forum 9: week of 12 March: Fisher and the design of experiments
After the discussion last class on the difficulty of attaining knowledge of causation, I've been wondering why we place such emphasis on causation anyways? Since the dawn of philosophy in Ancient Greek, philosophers have been searching for the arche, the cause, of things. But causation if incredibly difficult - if not outright impossible - to know for certain. I could observe two events, and find their correlation. This is a pretty plain-vanilla observation of the physical world.
But causation is a special form of correlation. And getting there takes a quantum leap in effort whereas the marginal utility gained is relatively much smaller. For our pragmatic interests, the two aren't that different. Suppose we know there's a negative correlation between greenhouse gas emission and global warming such that if we decrease our greenhouse gas emissions, the temperature will stabilize or go down. Great. Now we have a powerful tool for action and policy. It's not really necessary (for our practical concerns) to know whether the decrease in temperature is really brought about by a decrease in greenhouse gas emissions, or by some unknown and unconsidered third factor.
If it's not our practical concerns that is driving us, then could our search for causal chains and causes be theoretical in nature? That present a problem as well. You can never get inside causes, and examine them, and say for sure. The system is simply too complex to allow you to draw that conclusion most times. Besides, there's also the theoretical worry that causes can never be known for sure. Causes operate in the physical world. There is no cause in theories and formulae. I can't say "1" is caused by "1+1", or that the Earth is caused by the Sun just by looking at general relativity. I can't remember where I read it, but someone pointed that no matter how long you observe a watch from the outside, you can never tell for sure how it works. You can only guess, make predictions, see if those predictions materialize, and if not, refine your theory and repeat. The universe is rather like a large watch, of which you will never see the inside.
So if it's not practical or theoretical, why are we so obsessed with causes?
Edward, I agree with you to some degree on questioning why we (scientists, philosophers of science) are obsessed with causes. While the idea of causation has been around for a long time, the idea of correlation representing causation has not been around for that long! Karl Pearson insisted that correlation is fundamental to science, and that correlation is to replace causation. Hence, the idea about causation being a special form of correlation was driven primarily by Karl Pearson in the (late 19th)/(early 20th) century. From my (limited) exposure to studying the history of statistics, it seems that Pearson's argument about correlation being fundamental to science has gone out of hand, with numerous scientists not using the concept properly and almost always misinterpreting the inference from observed correlation. In other words, Pearson presented his argument for correlation replacing causation, then many scientists have been misguided in their use of Pearson's correlation coefficient as thinking that statements of causation are the norm (or de facto standard) when inferring correlations. I say that they (scientists) have been (and still are) misguided because that's what Pearson taught them, yet no one has questioned the grounds for inferring those causal statements from correlations until much later (e.g., since Nancy Cartwright came along in the 1980s)! Even though I am unable to (fully) answer your question, I hope that I have been able to shed light on the issue in an effective manner. I am able to give insight to this question, even though it is not really related to the reading on Fisher, because of my research interests in (probabilistic) causal inference. Yes, causal inference is a whole separate topic in itself, distinct from design and analysis of experiments! I hope that everyone can see by now that there are several sub-fields within the domain of statistics as a discipline. There's so much work to be done in accounting for the philosophical issues surrounding statistical techniques, it's not even funny!