Joel Gustafson / Posts / 2025-05-16

There's a classic Mitch Hedberg joke that goes:

I think Bigfoot is blurry, that's the problem. It's not the photographer's fault.

Ultimately, everything in the entire world is blurry, in the sense that it only exists at a certain layer of abstraction. If you zoom in on a thing, or start varying the environment, its boundary will become less defined, its properties less stable, and identity less self-evident.

Everthing is an example of this, so it feels trite to single any of them out. A forest is a real thing, but we don't expect to be able to say exactly where it starts or ends, or exactly which trees it contains. Does this mean the forest exists "less" than its constituent trees? Not at all. And trees aren't any easier to define either: could you definitively say exactly which molecules comprise the tree? The bark? Lichen on the bark? Dirt on the lichen on the bark? Carbon and oxygen in different stages of photosynthesis?

Could you even definitively say whether any given tree is really one tree, or should be really counted as two or three?

Thought experiments like the Ship of Theseus or the pile of sand (if you take away one grain at a time, when does it stop being a pile) play on a similar state of affairs. Somehow, the pile of sand is a real thing, and each grain is a real thing, but how the whole both "arises from" and "coincides with" its parts is hard to definitively explain. At the same time, it's the most obvious thing in the world.

You may be tempted to "defer to physics" to sidestep the issue. Does the exact boundary of the forest really matter when we can all agree on the objective reality underlying it? The atoms are the only things that really exist, right?

First, our understanding of physics only goes so deep, and we have no way of estimating how far away from the bottom we are, or even if a bottom exists. We have only ever had models of things, like the Bohr model of the atom, that get iteratively replaced with more useful models. At any point, including now, our concept of an atom is not categorically different than our concept of a tree. There's no line called "objective reality" dividing them. Most people would take trees to belong to objective reality anyway.

Second, even if we somehow knew that we had solved physics, and had direct access to some computational automata underlying it all, we would still care about trees and forests, and having a solved physics would not necessarily help us understand them better, or answer questions about where the pile of sand went. There's one type of uncertainty that comes from insufficient data, and a completely different type of uncertainty that comes down to ambiguous interpretation. An atom-for-atom account of the Ship of Theseus doesn't help us answer the questions of identity at all.

Dismissing the forest's status as a real thing is not an option: whatever type of thing a forest is is exactly the type thing we're interested in. How can it exist without definite components? Avoiding the question is cowardice.

The fact that something can exist without having a definite boundary is not surprising by itself. Clouds are like this too. But there's not some special category of "collective object" or "diffuse ensemble" or what-have-you. Everything - atoms, sand, trees, people, clouds, Bigfoot - is fundamentally blurry in the same way, only coherent up to a certain resolution, beyond which things fray into ambiguity.

Identity and boundaries are just an example. Blurriness is everywhere, in properties, in relations, in ontologies, everything. Is a hot dog a sandwich? A tomato a vegetable? Even things that feel decisive can be found to have grey areas if you look hard enough. A person's name is a notoriously nuanced property. Or marital status: common law marriage? In one jurisdiction but not another? Separated? Divorce papers not served? Records lost in a courthouse fire?

One response might be to chalk it all up to the fundamental limits of language, or perhaps simply its imprecise use. But we easily develop language to communicate extremely precise ideas in technical fields, and have a whole zoo of notations to express formal statements in mathematics. The fundamental limit is not with language, but with the world itself: Bigfoot is blurry, even seen through the fanciest cameras in the world. It's really a feature language to adapt to the intrinsic blurriness of phenomena at different levels of abstraction, letting us say things that are only as specific as we mean, no more and no less.

A similar response is to say that trees, etc are mere abstractions created within the mind, or picked up from society. This is on the right track, but obscures half of the picture. Dismissing ideas as mere "abstractions" glosses over the fact that there was something there which was amenable to abstraction in the first place. What type of thing is that!?

This is the first post in a series on vagueness. In the next post, we will answer the question "what type of thing underlies abstractions", and explore whether things can ever be true in a fundamentally blurry world.