Why I am not a naturalist

Philosopher Timothy Williamson published in NY Times an essay titled What is Naturalism? I find it unsatisfactory for many reasons. I want to share here my thoughts about the method of science in this context.

Williamson defines naturalism as a position which maintains that “there is only the natural world, and the best way to find out about it is by the scientific method.”  This statement is meaningless unless “natural world” and “the scientific method” are defined clearly. He characterizes the scientific method as:

For naturalists, although natural sciences like physics and biology differ from each other in specific ways, at a sufficiently abstract level they all count as using a single general method. It involves formulating theoretical hypotheses and testing their predictions against systematic observation and controlled experiment. This is called the hypothetico-deductive method.

If that is what he means by the scientific method, I am not a naturalist. I don’t think the method described above is sufficient for studying nature. What’s described is so vague and sketchy that it hardly counts as a method. According to this description, this is what a naturalist says: “The scientific method is great. It’s the best way to find out things about the nature world. How do you do it? You first come up with a hypothesis, and then you test it! If you do this a lot, you’ll find out a great deal about nature.” Duh! Obviously something is left out. The problem is this: exactly how do we formulate a hypothesis? The space of possible hypotheses is vast. Without a strategy, it’s very unlikely that we’ll ever come up with any hypothesis that has any chance of being right. If all the hypotheses we formulate are bad, this method will not work because the predictions will fail all the time, and we’ll never get anywhere.

So how do scientists come up with scientific theories? My opinion is that we don’t really know. Perhaps there isn’t a thing called the scientific method. The way I see it, what we have is a collection of tricks that we use to attack the research problems that we have at hand and we improvise when necessary. Furthermore, I also believe that this bag of tricks is share by plumbers, mathematicians, engineers, programmers, game designers, movie directors, novelists, politicians, chefs… etc. This would disqualify me as a naturalist because I doubt that science has a fixed method. My intuition would have to be researched by sociologists and cognitive anthropologists and I don’t insist on it. However I want to emphasize that scientists’ bag of tricks does includes mathematics. This is a point I think is worthy of noting because Williamson claims that the existence of mathematics posts a problem for naturalism. His argument, as far as I can tell, is this: How can the scientific method be the best method? Isn’t math equally good or even better? I don’t see how this can be a problem if we count math as part of the scientific method. Williamson says this move is problematic because if we count math as a science, “the description of scientific method just given is wrong”. No. It does not follow. His description of scientific method is not wrong. It is just sketchy.

I believe what Williamson tries to say is that science is justified by empirical results whereas math is justified by deduction (ie. axiomatic proofs). Since these two modes of justification are so different, they don’t mix together. I disagree with it because it leaves out a big chunk of theoretical sciences*. A lot of work in theoretical sciences is deductive. I want to bring up one particular example that I am more familiar with. I am sure that physicists can give much better examples but I want to show that even in biology and psychology, two branches of science that are only loosely integrated with math, there are deductive studies. In fact, there are a lot.

Given some knowledge about the structure of the eye and the retina, it is possible to use geometry, optics, and sampling theorems (from signal processing) to derive a theoretical limit of optical performance of human vision. The procedure is purely deductive. The result is also justified deductively. In other words, we know that the result is right because the derivation is flawless, not because of experimental verification. The theoretical limit cannot be verified experimentally because the conditions assumed in the calculation are idealistic and they are never realized by any real biological systems. However, this piece of information is important (it is actually the foundation of any vision research) because experimental biologists and psychologists can compare the theoretical values to experimental results and use the difference to make inferences about the mechanisms that contribute to the deviation. The theoretical limits are also used as baselines when we compare across different subjects or different species. This does not fit into the hypothetico-deductive method that Williamson described but it is done in psychology and biology all the time. It’s so commonplace that the practice is not reserved for theorists anymore. Even experimental scientists know enough math to do the calculations these days.

I want to contrast this type of research to the kind of work that is made famous by Einstein’s theory of relativity. Special relativity was derived almost completely deductively but it was (at least partially) justified experimentally. It was not justified purely deductively because it was proposed as a theory of physics. It is supposed to make precise predictions about nature and therefore the predictions have to be verified. On the other hand, the theoretical limit of human vision is not a theory of vision. It makes no prediction by itself (except that the performance of any biological system cannot exceed the limit). In fact it does not by itself say anything directly about nature. What it does is that it creates an artificial world. It creates a world that is simple enough that we can understand, so that we can evaluate how much of the complexity in nature is capture by something simple. I am tempted to call this practice not a science but an evaluation of science. I am even tempted to call it philosophy because it is what some philosophers claim that they do. But it is much simpler if we just call it science. In fact I suspect that it supplies the missing component of the hypothesis-testing idea because it explains how hypotheses are formulated and how theories are advanced. We start with a very simple model of the world. We compare it against nature and check what is not explained by the model, and then we try to add more complexity to the model. The model does not always make predictions. Instead it is used to evaluate what isn’t sufficiently explained.

This view of science is continuous with math. Math is essentially artificial worlds that we created. Some mathematical worlds were created to approximate nature (euclidian geometry, for example), whereas some were created to be very different from nature. Scientists like their mathematical worlds to be close enough to nature whereas mathematicians like to venture a lot farther. There is no real difference between the two.

* It also leaves out a big part of math. Mathematicians do proofs but they very seldom do axiomatic proofs. A lot of math is not axiomized. But this is a different topic.

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~ by hhyu on October 3, 2011.

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