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[My friend Fred is a metaphysical naturalist of 50 years standing. His illuminating analysis below of deductive and nondeductive inferences, and the parts played by each in science, philosophy, and practical life may be seen as consistent or inconsistent with the passage to which it is linked. It all depends on the scope given to the words “reason” and “reasoning.” The ambiguity and disagreement surrounding these terms are a constant source of confusion and controversy in philosophical and religious discussion. It is very unlikely, in my opinion, that the confusion will ever be significantly reduced by fiddling with terms and definitions.]

Here’s another way of simplifying it. There are demonstrative inferences, which are essentially forms of deductive reasoning, which if valid, entail the truth of the conclusion whenever the premises are true. And then there’s everything else! So, there’s deductive reasoning, inductive reasoning, fact gathering, hypothesis and theory formulation, etc. Hypothesis and theory formulation may involve intuition, meaning unconscious mental processes in which we’re unaware of all the steps involved.

When this collection of activities is sufficiently organized and formalized, it’s often called science. When it’s less organized and less formal, but still conducted well, we could call it informal rational thinking, or just reasoning.

It’s a mistake to equate logic or syllogistic reasoning with the whole of reasoning. Deductive reasoning is a powerful tool for linking together other parts of the web of reasoning. But it’s well to remember that, in one sense, the conclusions reached from purely deductive reasoning do not introduce anything new, i.e., anything not contained in the premises, even though the results are sometimes surprising. The surprise is the result of our finite thinking abilities not being able to immediately intuit the results of the premises without the aid of the tool of formal syllogistic reasoning.

We could learn very little about the world by means of deduction alone, except in the narrow realm of formal systems. I wonder if this is a (perhaps unpleasant) fact which mathematicians tend to learn later than scientists or even nonscientists who just happen to be good at reasoning. [Bertrand] Russell was a mathematician before he was a philosopher, and I often wonder whether he never quite got over the loss of certainty involved in moving outside the world of mathematics, in which deductive reasoning reigns supreme. Of course, mathematicians use induction, and I don’t mean just in the special technical meaning given to the concept by mathematicians (proof by induction), and intuition. One of my calculus profs from many years ago made the off-hand remark that mathematicians come up with conjectures (which become theorems when proven) by intuiting the answer. They then seek to prove their intuition, partly because mathematicians don’t entirely trust their intuitions (they are, after all, sometimes wrong).

Someone looking at a bunch of facts may use induction to see a pattern or may intuit a pattern. Then deduction is brought into the picture. The person deduces from the hypothesis underlying the pattern some way in which the world must be different if the hypothesis is correct. If the world is found not to be different in that way, then the hypothesis is shown to be incorrect, and it’s back to the drawing board. Science proceeds this way, and so does much informal reasoning. Police detectives, for example, proceed in this way. The only inferences in this process which are strictly demonstrative are the deductive ones.

The process of reasoning writ large is a fabric of deductive and nondeductive processes. It can be done well or poorly, and there are many pitfalls, but the fact that it’s not all demonstrative is not one of them—at least not if one is aware of that.

Deduction is a necessary and powerful tool of science, but is the essential core of mathematics and similar formal systems. Its role in philosophy perhaps lies somewhere between its place in science and mathematics.

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