The introduction of such irregular lines [lines that are undefinable and non-causal] is in no way superior to the “sympathy,” “antipathy,” “occult properties,” “influences” and other terms employed by some philosophers as a cloak for the correct reply, which would be: “I do not know.” That reply is as much more tolerable than the others as candid honesty is more beautiful than deceitful duplicity.” (p. 241 The Discoveries and Opinions of Galileo, trans. Stillman Drake, Double Anchor Books, (c) 1957 Stillman Drake, LOC #57-6305.)David Harriman has the right idea: induction is valid. It should be recognized as such, and should be studied, as are things in physics, to understand what exactly it is and how exactly it works. In the blog post “Induction Hanging By A Thread,” Harriman says:
Let’s start with the philosophers’ description of induction as a giant, illogical leap from a few observed cases to a universal generalization. That does sound like a dubious procedure. How can we possibly justify accepting a conclusion that transcends the evidence in this way? And we do accept such conclusions all the time; we couldn’t survive if we didn’t. But we don’t want to say that induction is illogical, and yet we do it anyway because it works. That leaves us in a position of not being able to distinguish science from pseudo-science, or rationality from irrationality. If we say that even the best thought processes are illogical, that’s a disaster.
So how do we respond to the charge that induction, by its nature, is an illogical leap? The best place to start is with actual examples of scientific induction. Let’s consider Newton’s experiment with the thread that was painted half blue and half red. Recall that when he viewed it through a prism, the two halves appeared discontinuous–and then analysis showed that the prism shifted the blue part more than the red part. On this basis, Newton reached a generalization: blue light is refracted by glass at a greater angle than red light.
Where is the illogical leap here? Oddly enough, there doesn’t seem to be one. The generalization seems to follow with perfect logical necessity from the observations.