Tuesday, December 29, 2009

Science and Philosophy, Part I: Hume and Popper

I've been listening to a lecture series on philosophy recently, and, even though I haven't gotten past the Greeks yet, it has reminded me of a number of issues that trouble me about science. I want to take the opportunity to express my concerns here. Along the way, I will probably oversimplify philosophy a great deal -- not on purpose, but rather because I have only a simplistic understanding of it. I welcome responses to clear up my misconceptions.

One of my issues with science is the famous idea of Karl Popper that it can never establish positive claims, only falsify wrong ones. The history of this goes back to David Hume, the 18th century Scottish sceptic. He shook up the philosophical world by claiming that science could never prove anything through induction -- that is, drawing conclusions about physical laws based on observations. The classic illustration is the sun's rising. Even though the sun has risen every day for our whole lives, and for countless human lives past, we cannot therefore conclude that the sun will rise tomorrow. Popper took this a step further and argued that science can never prove anything. A thousand experiments that produce the same results do not prove that the next experiment would end up the same. On the other hand, one observation is sufficient to disprove a hypothesis. If we say that the sun comes up every morning, and we observe that it does for years in a row, we have not proven that it will rise tomorrow. On the other hand, if the sun does not rise one morning, our hypothesis has been proven wrong.

The true goal of science, according to Popper, is to produce falsifiable hypotheses that it can test. There is a lot of benefit in this method, as it tends to prevent speculation about unprovable ideas; and scientists have largely adopted Popper's ideas. In graduate school, for instance, I took a course on statistics. We learned methods to demonstrate a statistically significant correlation between two things that we can't measure directly. We don't know, for example, how individuals vote, but we know the vote breakdown by precinct. By comparing vote counts across precincts with different characteristics, we could infer a correlation between how people vote and things like how much money they made or what race they were.

Only, we weren't allowed to draw direct conclusions. Because of Popper's ideas, we could only deny the reverse of our conclusion. For instance, we could not say that people tend to vote for candidates of their own race; we would have to say that "we reject the hypothesis that people do not vote for candidates of their own race disproportionately."

I didn't see the point of this exercise at the time, and I continue not to see it today. I actually agree with Hume and Popper that induction can never demonstrate logically conclusive physical laws; only abstract principles like mathematics can do that. The Pythagorean Theorem is true, and it will always be true in all cases, and I have absolutely no concern that anyone is going to prove it wrong. Newton's laws of motion, however, were only true up to a point, and Einstein demonstrated the point at which they cease to be true.

The problem is that I don't see the correlation between these cases. Science aims to produce the best possible model of the universe. While some scientists may believe that they arrive at essential truths, I think most would acknowledge that they can never apprehend the "thing in itself" (Ding-an-sich, a Kantian term for the ultimate nature of a thing). That doesn't matter; they are not producing logically infallible models, but models that correspond closely with observed behaviour. They've done a good enough job that I cross a bridge without worrying, usually, about whether it will collapse, and I fly without worrying that the principles of aerodynamics are actually different that what scientists say they are and the plane will suddenly plummet to the earth.

Moreover, I fail to see how reducing everything to falsifiability assists the process of scientific inquiry (besides encouraging people to make testable claims, as I indicated above). We may observe millions of sheep and find them all to be various shades of black, white, or grey, but never purple. Popper is correct that we could not therefore infallibly conclude that sheep are never purple, but would the existence of a single purple sheep disprove our hypothesis? Perhaps there is something wrong with our observation -- maybe we were drunk, or maybe we were viewing the sheep through purple glasses, or in a purple light. Or maybe someone dyed the sheep purple. That would indeed falsify the idea that no sheep are purple, but it wouldn't falsify the idea that no sheep are born purple.

The idea of falsification seems even more dubious in the case of statistical studies, such as the ones mentioned above. Falsification is an extremely rigorous standard; by it, you are only allowed to make statements that are tautological, to the extent that you know (assuming your observations to be correct) that you are rejecting a false claim because you have seen something that directly refutes it. It works if you want to prove everything with the same certainty as the Pythagorean theorem. Statistical methods, however, are exactly the wrong kind of approach to use if you want falsifiability. You can never demonstrate with apodictic certainty that a statistical correlation matches a real causal relationship; you can only demonstrate that it is very unlikely to be false. But if you are dealing in the realm of probabilities, why use a method designed to grant a priori certainty? A statistical correlation of voting patterns shows that some aspect of voters is likely influence how they vote, never a 100% chance that it does. Why not phrase this in the positive form rather than the negative? And the same logic can be extended to cases where statistics are only used inferentially: if I have seen a million sheep from all parts of the world, and I have never seen a purple one, I am on a statistically sound basis if I assert that sheep are not purple. I can't prove that no one will ever see a purple sheep, but that doesn't stop my observation from being scientifically useful.

Perhaps Popper took some account of these concerns -- I don't pretend to be an expert in his thought. There are just the things that make me doubt the dogma of falsification as a useful tool, and I really doubt whether most scientists actually think in terms of falsification rather than positive assertions.

Next time, I will consider the scientific views of one of Popper's opponents, Thomas Kuhn.

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