Does São Paulo Cathedral Have More Beaut-Ls than a Dilapidated Shack?
|August 14, 2012||Posted by Barry Arrington under Intelligent Design|
One of our Darwinist friends’ favorite tactics is to insist that if something cannot be precisely quantified in mathematical terms then there is no warrant for believing it exists at all. For example, ID proponents might point out that Mount Rushmore exhibits complex specified information (“CSI”). “How much CSI does Mount Rushmore exhibit?” a Darwinist might ask. “Oh, you can’t give me a figure? Then CSI obviously does not exist.”
MathGrrl, one of my favorite materialists, put it this way: “My conclusion is that, without a rigorous mathematical definition and examples of how to calculate [CSI], the metric is literally meaningless. Without such a definition and examples, it isn’t possible even in principle to associate the term with a real world referent.”
Let us set aside for the moment that CSI is often subject to rigorous mathematical definition and calculation (as Kairosfocus has demonstrated several times). Let us assume for the sake of argument that sometimes it might be exceedingly difficult or even impossible to quantify a particular example of CSI (like that exhibited in Mount Rushmore). Does it follow that MathGrrl is right, that the concept of CSI is therefore meaningless? No it does not for the simple reason that not every phenomenon is precisely quantifiable.
Consider for example the concept of “utility” in economics. Utility is a representation of preferences. For example, say I have ten franks and you have ten buns. If I want to make hotdogs for dinner I might trade you five of my franks for five of your buns. This means that to me the utility of franks 6 through 10 is less than the utility of buns 1 through 5 and therefore I am willing to give those franks up to get those buns, so we make a trade.
Closely related is the concept of declining marginal utility. If I am hungry I might place a high level of utility on a frank (extremely high if I am starving). I might even enjoy a second or third frank. But surely by the time I have eaten, say, ten franks, the 11th frank is not going to be very appealing to me. The more franks I eat the less value each successive frank has to me. So we see that the “marginal utility” (i.e., the utility of the next unit) declines after a certain point.
“Utility” defies precise quantification even though economists sometimes treat it as if it were quantifiable. There is even a unit of measure for utility called the “util,” and an economist might speak of a certain consumption set (e.g., three apples) as having a utility of say 75 utils. Clearly, however, the concept of “utils” has meaning only in the context of ranking the consumption set with other consumption sets. It has no meaning in itself. Thus, economists say that the number of utils has only “ordinal” and not “cardinal” significance.
Does the fact that utility is not subject to precise quantification mean that it is a meaningless concept? Obviously not. Can there be any doubt that people make exchanges because they believe the goods they currently possess have less utility to them than the goods they could acquire by trading them? Such trades happen billions of times each day. Similarly, can there be any doubt that I will prefer the first frank that I eat much more than the 30th? Thus we conclude that “utility” is a real and useful concept even though the exact utility a good has with respect to a particular consumer might defy quantification.
The photographs at the top of this post lead us to another concept that is real but unquantifiable. Does anyone reading this post doubt that São Paulo Cathedral is more beautiful than the dilapidated shack? Of course not.
Let me now coin a new term – the “beaut-L.” Like the economists’ util, a beaut-L is a unit of beauty.
Now that we have a unit by which we may quantify beauty, can anyone tell me precisely how much more beautiful the São Paulo Cathedral is than the dilapidated shack? Does the cathedral have 500 beaut-Ls while the shack has only 20 (or negative 20) beaut-Ls?
The answer, of course, is that the question is meaningless. Any attempt to assign precise mathematical quantities to beauty is facile. Nevertheless, beauty exists and some objects are more beautiful than other objects.
We can conclude from these examples that our Darwinist friends are wrong when they insist that a concept must always be precisely mathematically quantifiable in order for it to be meaningful. And I further conclude that my inability to assign a quantity of CSI* to Mount Rushmore does not mean that the sculpture does not nevertheless exhibit CSI.
*I hereby coin another term — ceezi (pronounced “seez eye”) for a unit of CSI. No? OK.