Are all categories fuzzy?
A reply to Elle Benjamin, a graduate student in academic philosophy at UMass Amherst, in a thread about whether democracy is best understood as a binary classification or a matter of degree. Benjamin had argued that democracy doesn’t have necessary and sufficient conditions; Alyssa generalizes the point, drawing on Eliezer Yudkowsky’s LessWrong essays on category structure to argue that almost no naturally occurring category does.
The remark that “it’s pretty clear to me that democracy doesn’t have necessary and sufficient conditions” deserves a stronger generalization. I’m not used to academic philosophy terminology, so forgive me if I’m misinterpreting, but it sounds like “necessary and sufficient conditions” implies a view of democracy as binary/Boolean, ie. countries can be divided cleanly into democracies and non-democracies. However, it looks to me that, not just democracy, but all (or almost all) naturally occurring categories are continuous, even when they seem like they aren’t. By “continuous” I mean… not sure if there’s a formal name for it, but like how Eliezer describes in A Human’s Guide to Words , where some things are central examples of a cluster, others are slightly less central, and so on until you come to completely unrelated things. The generalized argument runs like this: Suppose a category is usually held to be Boolean, like “alive” vs. “dead”. Consider two examples which are reasonably similar, but on opposite sides of the category divide. Like a person before having a heart attack vs. afterwards.
The two examples are both made of atoms (and technically photons, free electrons, etc., but I’ll use “atoms” for simplicity).
Since they are selected to be reasonably similar, we can assume that the same set of atoms are in both, or at least that there exist two members of both categories such that they contain the same atoms.
Therefore, if we (suspending time) moved one atom to a new position of our choice, then a second, then a third, and so on, eventually, we could change the first category member into the second category member, or the second into the first. Likewise, we can still do this even if each atom is only moved some small distance (a picometer, say), since we can move it as many times as necessary.
Since the category is binary, all the intermediate stages must, logically, belong to one category or the other. Since the first stage is a member of one category and the second is a member of the other, they must switch over from one to the other at at least one point.
Therefore, there exist two (possibly hypothetical) entities, one of which is a member of the first category and the other of which is a member of the second, and yet they are only separated by moving a single atom by a single picometer.
From our perspective as observing humans (un-suspending time again), there can’t realistically be any meaningful difference between the first entity and the second. A movement of one atom by such a distance would not even be detectable with sensitive instruments. We might as well flip a coin to determine which entity went in which category, it would make no difference.
Hence, in practice, in at least some situations, the category boundary must be arbitrary and meaningless, and so a continuous/non-binary model must fit reality better.
Although this is an abstract argument, there are a ton of important, practical examples. People thought that alive/dead was a magical sharp line, until they learned that it wasn’t, and that was what enabled cryonics (and various types of less-controversial emergency medicine). People thought that male/female was a magical sharp line, until they learned that it wasn’t, and so you might have seen a trans woman breastfeeding in the news a few days ago. A few decades ago, people thought of capitalism and communism as two sides of a sharp divide, or developed country vs. developing country; it’s now a lot clearer that they’re not (from whence has come a tremendous amount of poverty reduction). The Nazis famously wanted race to be a magical sharp line, but clear-thinking people (even back then) knew that it wasn’t, and so on and so forth.