Saturday, July 14, 2007

Making No Difference At All

We need to stop treating science as if it were a single monolithic entity, a solid kingdom embattled against rival kingdoms. On the one hand, the various sciences differ hugely. Ecology and anthropology are not at all like physics, nor is biology, and this is not disastrous because they do not have to be.

This passage is from a book I am reading about symbols and science, and an elegant and well-written book it is too. But I am suspicious of the line of reasoning evident in the quoted passage, and I think there is a mistake in that line of reasoning that is made quite often. The mistake is to think that, if a group of objects are such that each object differs hugely from each other object, then there is no hope of finding any commonality in that group. Below are three reasons why commonality can exist despite large differences.

First, objects usually differ in respect of one or more qualities; and, since different respects are often independent of one another, a group of objects can differ greatly from eachother in most respects, yet be very alike in other respects. The set of complete sentences varies greatly in respect of length, tone, syntax, and content; but this does not stop them being alike in respect of their basic grammatical structure.

And in the scientific case, ecology and physics may differ greatly in respect of the precision their statements, and in their subject matter, and in their affinity with mathematics, but perhaps they share a common method. Perhaps they do not share a common method, in which case there is some reason to doubt the “monolithic” character of science. But simply saying that different sciences “differ hugely” is not enough to establish the lack of commonality in the sciences.

Another reason is more causal than conceptual. Small variations at a microscopic level can lead to highly divergent behaviors at a macroscopic level; hence a group of objects can appear to differ hugely in their everyday appearance, yet still have very clear structural similarities. The set of all tri-molecules (that is, the set of all molecular substances such that each molecule contains three separate atoms, a group I just made up then), is clearly a quite homogeneous set; yet it contains substances that are as different in appearance and behavior as CO2 and H2O.

The third reason draws on the fact that statements about similarity and difference only really make sense in relation to some standard of comparison. In respect of size, is a plate similar to a table? There is no way of getting a determinate answer to this question, I think, except by bringing in some standard of similarity to compare the plate/table case to. We may not be able to say whether a plate is similar to a table, in respect of size, but we can say whether a plate is more similar to a table than (say) a plate is to house.

This point is relevant because, as soon as one relativises similarity in this way, one universalizes it. If two objects can be similar simply by being more similar than some other two objects, then almost any two objects can be similar. If your scope is broad enough, any two objects in your vision will look close together. It doesn’t matter how much anthropology differs from physics; what matters is how the difference between those two pursuits compares to the differences between those pursuits separately, and non-scientific pursuits (say, English and History). One can bang on all one likes about how different anthropology is from physics. But as long as one has not shown that one of those pursuits is more similar to English (say) than it is to the other of those pursuits, then one has given no reason to question the “monolithic” character of the sciences.

But perhaps I have been a bit unfair here. The standard of comparison I have mentioned is, I think, usually established implicitly, by context. And by demanding that all statements of similarity and difference carry with them an explicit standard of comparison, I am showing a kind of insensitivity to ordinary usage that (some might say) only a philosopher could suffer from. When someone says that the temperature on Tuesday will be “similar” to that on Wednesday, we don’t all put on puzzled expressions and ask the speaker to relativise her statement to some standard. If it turns out that Tuesday’s temperature differs from Wednesday’s by 2.5 degrees, we are not surprised, even though this difference would (in some scientific contexts, for example) be vast. We are aware, in an intuitive sort of way, that the context of everyday weather fixes certain rules about which pairs of temperature are to be considered similar, and which are not.

And perhaps the reader is expected, from the passage above, to intuit some kind of context. And the natural context to use is that of prior expectation. That is, what the author means when she says “physics and anthropology differ hugely” is really “physics and anthropology differ much more than is commonly appreciated.” And the latter statement both makes pretty good sense, and is interesting.

Nevertheless, it is also pretty clear that the latter statement is milder than the claim that the author is trying to make. The claim is that it is somehow impossible to warrant the grouping of physics and anthropology, that they are hopelessly disparate. And, for the three reasons given above (though only the first and third only really apply here) this strong claim does not follow from the milder claim about the inaccuracy of popular beliefs.

A similar pattern of thought is sometimes present in discussions about ethnicity. When discussing the census, for example, commentators sometimes protest (for example) that Korean and Chinese should not be grouped together (eg. under the label of Asian), on the basis that Korean culture is “vastly different” from Chinese culture, or that the two have “very little in common.”

Again, it may be that people do often make genuine mistakes about the closeness of Korean and Chinese culture, and it is worthwhile to counter these mistakes by clarifying the distinctive qualities of each. But the fact that the two cultures are less similar, or similar in fewer respects, than is commonly imagined, does not mean that they should never be grouped together. They may differ greatly, and yet still differ less than what Chinese culture differs from any given European culture. Or in some respects (say, population size) Korea may be more naturally grouped with European countries than with China; and yet in all relevant respects they are enough alike to be put in the same box.