Inductive Reasoning

I. Definition

Inductive reasoning, or induction, is one of the two basic types of inference. An inference is a logical connection between two statements: the first is called the premise, while the second is called a conclusion and must bear some kind of logical relationship to the premise.

Inductions, specifically, are inferences based on reasonable probability. If the premise is true, then the conclusion is probably true as well. This is in contrast to deductive inferences, in which the conclusion must be true if the premise is.

Examples

Premise: Every day so far, the sun has risen in the East and set in the West.
Conclusion: The sun will probably continue to rise in the East and set in the West.

Premise: Every time I use the can opener, my cat comes running into the kitchen.
Conclusion: The cat probably thinks I am opening a can of tuna or wet food.

Premise: Ben has visited four places today, and Sam has gone to those places soon after.
Conclusion: Sam is probably following Ben.

Often, Inductive reasoning produces a general conclusion from a specific premise. They start with particular observations of a pattern, and then infer that there’s a general rule. For example, everyone knows the general rule in Example #1: the sun always rises and sets the same way. That rule is based on a huge accumulation of data points, not on a mathematical “proof” or derivation from other abstract rules. This is a common feature of inductions, but it isn’t always present (for example, #2 is not deriving a general rule).

II. Inductive reasoning vs. Deductive reasoning

Unlike inductive reasoning, deductive reasoning, or deduction, is based on absolute logical certainty. If the premise is true, there’s no way for the conclusion not to be true. Deduction is the basis for mathematics, but is also used in formal statements such as definitions or categorizations.

Exmaples

Premise: 2+2=4

Conclusion: 4-2=2

Premise: All gorillas are primates, and Koko is a gorilla.

Conclusion: Koko is a primate.

Premise: The cat always comes running when I ring this bell, and she isn’t coming.

Conclusion: I haven’t rung the bell.

Although deductive reasoning is logically certain, they do not provide new information. In each of these examples, the conclusion is already contained in the premises; the conclusion is just another way of stating the premise. Thus, inductive reasoning is often more useful in science and everyday life because they allow us to generate new ideas about the world, even if those ideas are based on probability rather than certainty.

In addition, deductions are sometimes misleading in their certainty. That’s because the conclusion will only be true if the premise is true, and in the real world things are usually too messy for that. For example, in the third example we can be absolutely certain of the conclusion if the premise is true; but are we sure that it is? There are probably no actual cats who are so reliable that we can say they will always behave a certain way.

III. Quotes about Inductive reasoning

Quote 1

“One attempt to avoid the problem of induction involves weakening the demand that scientific knowledge be proven true, and resting content with the claim that scientific claims can be shown to be probably true in the light of the evidence.” (Alan Chalmers, What is This Thing Called Science)

Alan Chalmers is a philosopher of science who, like others in his profession, tries to understand how science works and what makes it so successful at certain tasks. In this quote, he argues that science is based on inductive reasoning rather than logical “proofs.” Although math is all deductive, science has to depart from pure mathematics when it looks out at the world around us. Because that world is messy and complicated, it may be impossible to prove anything conclusively. However, we can base our reasoning on probability and seek more probable answers rather than seeking the absolute, proven truth.

Quote 2

“Perfect knowledge alone can give certainty, and in nature perfect knowledge would be infinite knowledge, which is clearly beyond our capacities. We have, therefore, to content ourselves with partial knowledge—knowledge mingled with ignorance, producing doubt.” (William Stanley Jevons)

In this quote, the logician William S. Jevons explains the importance of inductive reasoning in human knowledge. Like Chalmers in the first quote, Jevons here is arguing that perfect certainty is impossible in the real world. We can only have logical certainty when it comes to abstractions, and therefore deductive reasoning will only get us so far — at a certain point, we have to rely on induction to tell us what’s probably true, giving up on absolute certainty.

IV. The History and Importance of Inductive reasoning

For as long as living things have had brains, they have been making inductive inferences: mice learn to avoid the electrified corner of their cage, inferring probable future events from painful past experience; zebrafish detect small fluctuations in the water and infer (consciously or not) the likely size of an approaching fish through murky water. In cases like these, the animal’s brain is making an inductive inference.

If we couldn’t use inductive reasoning, we wouldn’t survive a single day. When you go to the fridge for a snack, you do it on the basis of an inductive inference: normally when I go to the fridge there’s something there to eat; therefore there will probably be food there today as well. You walk to school following the induction that the building will probably still be standing and the doors will be open for you. In a bigger sense, inductive reasoning tells you that making bad choices will probably lead to unhappiness down the road. These inferences are all based on probability and prior experience, not logical certainty.

Because inductions are not logical certainties, some philosophers see them as inferior to deductions. In their eyes, philosophy needs to be rigorous and skeptical, accepting only those truths that can be logically proven. But the Scottish philosopher David Hume pointed out that this was an impossible way to live. Hume demonstrated that some of our most basic beliefs are based on inductive reasoning: it’s only by induction that we believe the sun will rise tomorrow, or that we have a personal identity that lasts from day to day. These are central truths for human existence, but they can’t be proven through deductive logic. Thus, for Hume deductive certainty was an unrealistic standard for philosophy to hold itself to.

V. Inductive reasoning in Popular Culture

Example 1

In the South Park movie, Cartman’s mom is trying to train him not to swear so much. When other options fail, she sends him to a doctor who sticks an electroshock chip in Cartman’s brain. When Cartman swears, he gets a painful shock. After a few trials, Cartman inductively infers that swearing will bring pain, and he stops immediately. Notice that this scene has both of the classic attributes of an inductive reasoning: it’s based on probability, not certainty; and it uses specific past experiences to work out a general rule for the future.

Example 2

“Here is a gentleman of the medical type, but with the air of a military man. Clearly an army doctor, then. He has just come from the tropics, for his face is dark, and that is not the natural tint of his skin, for his wrists are fair. He has undergone hardship and sickness, as his haggard face says clearly. His left arm has been injured: He holds it in a stiff and unnatural manner. Where in the tropics could an English army doctor have seen much hardship and got his arm wounded? Clearly in Afghanistan.” (Sherlock Holmes, Sherlock)

Sherlock Holmes has a website called “The Science of Deduction,” but his talent is clearly for inductive reasoning! In this quote, he makes a long series of observations, and builds them into a story that’s probably true. But it’s not a deduction at all! It’s logically possible that all this evidence could be accounted for by some other story (or by sheer coincidence.)