Although I’m a realist about scientific entities, I’m not a realist about natural kinds. In fact, anti-realism about natural kinds was, at one point, going to be the focus of my dissertaion (around and about my second year). Nothing *deeply* has changed about my problems with most standard accounts of natural kind terms, but I do think I can articulate some of those problems a bit more clearly and succinctly. This week, I’ll look at one of the few relatively empiricism-friendly accounts of natural kinds: Quine’s.

### Quine’s Argument

Quine introduced natural kinds to solve a well-known problem in the philosophy of scientific reasoning: The fact that some generalizations seem to be *projectable*, while other generalizations aren’t. What’s a projectable generalization? A projectable generalization is a sentence of the form “All Ps are Qs” such that checking *particular* Ps, and verifying that they are in fact Qs, counts as amassing evidence for the generalization. Some famous examples of projectable generalizations are Hempel’s famous “All ravens are black” and Goodman’s famous “All emeralds are green.” Finding lots of ravens, and verifying that they’re black, is a good way to go about getting evidence that all ravens are black, and finding lots of emeralds and verifying that they’re green is a good way to go about getting evidence that all emeralds are green.

You can contrast these projectable generalizations with some other generalizations that *aren’t* projectable. For example, consider Hempel’s own example, the sentence “All non-black things are non-ravens.” If you assume this sentence is projectable, you can amass evidence for it by finding lots of non-black things (swans, the moon, blades of grass, and so on), and verifying that they’re all non-ravens. But *should* that count as evidence? If it does, it also counts as evidence for the logically equivalent sentence “All ravens are black,” suggesting that you can amass lots of evidence that all ravens are black from the comfort of your own swan-studded (but ravenless) grassy lawn at night. That’s pretty clearly absurd, so the generalization “All non-black things are non-ravens” must not be projectable.

Goodman has what I think is an even better, and more mystifying, example of a non-projectable claim, involving the ingenious predicate “grue.” I’m not going to get into that here, because a lot of first-time readers have a lot of trouble following the example, confusing the correct definition of “grue” with a lot of superficially similar but importantly different properties (such as an inclination to change color from green to blue). Go look it up if you’re curious; I think that understanding Hempel’s example is sufficient to understand the Quinean argument for natural kinds.

The problem that Quine hopes to address with natural kinds realism is the problem of how we tell the projectable generalizations from the unprojectable ones. According to Quine, the issue is with the particular *kinds* of objects that the P and Q in “All Ps are Qs” pick out. Some kinds, Quine proposes, are true, *natural* kinds. They actually pick out the really-existent seams in the fabric of reality; grouping things that are fundamentally *alike*, and excluding things that are fundamentally *different*. Examples of natural kinds include ravens, black things, emeralds, and green things. Examples of non-natural kinds include non-ravens, non-black things, “prime numbers and U.S. presidents”, and “people who have voiced muppets from *Sesame Street*.”

Projectable generalizations, according to Quine, are exactly those generalizations where both P and Q are natural kind terms. Now, I think I can come up with lots of counterexamples to this, but instead, I’m going to give a general argument about why this doesn’t really work. It’s an argument based on a well-known argument from a completely different field–the philosophy of language.

### My Response

The argument is Putnam’s 1980s-era (as opposed to his very different 1970s-era argument) against linguistic internalism. Putnam makes use of the mathematical concept of an *automorphism*–a 1-1 mapping of a collection onto itself. For example, imagine any way that the objects in the universe could be shuffled around–with each object getting mapped either to itself or to another unique object, and each object having exactly one other object mapped to it. It’s pretty easy to show that there are a vast number of automorphisms of, say, the physical things in the universe onto themselves (considerably more, in at least some sense, than there are things in the universe).

Let’s call this automorphism “f.” For any object x, f(x) is the object x is mapped to. We’ll also use a slightly less standard terminology. For every predicate P, we’ll use f(P) to denote the predicate “being f(x) for some P x”. So, for example, f(ravens) is the kind containing f(x) for all and only ravens x.

What Putnam pointed out is that, if you replace every reference to an object x with a reference to f(x), and every reference to a predicate P with a reference to f(P), you preserve truth value. “x is a P” is true if and only if “f(x) is a f(P)” is, and “All Ps are Qs” is true if and only if “All f(P)s are f(Q)s” is. His reason for doing this is fascinating, and worth several long papers by itself, but let’s not look at it here. One thing he did demonstrate we will use: If S1, S2 are kinds of the same cardinality, there is some automorphism f of all the things in the universe such that f(S1)=S2.

Now, suppose we have a projectable sentence, “All Ps are Qs.” Is the sentence “All f(P)s are f(Q)s” also projectable? Yes, it is.

Here’s why. Suppose we have found an f(P), which we’ll call y, and established that it’s an f(Q). Because f is an automorphism, we know that there’s some object x such that f(x)=y. In fact, x must be a P, or y wouldn’t be an f(P). With me so far?

It’s pretty easy to figure out that x is a Q as well, for the same reason (that f(x) is an f(Q)). So, by finding an f(P), and discovering that it is an f(Q), we have effectively found a P, and then demonstrated that it is a Q. Since “All Ps are Qs” is projectable, this counts as evidence that all Ps are Qs. But since “All Ps are Qs” and “All f(P)s are f(Q)s” are equivalent, this evidence is in fact also evidence that all f(P)s are f(Q)s.

So whenever we find an f(P), and demonstrate that it is an f(Q), we are amassing evidence that all f(P)s are f(Q)s. So “All f(P)s are f(Q)s” is projectable.

Is there a problem with that? There sure is, for Quine. Remember, for *any* collection with the same cardinality as P, there is *some* automorphism such that that collection is f(P). So if natural kinds are exactly those kinds that occur in projectable generalizations, then any collection with the same cardinality as a natural kind is also a natural kind. So, for example, assuming that there’s been exactly 2,498,923 of some rare organism in existence in the history of the world, it follows that *any* collection of 2,498,923 objects constitutes a natural kind. If you’ve got a notion of “natural kind” where that doesn’t count as a reductio, I’d like to hear it.

Actually, it occurs to me that I’m understating my case here. The real take-home message isn’t just that natural kinds don’t solve the problem of projectability. It’s that, *whatever projectability is*, it’s *not* a property of predicates. What makes “All ravens are black” projectible is not a property held separately by “raven” and/or “black”, because *any* predicate can participate in *some* projectable generalization. It is, rather, some *relationship* that holds between “raven” and “black” (and that does not hold between arbitrary pairs of predicates).

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