Not long ago, I wrote here about the "process theory" of causality, and attributed it to Wesley Salmon.
Today, I'll go a little further, and present a quotation for Salmon's writings on the distinct but closely related question on induction, and the post-Humean debate on induction in the sciences.
The idea of a philosopher discussing inductive inference in science is apt to arouse grotesque images in many minds. People are likely to imagine someone earnestly attempting to explain why it is reasonable to conclude that the sun will rise tomorrow morning because it always has done so in the past. There may have been a time when primitive man anticipated the dawn with assurance based only upon the fact that he had seen dawn follow the blackness of night as long as he could remember, but this primitive state of knowledge, if it ever existed, was unquestionably prescientific. This kind of reasoning bears no resemblance to science; in fact, the crude induction exhibits a complete absence of scientific understanding. Our scientific reasons for believing that the sun will rise tomorrow are of an entirely different kind. We understand the functioning of the solar system in terms of the laws of physics. We predict particular astronomical occurrences by means of these laws in conjunction with a knowledge of particular initial conditions that prevail. Scientific laws and theories have the logical form of general statements, but they are seldom, if ever, simple generalizations from experience.
I gather that what he is saying here is that the revolution of the earth around its north-south axis is a continuous process, and the key proposition is that the process will, so to speak, continue to continue. The rising of the sun, for observers at a particular spot on the surface of the earth, only seems like a discrete event because of the limits of the point of observation.
Now let us take a cause-effect statement of the standard form: "After the sun rises, the atmosphere in a vicinity warms up." That is a statement of two discrete events, seen from the "prescientific" point of view of this locality. We might say that we have observed A many times, and it is always followed by B. But Salmon seems to be saying, to characterize induction in that way, and to treat such inductions as foundational to science, is to get things wrong all around. It gets induction wrong, science wrong, and causation wrong.
The only difference that I see between "prescientific" reasoning and scientific reasoning is that the former omits steps. Aren't the laws of physics, in general, derived inductively? Isn't the belief that the revolution of the earth around its north-south axis will continue to continue derived inductively?
ReplyDeleteI think the laws of physics have generally been derived more through guess-and-test than through the gathering up of examples and then the act of generalization that textbooks call induction. "Guess and test" is what Peirce called abduction, what calculus teachers call the Newton-Raphson method, and it is not identical to but it explains the appeal of Popperian falsificationism in the philosophy of science.
ReplyDeleteWe guess that certain phenomena might be placed under a general law X. We then test it. Ideally the test is devised in such a way that, if it is proven to be wrong, the results will also tell us something about in what direction it is wrong. So the second guess (X+) can be more accurate. In this way, repeated falsified guesses lead to ever better approximations (X++), until something comes along that isn't falsified by our tests.
This is a better description of most inquiry than either induction OR deduction. Consider an example in the "pure deduction" field of arithmetic. The graduating class of Sigmund High School contained 110 students. The number of women among them was 50 higher than half the number of men. How many people of each sex were there in the class?
You can solve this deductively, by setting up the necessary equations, solving x for y, then solving y. Or, you can take a guess, which is what I would do.
Intuitively, in such situations, I might guess that there are 80 women in the class, leaving room in the auditorium for 30 men. Does that work? Testing .... 80 - 50 = 30. But 30 is not twice itself! So I'm wrong. This experiment's results suggest a lower number. Try 70.
70 - 50 = 20. Aha! 20 is 1/2 of 40. 70 + 40 = 110 which is the postulated size of the class. Guess and test got me to my result. Seventy women and forty men.
This sort of thing sounds more sophisticated in calculus. Google "Newton-Raphson." Anyway....
More empirical inquiries follow much the same procedure. The laws of nature came to be formulated in this way. Heck, the law of conservation of energy (that it can be "neither created nor destroyed,") was a good guess by Helmholtz, one which lasted until the Curie family tested it against radium and found that there was a problem. Then Einstein reformulated it as the law of the conservation of mass-energy. THAT situation was surely not the sort of crude induction that Salmon is attributing to primitive minds....