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Your examples bely either a fundamental misunderstanding of the mathematics of correlation, or a willingness to ignore them to fake an argument. First, you can't "correlate" with incidence of death -- it's not even a binary variable, since everyone dies. Of course, you can correlate with onset of death, but that would make your example silly; if there were an observed acceleration in onset of death due to carrot consumption, it would only serve to illustrate the value of correlative studies in science. Likewise with sunlight exposure -- you've just flipped the constant to the predictor (everyone has experienced sunlight exposure), and attempted to correlate with a variable output (cancer occurrence). Again, mathematical nonsense. That said, I don't dispute anything you've said about models, abductive, deductive or inductive reasoning. But you can reason all day long, and without empirical data, you've got nothing but a castle on a cloud. Ultimately, you're always going to come back to correlating at least one observed variable with another -- the predictor, and the response. This is basic science. Why do I refer to "armchair scientists"? Because I couldn't think of a better term to describe those people who want science to be just like math, but conveniently forget that mathematics rests entirely upon a set of fundamental axioms that are simply asserted to be true. The people who learned about one logical fallacy some time in high school, and latched on for dear life, conveniently forgetting that every scientist in the world knows about the same fallacy. Moreover, these folks aren't familiar with the details, so they don't see that the places where mathematics most closely touch science -- quantum theory, string theory, etc. -- tend to be extraordinarily messy. The math frequently depends on assumptions and approximations that are accepted based on their similarity to observed data. For example, right now, thousands of scientists are banging subatomic particles together in a subterranean tube in France, in order to observe something that the mathematicians think might be there. If it isn't, the mathematicians get to start over. Again: it all comes back to observing things. And as long as we're observing things that are difficult to observe, I have a feeling that cranky internet scientists will be there to argue from the comfort of an easy chair that empiricism has it all wrong. |