Inductive and Deductive Reasoning
Inductive reasoning starts with facts and details, and moves to a general conclusion. So, it lists different details, different examples, and moves to a general conclusion, or helps you come to a certain conclusion.
Now, inductive reasoning is probabilistic, which means that it’s based on probability. You hear certain facts and you come to a conclusion, and that conclusion is going to have some level of probability to it.
The next lesson for you: Inference; these lessons are included in the Math practice tests.
Now, these conclusions can be strong or weak, and they can be proved false. You could come up with a conclusion that doesn’t actually happen. It’s not something that’s true. But, based on the examples you are given, or the facts you were given, the conclusion makes sense, even if it’s not true. And that’s how inductive reasoning works.
So, let’s look at some examples.
“We have seen 30 white swans. Therefore, all swans are white.”
Well, based on the 30 examples that we’ve seen, this statement makes sense. This conclusion that we drew using inductive reasoning based on our 30 examples would make sense. But, is it true? No. Not all swans are white. You’ve got other colors. So, this isn’t a true thing. This is a false conclusion. But, we did use inductive reasoning to get there, basing our conclusion on our examples.
Let’s look at the next one.
“Basketball players are tall. John is a basketball player. John must be tall.”
Well, we don’t actually know John, so we’re not sure about this one. It’s very probable, so this one would be a stronger conclusion than our one about the white swans, but we don’t know John. John could be short. John could just be really good at making goals. That doesn’t mean that he is going to be a tall person.
So, it’s probable, it’s a stronger conclusion, but we don’t know for sure. We just use inductive reasoning, knowing that basketball players are generally tall, and knowing that John is a basketball player to figure out that John is probably tall.
This is called “bottom-up” logic. We start at the bottom with our examples, and we build on those facts, details, examples to come to a conclusion. So, bottom up to the top to build our conclusion.
Next, let’s talk about deductive reasoning. Deductive reasoning starts with a conclusion and then explains the facts, details, and examples that support it. So, you start with one basic conclusion, one basic statement, and then give facts and details that can support it, or that our examples of that statement.
This one links premises with conclusions. So, you come up with the certain premise, and it’s linked to your conclusion that you started with. If all premises are true and clear, then the conclusion must also be true.
So, you start with this one.
“All dogs are mammals.” Okay.
“All mammals have hearts.” Okay.
So, based on the fact that all dogs are mammals, and all mammals have hearts, all dogs must have hearts.
So, you’ve got dogs are mammals, and mammals have hearts, which means that dogs must have hearts, since they are mammals, and all mammals have hearts.
This is a true conclusion, and that’s because all the premises are true. So, if all premises are true and clear, then the conclusion must also be true.
So, on this one, we have true, all dogs are mammals. True, all mammals have hearts. So, it’s true that all dogs must have hearts. And this one is a true conclusion based on deductive reasoning.
Now, let’s look at example two.
“All birds can fly. An ostrich is a bird. All ostriches can fly.”
So, we use the fact that we know all birds can fly, and an ostrich is a bird, to tell us that an ostrich must be able to fly. So, let’s look at each of those statements.
“All birds can fly.” Well, that one is false. There are actually about 40 different species of birds that can’t fly and are called flightless birds.
“An ostrich is a bird.” Well, that one’s true.
“All ostriches can fly.” That one is false. Ostriches are a species of flightless birds.
So, since the first sentence was false, our conclusion ended up being false. And that may not always be the case, but whenever you don’t have all your premises leading up to your conclusion true, your conclusion might not be true either.
Now, we did use deductive reasoning to get there, so even though this is a false conclusion, we were basing it on the information we were given. On the conclusions that were given to us, we came up with this example of an ostrich, and it just wasn’t correct. It wasn’t true. So, over here, we had false conclusion, possibly false conclusion, true conclusion, and false conclusion.
So, using inductive and deductive reasoning is not going to be 100% accurate. But, it is going to give you different ways to reason out information you have, so try to make a conclusion based on one of these kinds of logics.
And deductive reasoning is also called “top-down” logic, because you start with known conclusions, and work your way to specific examples at the bottom. So, you start at the top, known conclusion, work your way down to the bottom to specific examples.
So, whenever you are trying to figure out a problem, or figure out how to connect information that you have, you can use inductive reasoning and deductive reasoning, and just make sure that you are paying attention to whether you have facts and details to start with that you can base the conclusion on, or whether you’ve got broader conclusions that you’re going to be coming up with examples for.
And remember that they won’t always be true, you might still have to go and research whether the conclusion you come up with is accurate or not.