, showing that something has gone wrong or can’t be completed
Relation	Supposedly what connects two or more things together, but Bradley argued relations can’t actually do this job
External relation	A relation that exists independently of the things it connects (Russell believed in these)
Internal relation	A relation that depends on the nature of the things it connects (Bradley thought even these fail)
Monism	The view that reality is one single unified whole, not a collection of separate things connected by relations
Unity	The state of being one thing rather than a mere collection of parts—what relations were supposed to explain
Brute fact	Something accepted as basic without further explanation; some philosophers say facts themselves are the unifiers

Key People

Plato (c. 428–348 BCE): Ancient Greek philosopher who first noticed a version of the regress problem when trying to explain how many things can share a property
F. H. Bradley (1846–1924): British philosopher who made the regress argument famous; he argued that relations are impossible and reality must be one seamless whole
Bertrand Russell (1872–1970): British philosopher who defended external relations and argued that relations just do relate—no further explanation needed

Things to Think About

Bradley’s regress seems to show that if you try to connect two things with a third thing, you’ll need an infinite number of connecting-things. But what if you just said “the connection is nothing separate—the two things are simply together”? Does that solve the problem, or does it just hide it?
Is there a difference between a pile of bricks and a brick wall that’s been built? If so, what makes the difference? Is it something in the bricks, or something between them?
Think about friendship. Are two people “friends” because there’s a “friendship relation” between them? What would a “friendship relation” even be? If you can’t point to it, does that mean friendship isn’t real?
Some philosophers say that asking “how do relations relate?” is like asking “how does water wet things?”—it’s just what relations do. Does that feel like a satisfying answer to you? Or does it feel like giving up?

Where This Shows Up

In debates about how artificial intelligence works: when a computer combines different pieces of information into one conclusion, does it use something like relations? Could it fall into a regress problem?
In discussions about how our brains create unified experiences from different senses (sight, sound, touch)—sometimes called the “binding problem”
In arguments about whether the universe is made of separate particles or is one continuous field (physics is still divided on this)
In any situation where someone asks “what holds this together?”—whether it’s a team, a story, or a scientific theory