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Similarity Clusters

Once upon a time, the philosophers of Plato’s Academy claimed that the best definition of human was a “featherless biped.” Diogenes of Sinope, also called Diogenes the Cynic, is said to have promptly exhibited a plucked chicken and declared “Here is Plato’s man.” The Platonists promptly changed their definition to “a featherless biped with broad nails.”

No dictionary, no encyclopedia, has ever listed all the things that humans have in common. We have red blood, five fingers on each of two hands, bony skulls, 23 pairs of chromosomes—but the same might be said of other animal species. We make complex tools to make complex tools, we use syntactical combinatorial language, we harness critical fission reactions as a source of energy: these things may serve to single out only humans, but not all humans—many of us have never built a fission reactor. With the right set of necessary-and-sufficient gene sequences you could single out all humans, and only humans—at least for now—but it would still be far from all that humans have in common.

But so long as you don’t happen to be near a plucked chicken, saying “Look for featherless bipeds” may serve to pick out a few dozen of the particular things that are humans, as opposed to houses, vases, sandwiches, cats, colors, or mathematical theorems.

Once the definition “featherless biped” has been bound to some particular featherless bipeds, you can look over the group, and begin harvesting some of the other characteristics—beyond mere featherfree twolegginess—that the “featherless bipeds” seem to share in common. The particular featherless bipeds that you see seem to also use language, build complex tools, speak combinatorial language with syntax, bleed red blood if poked, die when they drink hemlock.

Thus the category “human” grows richer, and adds more and more characteristics; and when Diogenes finally presents his plucked chicken, we are not fooled: This plucked chicken is obviously not similar to the other “featherless bipeds.”

(If Aristotelian logic were a good model of human psychology, the Platonists would have looked at the plucked chicken and said, “Yes, that’s a human; what’s your point?”)

If the first featherless biped you see is a plucked chicken, then you may end up thinking that the verbal label “human” denotes a plucked chicken; so I can modify my treasure map to point to “featherless bipeds with broad nails,” and if I am wise, go on to say, “See Diogenes over there? That’s a human, and I’m a human, and you’re a human; and that chimpanzee is not a human, though fairly close.”

The initial clue only has to lead the user to the similarity cluster—the group of things that have many characteristics in common. After that, the initial clue has served its purpose, and I can go on to convey the new information “humans are currently mortal,” or whatever else I want to say about us featherless bipeds.

A dictionary is best thought of, not as a book of Aristotelian class definitions, but a book of hints for matching verbal labels to similarity clusters, or matching labels to properties that are useful in distinguishing similarity clusters.

Extensions and Intensions




Typicality and Asymmetrical Similarity