I think a case can be made that faith is one of the world's great evils, comparable to the smallpox virus but harder to eradicate.
—Richard Dawkins, professor of zoology,
Oxford University
History will judge neo-Darwinism a minor twentieth-century religious sect within the sprawling religious persuasion of Anglo-Saxon biology.
— Lynn Margulis, professor of biology,
University of Massachusetts
Science and religion are both ways of arriving at beliefs regarding things that are true of the world. What distinguishes one from the other? The most common answer would probably be that religion derives its teaching from some kind of supreme authority, however communicated, which must not be questioned or challenged, whereas science builds its world picture on the available facts as it finds them, without any prior commitment to ideas of how things ought to be.
This is pretty much in accord with our experience of life, to be sure. But I would submit that, rather than being the primary differentiating quality in itself, it comes about as a consequence of something more fundamental. The difference lies in the relationship between the things that are believed and the reasons for believing them. With a religion, the belief structure comes first as an article of faith, and whatever the recognized authority decrees is accepted as being true. Questioning such truth is not permitted. Science begins by finding out what's true as impartially as can be managed, which means accepting what we find whether we like it or not, and the belief structure follows as the best picture that can be made as to the reasons for it all. In this case, questioning a currently held truth is not only permissible but encouraged, and when necessary the belief structure is modified accordingly. Defined in that way, the terms encompass more than the kinds of things that go on in the neighborhood church or a research laboratory, and take on relevance to just about all aspects of human belief and behavior. Thus, not walking under ladders because it brings bad luck (belief in principle, first; action judged as bad, second) is "religious"; doing the same thing to avoid becoming a victim of a dropped hammer or splashed paint (perceiving the world, first; deciding there's a risk, second) is "scientific."
Of course, this isn't to say that scientific thinking never proceeds according to preexisting systems of rules. The above two paths to belief reflect, in a sense, the principles of deductive and inductive logic. Deduction begins with a set of premises that are taken to be incontestably true, and by applying rules of inference derives the consequences that must necessarily follow. The same inference rules can be applied again to the conclusions to generate a second level of conclusions, and the procedure carried on as far as one wants. Geometry is a good example, where a set of initial postulates considered to be self-evident (Euclid's five, for example) is operated on by the rules of logic to produce theorems, which in turn yield further theorems, and so on. A deductive system cannot originate new knowledge. It can only reveal what was implicit in the assumptions. All the shelves of geometry textbooks simply make explicit what was implied by the choice of axioms. Neither can deduction prove anything to be true. It demonstrates merely that certain conclusions necessarily follow from what was assumed. If it's assumed that all crows are black, and given that Charlie is a crow, then we may conclude that Charlie is black.
So deduction takes us from a general rule to a particular truth. Induction is the inverse process, of inferring the general rule from a limited number of particular instances. From observing what's true of part of the world, we try to guess on the basis of intuition and experience—in other words, to "generalize"—what's probably true of all of it. "Every crow I've seen has been black, and the more of them I see, the more confident I get that they're all black." However, inductive conclusions can never be proved to be true in the rigorous way that deductions can be shown to follow from their premises. Proving that all crows are black would require every crow that exists to be checked, and it could never be said with certainty that this had been done. One disconfirming instance, on the other hand—a white crow—would be sufficient to prove the theory false.
This lack of rigor is probably why philosophers and logicians, who seek precision and universally true statements, have never felt as comfortable with induction as they have with deduction, or accorded it the same respectability. But the real world is a messy place of imperfections and approximations, where the art of getting by is more a case of being eighty percent right eighty percent of the time, and doing something now rather than waste any more time. There are no solid guarantees, and the race doesn't always go to the swift nor the battle to the strong—but it's the way to bet.
Deduction operates within the limits set by the assumptions. Induction goes beyond the observations, from the known to the unknown, which is what genuine innovation in the sense of acquiring new knowledge must do. Without it, how could new assertions about the world we live in ever be made? On the other hand, assertions based merely on conjecture or apparent regularities and coincidences—otherwise known as superstition—are of little use without some means of testing them against actuality. This is where deduction comes in—figuring out what consequences should follow in particular instances if our general belief is correct. This enables ways to be devised for determining whether or not they in fact do, which of course forms the basis of the scientific experimental method.