What's the difference between deductive reasoning and inductive reasoning?

Deductive reasoning, also known as deduction, is a basic form of reasoning that uses a general principle or premise as grounds to draw specific conclusions. 

This type of reasoning leads to valid conclusions when the premise is known to be true — for example, "all spiders have eight legs" is known to be a true statement. Based on that premise, one can reasonably conclude that, because tarantulas are spiders, they, too, must have eight legs.

The scientific method uses deduction to test scientific hypotheses and theories, which predict certain outcomes if they are correct, said Sylvia Wassertheil-Smoller, a researcher and professor emerita at Albert Einstein College of Medicine. 

"We go from the general — the theory — to the specific — the observations," Wassertheil-Smoller told Live Science. In other words, theories and hypotheses can be built on past knowledge and accepted rules, and then tests are conducted to see whether those known principles apply to a specific case.

Deductive reasoning begins with a first premise, which is followed by a second premise and an inference, or a conclusion based on reasoning and evidence. A common form of deductive reasoning is the "syllogism," in which two statements — a major premise and a minor premise — together reach a logical conclusion. 

For example, the major premise "Every A is B" could be followed by the minor premise "This C is A." Those statements would lead to the conclusion that "This C is B." Syllogisms are considered a good way to test deductive reasoning to make sure the argument is valid.

In deductive reasoning, if something is true of a class of things in general, it is also true for all members of that class. 

Deductive conclusions are reliable provided that the premises they're based on are true, but you run into trouble if they're false, according to Norman Herr, a professor of secondary education at California State University, Northridge. For instance the argument "All bald men are grandfathers. Harold is bald. Therefore, Harold is a grandfather," is logically valid, but it is untrue because the original premise is false.

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Here are some examples of deductive reasoning:

Major premise: All mammals have backbones.
Minor premise: Humans are mammals.
Conclusion: Humans have backbones.

Major premise: All birds lay eggs.
Minor premise: Pigeons are birds.
Conclusion: Pigeons lay eggs.

Major premise: All plants perform photosynthesis.
Minor premise: A cactus is a plant.
Conclusion: A cactus performs photosynthesis. 

Inductive reasoning uses specific and limited observations to draw general conclusions that can be applied more widely. So while deductive reasoning is more of a top-down approach — moving from a general premise to a specific case — inductive reasoning is the opposite. It uses a bottom-up approach to generate new premises, or hypotheses, based on observed patterns, according to the University of Illinois.

Inductive reasoning is also called inductive logic or inference. "In inductive inference, we go from the specific to the general," Wassertheil-Smoller told Live Science. "We make many observations, discern a pattern, make a generalization, and infer an explanation or a theory." 

In science, she added, there is a constant interplay between inductive and deductive reasoning that leads researchers steadily closer to a truth that can be verified with certainty, 

The reliability of a conclusion made with inductive logic depends on the completeness of the observations. For instance, let's say you have a bag of coins; you pull three coins from the bag, and each coin is a penny. Using inductive logic, you might then propose that all of the coins in the bag are pennies.

Even though all of the initial observations — that each coin taken from the bag was a penny — are correct, inductive reasoning does not guarantee that the conclusion will be true. The next coin you pull could be a quarter. 

Here's another example: "Penguins are birds. Penguins can't fly. Therefore, no birds can fly." The conclusion does not follow logically from the statements, because the only birds included in the sample were penguins.

Despite this inherent limitation, inductive reasoning has its place in the scientific method, and scientists use it to form hypotheses and theories. Researchers then use deductive reasoning to apply the theories to specific situations.

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Here are some examples of inductive reasoning:

Data: I see fireflies in my backyard every summer.
Hypothesis: This summer, I will probably see fireflies in my backyard.

Data: I tend to catch colds when people around me are sick.
Hypothesis: Colds are infectious.

Data: Every dog I meet is friendly.
Hypothesis: Most dogs are usually friendly. 

Another form of scientific reasoning that diverges from inductive and deductive reasoning is called abductive. Abductive reasoning is a form of logic that starts with an incomplete set of observations and proceeds to the likeliest possible explanation for that data, according to Butte College in Oroville, California. 

It is based on making and testing hypotheses using the best information available. It often entails making an educated guess after observing a phenomenon for which there is no clear explanation. 

For example, a person walks into their living room and finds torn-up papers all over the floor. The person's dog has been alone in the apartment all day. The person concludes that the dog tore up the papers because it is the most likely scenario. It's possible that a family member with a key to the apartment swung by and destroyed the papers, or it may have been done by the landlord. But the dog theory is the most likely conclusion based on the data at hand. 

Abductive reasoning is useful for forming hypotheses to be tested. For instance, abductive reasoning is used by doctors when they're assessing which ailment a patient likely has based on their symptoms. They then check which potential diagnosis is correct using medical tests. Jurors also use abductive reasoning to make decisions based on the select evidence presented to them by lawyers and witnesses.

Related: What is Occam's razor?  

Here are some examples of abductive reasoning: