Читать книгу This is Philosophy of Science - Franz-Peter Griesmaier - Страница 15

This form of inference is a bit more difficult to characterize to any great degree of precision. In fact, not even the name is widely agreed upon. Sometimes, IG is used to refer to what we call SI. Since nomenclature is a matter of convention, nothing really turns on it, as long as we are reasonably clear about the differences among the kinds of inferences. In order to begin developing a good understanding for what we decided to call IG, it’s best to start with an example.

Suppose you are interested in determining the functional relation between the period of a pendulum (how long it takes to pass through one cycle) and the length of its string. Dutifully, you plot changes in the dependent variable (the period) against variations in the independent variable (the length of the string). Unavoidably, you’ll get a general trend with a somewhat messy point distribution. If you were to precisely connect all the points, you’d end up with a jittery line. “Nature can’t be that crazy,” you mutter to yourself, as you begin accepting that some of the points might not fall exactly on the line describing the actual relationship. You know about air resistance, the variable elasticity of the string due to changes in ambient humidity levels, the imprecision of your starting and stopping the timing device, and other factors that really have nothing to do with the true relation between length and period (that’s why we call those factors “noise”). Thus, you decide to go for a nice, neat line – a section of a parabola, as it were. Then, you find the algebraic expression that generates that line. Finally, you make an inductive generalization and conclude that the period T of all pendula is related to the length l of their respective strings as follows: T=2π√l/g, where g is the gravitational acceleration. In fact, you are proud to have discovered the ideal pendulum law, which holds for all pendula with sufficiently small angular displacement. We will say more about the question of what a law of nature is in Chapter 12.