The Relations of Possibility: II. Difference Makes a Difference

Not every difference matters.

A stone may differ from another stone in colour, weight or shape. Some of those differences may matter for what we do with them. Others may make no difference at all.

So it is not difference alone that interests us.

It is difference that makes a difference.

A door that is open differs from a door that is locked. The difference may be physically small, but relationally it is enormous. One permits passage; the other does not.

The important thing is therefore not simply that two states are different.

It is that the difference changes what can happen.

This gives difference a more active role than we usually give it. We tend to think of differences as features that can be observed: this is larger than that, this is nearer than that, this happens before that.

But some differences do more than distinguish.

They differentiate possibility.

A river and a road may both provide routes across a landscape, but they do so through very different relations. A bridge changes those relations. What was previously difficult or impossible becomes accessible.

Nothing magical has been added to the world.

The relations have changed.

And with them, the possibilities.

This is why constraint is so important. A constraint is not simply something that prevents an action. It establishes a difference between futures: some remain available, while others do not.

The wall does not merely occupy space.

It makes one trajectory possible and another impossible.

The horizon of a black hole provides an extreme physical example. The geometry does not merely tell us where an object is. It changes the distinction between possible future-directed paths. Inside the horizon, escape to the exterior is no longer among them.

The geometry has made a difference.

And that difference makes a difference to the future.

We can now see why relations matter.

Relations differentiate the world, but some differentiations alter the possibilities that follow from them. A changed relation can therefore become a changed future.

Perhaps, then, possibility does not begin with a list of things that might happen.

Perhaps it begins much earlier:

with a difference in the relations that constitute the present.

The next question is unavoidable.

When does a difference become a constraint?