Where Is the "West of" When Glasgow Is West of Edinburgh?
Two Cities and a Puzzle
Open a map of Scotland. You’ll find Glasgow on the west coast and Edinburgh on the east. It’s true that Glasgow is west of Edinburgh. But here’s the puzzle: you can point to Glasgow, and you can point to Edinburgh. Where exactly do you point to find the relation “west of” itself?
A relation is a way things stand to each other: taller than, next to, between, loves, married to. We use relations all the time to describe the world. But are relations real entities, like tables and people? Or are they just a kind of mental shorthand — nothing extra beyond the things themselves?
The attempt to answer this question has kept philosophers busy for more than a century. And as we’ll see, the answer matters not just for your map but for how we understand space, time, and even physics.
Bradley’s Regress: The Infinite Glue
F. H. Bradley (1846–1924) was one of the first philosophers to take the puzzle seriously. He focused on external relations — relations that are not fixed by the things themselves. For example, Glasgow and Edinburgh could have been built in different spots, so “west of” isn’t baked into what each city is. Bradley asked: if a relation is something separate from Glasgow and Edinburgh, how does it manage to hook the two cities together?
He imagined a relation as a kind of extra glue. But glue only holds things if it, too, is attached to the things. So if you place relation R between a and b, you need a further relation R’ to attach R to a and b. And then you need yet another relation R” to attach R’, and so on forever. This is Bradley’s Regress — an infinite chain that never actually links anything.
Bradley concluded that external relations make no sense. If we cannot explain how they connect, we should stop believing they exist. His argument is a form of eliminativism: the view that there are no relations at all; only the ordinary things themselves.
Not everyone agreed. Bertrand Russell (1872–1970) pointed out that science is full of talk about external relations — spatial distances, velocities, forces. If we threw out all relations, we’d have to rewrite physics from scratch. Russell thought it was more likely that Bradley’s argument hid a mistake than that science had fundamentally misdescribed the world. Still, pointing out that an argument must be wrong is different from showing exactly where it goes wrong. That task is still debated today.
Internal Relations: No Extra Furniture?
Even if we keep external relations, what about internal relations — ones that are completely determined by the things themselves? Many philosophers have argued that we don’t need to add internal relations to our picture of the world. They’re “no addition of being,” as David Armstrong (1926–2014) put it.
Take the Scottish mountains Ben Vorlich (3094 feet) and Ben Vane (3002 feet). Once you know their heights, the fact that Ben Vorlich is taller than Ben Vane is already settled. You don’t somehow drop in a separate “taller than” relation as an extra piece of cosmic furniture.
This reductionist view claims that internal relations are nothing over and above the ordinary qualities of things. So when we say “Aardvark is the same shape as Baboon,” we aren’t pointing to a spooky relation floating around; we simply notice that both animals are, say, round. Armstrong and others concluded that internal relations don’t exist at all in the fundamental inventory of the universe.
But critics have pushed back. If two heights determine that one mountain is taller, we still need to explain why those heights make that true. The numbers 3094 and 3002 only do the job because the number 3094 is greater than 3002 — and “greater than” looks a lot like a thin internal relation. So perhaps we can’t get rid of all internal relations; some very basic ones might be needed to explain why the ordinary qualities have the consequences they do.
This debate has real teeth because much of science, and much of daily life, depends on whether relational truths have monadic foundations — i.e., whether they boil down to qualities of single things. If physics turns out to describe a world without many intrinsic qualities, the reductionist strategy looks shaky. We’ll come back to that.
Why Order Matters: Loves Is Not a Two-Way Street
Relations aren’t always mutual. Glasgow is west of Edinburgh, but Edinburgh is not west of Glasgow. Aardvark loves Baboon, but that doesn’t guarantee Baboon loves Aardvark back. Philosophers call these non‑symmetric relations, and they introduce a new puzzle: order.
What’s the difference between Aardvark loving Baboon and Baboon loving Aardvark? Both involve the same two aardvarks and the same loving relation, yet the two situations are completely different. A relation must therefore have a way of applying that distinguishes one direction from another. This feature is called differential application.
The oldest explanation is directionalism (championed by Russell): a non‑symmetric relation literally travels from one thing to another, like an arrow. The loving goes from Aardvark to Baboon. But this creates a problem. If there’s an arrow in one direction, there seems to be a converse arrow in the opposite direction — “is loved by.” That would mean every non‑symmetric relation comes with a distinct twin relation, and we’d have to ask whether “Aardvark loves Baboon” is the same state as “Baboon is loved by Aardvark” or a different one. The theories that try to answer this run into trouble with contradictions or with generating too many relations out of thin air.
So some philosophers give up on arrows. Positionalism, developed by thinkers like Kit Fine (b. 1946), says relations have slots or argument positions without any built-in order. The loving relation has two slots: one for the lover and one for the beloved. You explain the difference between a loving b and b loving a by how you fill those slots.
But slot‑based views then have to explain what these slots are and why they don’t smuggle in order all over again. Anti‑positionalism (also from Fine) abandons local explanations entirely. It says you can only tell whether Aardvark loves Baboon or Baboon loves Aardvark by comparing this situation to other loving situations — for example, seeing that it matches the pattern of Cleopatra loving Antony rather than the reversed pattern. A final view, primitivism, simply accepts that the difference between a loving b and b loving a is basic and cannot be broken down into further parts. No theory of order is offered, because order is taken as a bedrock fact.
Each of these approaches has strengths and weaknesses, and none has won the day. The struggle to understand direction in relations is still wide open.
From Two Cities to the Whole Universe
Why does this old philosophical puzzle still matter? Because the modern picture of the physical world has become deeply relational.
Classical mechanics already hinted that forces, stresses, and velocities aren’t properties of single things but relations between things. Relativity theory went further: mass and energy are intertwined, and the shape of spacetime depends on the matter and radiation within it. You can’t just examine a point in isolation; its properties depend on its relations to everything around it.
Quantum theory pushes the relational picture even harder. In quantum field theory, particles are really excitations of all‑pervading fields. The mass and charge of what we call an electron depend on the length scale at which you examine the field — they are relational properties, not intrinsic stickers. Quantum entanglement, where the state of one particle cannot be described independently of another, suggests some relations don’t even need a local explanation.
This puts pressure on the reductionist dream that all relations can be reduced to qualities of individual things. If the universe at its deepest level is a web of relations, then perhaps Bradley was half‑right to be suspicious of independent “things,” but wrong to conclude relations are impossible. Maybe relations are the fundamental furniture, and ordinary objects are the secondary patterns.
The next time you say “the cat is on the mat” or “I’m taller than my friend,” you’re dipping into one of philosophy’s oldest and most live debates. Where exactly is that “on” or “taller than”? The answer isn’t settled, but asking the question reminds you that even the simplest sentence hides a world of mystery.
Think about it
- If you had a perfect map of everything in the universe, including all objects and all relations, would you still need something “extra” to explain why the relations hold, or is the map already complete?
- Can you imagine a world where no two things are related in any way — no distances, no comparisons, no connections? Would you be able to point to a single object in that world?
- When you say “I trust my friend more than a stranger,” is the “trust” relation inside your head, between your actions, or somewhere else entirely? How could you find out?
