Saturday, 21 November 2009

From 'the' to 'every'

One of the bizarre consequences of Russell’s theory of definite descriptions is that the following argument is perfectly valid:

The monkey in the Bronx Zoo pulls funny faces.
Therefore, every monkey in the Bronx Zoo pulls funny faces.

At first glance, this cannot be right! An average user of the English language reasons like this: I’m thinking of a particular monkey in the Bronx Zoo. It simply doesn’t follow that just because that monkey pulls funny faces, every monkey in the Bronx Zoo does. But the preposterousness is only superficial.

The question, of course, is: how many monkeys are there in the Bronx Zoo? If there is just one, then the conclusion follows trivially. For if there is just one monkey in the Bronx Zoo, then that monkey is every monkey.

And this is how Russell would have liked us to interpret ‘the’. First, that there is a monkey in the Bronx Zoo at all. Second, that all monkeys in the Bronx Zoo are identical to that particular monkey (or, if there are any, then they are identical to it). Finally, that the monkey in question pulls funny faces. The second condition makes the monkey unique, because, in conjunction with the first condition, it simply says that there is at least one monkey and at most one monkey in the Bronx Zoo, that is, that there is exactly one monkey in the Bronx Zoo.

As a thought experiment, the truth of the premise in our argument is conceivable. As a reflection of reality, the situation is rather unlikely. There is bound to be more than one monkey in the Bronx Zoo. A more accurate argument would probably run like this:

A monkey in the Bronx Zoo pulls funny faces.
Therefore, every monkey in the Bronx Zoo pulls funny faces.

Except, of course, that this argument is invalid. The premise says that there is at least one monkey but doesn’t set an upper limit. If it turned out indeed that there was only one monkey, then, yes, the conclusion would follow, but this would take us back to the first example. Our set would have shrunk to a one member set again.

Russellian analysis soon gives the game away. Suppose there is more than one monkey in the Bronx Zoo, but we are thinking of one particular one, the one that habitually twirls its tail. The original argument doesn’t work:

The monkey in the Bronx Zoo that twirls its tail pulls funny faces.
Therefore, every monkey in the Bronx Zoo pulls funny faces.

Here, the sets are not identical; the set in the premise is a subset of the set in the conclusion. For the argument to be valid, we would have to infer:

Therefore, every monkey in the Bronx Zoo that twirls its tail pulls funny faces.

And so on and so forth. Somewhere down the line in conversational English, a sufficient number of distinctive features would have been enumerated to satisfy ourselves that ‘the’ merges with ‘every’, for there would be no other monkey like it to fit the description.

There is another way in which ‘the’ can mean ‘every’, the generic ‘the’, which is not to be confused with a definite description.

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