August 11, 2007

The Semantics of Pork

A new controversy has arisen over the bill to expand health care for children. Hitherto, the controversy has been that proponents of the bill, roughly speaking, the Democrats, think that as many children as possible should have health care, whereas the opponents, roughly speaking, the Republicans, do not. According to the New York Times critics of the bill are now claiming, with some reason, that the bill is loaded with pork, that is, with allocations to specific hospitals and projects. The critics point out that Congress has undertaken both to reduce the amount of pork and to be more transparent about it. This bill violates that commitment by not naming the hospitals to receive special funding but instead specifying them indirectly.

For example, the bill provides that, for purposes of Medicare:

any hospital that is co-located in Marinette, Wis., and Menominee, Mich., is deemed to be located in Chicago

Now, as it happens, there is only one hospital, Bay Area Medical Center, that meets this description. Critics say that this is a way of obscuring where the pork is going. The effect of deeming such a hospital to be located in Chicago is to increase the reimbursement rate for physicians since physicians in Chicago are more highly paid than in outlying areas. Proponents of the bill argue that this allows hospitals in outlying areas to compete for staff with big cities. In theory, then, there is a virtue to the abstract formulation of the bill, namely that since all hospitals in a given area will be subject to the same conditions, the abstract formulation has the virtue of automatically including every such hospital, whereas, if the hospitals were specified by name, newly created hospitals or hospitals omitted inadvertently from the bill, would be excluded. As far as I know, no proponent of the bill has actually made this argument. I suspect that it isn't a very strong argument since the local Congressperson is not likely to forget about the hospitals in his or her district and new hospitals do not spring up very often.

Whatever we make of the politics, this controversy provides a beautiful illustration of an important concept from semantics, namely the distinction between intension and extension. The denotation of a referring expression such as a Noun Phrase may be defined as its extension, that is, as the set of entities to which the expression refers. The extension is simply a list. Another way of defining the denotation of an expression is by means of its intension, that is, the set of entities that satisfy constraints imposed by the expression. For example, if the expression is "red balls", I could tell you which balls it refers to by pointing at each of the balls, which would be an extensional definition, or I could explain to you the meaning of "red", which would allow you to identify the red balls by determining which of the entities in the universe are balls and are red.

The distinction between intension and extension is important because people are not always aware of the relationship between the two. The classic example is the assertion: "Hesperus is Phosphorus", which translated from classical terms into modern English is equivalent to: "The Evening Star is the Morning Star." The ancients thought of these two heavenly bodies as distinct, but we now know that they are actually the same entity, namely the planet Venus. If we look only at the extension, it is a mystery that the statement "The Evening Star is the Morning Star." is informative, since it is equivalent to "The planet Venus is the planet Venus.", a tautology. If we look at the intensional meaning, however, we can make sense of this, since what the proposition means is: "The entity with the properties we associate with the Evening Star is the same as the entity that we associate with the Morning Star." Unless and until we know that both are the planet Venus, this is not self-evidently true and is thus informative.

In the case discussed above, the language of the bill describes an intension. In the world as it is, the extension consists only of one entity, the Bay Area Medical Center. Although in this bill the use of intensional descriptions is questionable, in general it can be quite useful because it abstracts away from our ignorance and from changes that we cannot anticipate.

My favorite example of this distinction, albeit one that isn't quite as perfect, is due to Clint Eastwood. In 1980 he was interviewed during the filming of Bronco Billy. The interviewer said that some would define a Clint Eastwood picture as a violent, ruthless, lawless, and bloody piece of mayhem. He then asked Eastwood how he would define a Clint Eastwood picture. To the interviewer's intensional definition, Eastwood gave the (nearly) extensional response:

To me, what a Clint Eastwood picture is, is one that I'm in.

[The reason that the Eastwood example is not quite as clear as the hospital example is that "one that I'm in" is, if we are very fussy, still intensional. It comes close to being extensional both in that it is a small finite set and in that it is essentially arbitrary.]

Posted by Bill Poser at August 11, 2007 06:55 PM