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Deductive and Inductive Reasoning

What is the difference between deductive reasoning and inductive reasoning? The former is a matter of applying formal logic to premises to arrive at a conclusion. When used properly, and when the premises are correct, the conclusion is necessarily correct. "Inductive logic," as it is sometimes called, is perhaps not true logic at all. It is simply the process of drawing conclusions based on repeated patterns of observation or experience. Even when the premises are correct, when using induction the conclusions might be false.

Let's look at some examples. Using deductive reasoning, we might start with the premises that all life forms have carbon atoms, and that a given bacterium is a life form, and from there deduce that the bacterium has carbon atoms. As long as the premises are correct, the conclusion must be.

Notice that the fallibility of deductive logic is in the possibility of the premises being wrong. In fact, the premises themselves are often arrived at using induction. For example, where did we get the premise that all life forms have carbon atoms? From the following inductive reasoning: the life forms we have examined have carbon atoms, therefore all must have them.

Philosopher David Hume denied the logical admissibility of deductive reasoning. Europeans saw only white swans for centuries, and so by induction assumed that all swans were white. Then it was discovered that there were black swans in Australia. This demonstrates the primary problem with inductive reasoning: It is impossible to examine all particulars as they are potentially infinite in number, thus we cannot logically make a valid generalization in this way.

More than one person has pointed out that inductive reasoning is almost identical to superstitious reasoning. We note several instances where someone says "everything is going great," followed by everything going wrong, and we "learn" that it is dangerous to "tempt fate" by saying such things. That is superstition, but it is also induction. Some go as far as to say that inductive reasoning is just superstition dressed up as science.

This criticism is a bit severe, though. Examples of inductive reasoning are usually classified as "weak induction" and "strong induction." Superstitions are at best weak induction. They rely on relatively few particulars and a willingness to selectively focus on confirming evidence while ignoring anything that contradicts the given belief. At least when people believed all swans were white it was based on many thousands of examples over many centuries, making it strong induction even if it was later proved false.

Interestingly, although Hume said it is impossible to justify inductive reasoning (except by induction, making it a circular argument), he did not dismiss its necessity. He advocated practical skepticism and common sense that allows for the inevitability of induction. He pointed out, for example, that in our experience bread nourishes us, and although that does not logically prove it always will do so, we have to accept the inductive conclusion that it will. He added that a person who waited for sound deductive justifications for everything would starve.

Many philosophers accept this common sense skepticism as the most appropriate approach to knowledge in general. Both deductive reasoning and inductive reasoning can fail after all, and yet we need to reason in some manner. In fact, deductive arguments are not generally considered true or false, but only valid or invalid, and sound or unsound. A valid deduction is one in which the conclusion must be true provided that the premises are true. A sound deductive argument is one in which we have a high degree of confidence in the truth of the premises.

It is important to note that outside of closed systems of mathematics, virtually all deductive arguments rely on inductively-arrived-at premises, making all claims of knowledge worthy of a bit of skepticism. If we agree that more carbon dioxide in the air must lead to a warmer climate, and that we are adding more carbon dioxide to the air, it is valid to say we are contributing to global warming. Notice, though, that we only arrive at the first premise by way of induction: we note that higher carbon dioxide levels coincided with higher temperatures in the past and assume that it must always be that way. This isn't an argument against human-caused global warming, but it does suggest the possibility of our being wrong.

To repeat, as powerful and useful as deductive reasoning is, it is difficult to find an example (again, outside of mathematics) that does not have much weaker inductive reasoning somewhere in its foundations. But this doesn't suggest that total skepticism is called for. For myself, I'll still accept the deductive logic in the reasoning which says, "gravity acts on all objects, and I am an object, therefore I shouldn't step off a cliff if I don't want to fall." I'll also use my own experiences, and including seeing others fall, to form a similar conclusion through induction. In other words, I won't be too skeptical of gravity.

On the other hand, there is nothing wrong with acknowledging that the premise of gravity operating on all objects is based simply on our observations thus far. It is not outside the realm of the possible that we will someday discover objects which are not affected by gravity. An open and honest mind requires that we use deduction and induction, and also that we allow for the potential fallibility of all the ways in which we reason.

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