Wednesday, October 17, 2007

Deduction and Induction

Deduction and induction are two kinds of reasoning. Sometimes, deduction is defined as reasoning that goes from a generality to a specific result, while induction is defined as reasoning that goes from a specific fact to a generality. Instead, I'm going to go with the definitions outlined by the Skeptic's Dictionary, which I feel are much more precise. Deduction is reasoning in which the premises necessarily imply the conclusions, and induction is reasoning in which the premises only indicate a higher probability of the conclusions being true.

These definitions need some examples and explanation. Here's an example of a valid deductive argument, taken from the Skeptic's Dictionary.

All men are mortal. Socrates is a man. Therefore, Socrates is mortal.

Note that the first two sentences are premises. However, there is actually no need for any premises. We can reduce it to a single tautology--something that cannot possibly be false.

If all men are mortal and Socrates is a man, then Socrates is mortal.

All valid deductive arguments can be reduced to tautologies. Of course, if the premise is false, the conclusion does not follow, but the tautologies remain true.

Inductive arguments can be much more widely varied. Consider the following example from physics:

If Newton's laws are true, I cannot levitate. I cannot levitate. Therefore, Newton's laws are true.

Note that if the second premise was "I can levitate," then the conclusion, "Therefore, Newton's laws are false," would follow deductively. As is, it is an inductive argument. By itself, this inductive argument does not prove a whole lot, since we could use a similar argument to support any other number of scientific theories, as long as they all imply that I cannot levitate. However, if we added a large number of other inductive arguments (in particular, we would want inductive arguments that cannot also be used to support competing theories), we would have quite a persuasive argument. And yet we would still be wrong; Newton's laws have been contradicted by Special Relativity.

On the face of it, induction is much weaker as compared to deduction. No matter how many inductive arguments you might accumulate, a single deductive argument can beat them all. But the problem is that without induction, we can argue hardly anything. We'd just be limited to math and logic. We rely on induction to argue many things: The universe is ordered, our observations are accurate, the sun will rise again tomorrow, etc.

When I say science uses reason, I don't just mean deduction, I mean induction too. The whole scientific method isn't just some process someone randomly made up. First, induction is used to choose a hypothesis that successfully describes our observations. Then, we use deduction to predict further observations. Upon the confirmation of these predictions, we have acquired one more inductive argument supporting the hypothesis. Upon the failure of these predictions, we have, depending on the experiment, acquired an inductive or deductive argument against the hypothesis.

It is often said that "nothing is certain." Well, ignoring deduction for a moment, this saying is true. But that's ok, because we don't need to be certain. It's not certain that the sun will rise tomorrow, but we can still say it's true.


DeralterChemiker said...

Reasoning that appears to be deductive may be accurate only over a certain limited range of conditions. When the conditions are extended beyond that range, the well-reasoned conclusion may simply not apply. A very slightly curved line may appear to be a straight line only because we have not extended it far enough to perceive and detect the curvature. Science is filled with "laws" that are very useful over a limited range of conditions.

miller said...

But we know exactly what the limited range of deduction is. Deduction works within our "representation" of reality, but does not necessarily work with reality itself (which is why we need induction). It is within our power to choose the rules of our representation, and those rules are deduction.

Or something. I'm not a philosopher, I just take an intro course.

There will be more posts around this general topic.

Lage said...

I find it most interesting that sound deduction requires induction. That is, deduction is the application of general knowledge to a specific case and induction is required to develop that general knowledge in the first place.

Peace and love,