Hey everyone, it's Justin again. In this lesson, we're going to be discussing deductive and
inductive reasoning, which are two different types of logic that we can use to reach a conclusion.
By the end of this lesson, you will be able to determine a conclusion from given information and
classify your reasoning as deductive or inductive. There are probably a few words in here that you
don't recognize yet, like deductive and inductive, but don't worry. First up on our agenda, we're
going to define deductive and inductive reasoning. Then we'll complete two practice problems.
The first of the two types of reasoning we're going to talk about today is deductive reasoning.
Now I've already used the word reasoning a whole lot, so let's make sure we define it so that
we're all on the same page about what it means. Reasoning just means thinking about something
logically. Deductive reasoning specifically means reaching a conclusion based off of one
fact or a series of facts. The key word here is fact. Since we are only working with facts,
the conclusions reached by deductive reasoning will always be true. Let's take a look at an
example. We'll start with, you must be at least 18 years old to vote. This is a fact. It's
definitely not an opinion or an observation, and it is something that will always be true,
no matter what day we make this statement. Then we have, Kelly voted in the election.
What conclusion do you think we can make about Kelly based on this information?
Kelly must be at least 18 years old. We all have different ways that help us make sense
of information. I want to show you how we can take this same information and reframe it from
verbal sentences to a more visual representation. Let's say that this big circle represents all of
the people who can vote. We know that everyone in this circle has to be at least 18 years old.
Since Kelly voted, she must be inside this circle. Let's represent Kelly with this little
orange circle here. Since she's part of the group that can vote, all of the things that are
true about voters must also be true about Kelly. Therefore Kelly must be at least 18 years old too.
Inductive reasoning is a little bit different.
With inductive reasoning, we're reaching a conclusion by making an educated prediction
based on observations or patterns. Since these conclusions are based on patterns and
observations, it is possible for conclusions reached by inductive reasoning to be false.
Seeing this in action might help to show the difference. Every Friday for the last two months,
the Johnsons have ordered pizza delivery. Since this is not something that is guaranteed to always
be true forever and ever - for example, maybe a month from now their habits have changed and I'll
no longer be able to say this - we can't consider it a fact. This is a pattern that we've been
able to observe for the last two months. Today is Friday. What conclusion do you think we can draw?
The Johnsons will order pizza delivery today. This seems like a pretty likely outcome if they
keep following their current pattern. But can you guarantee that this will happen?
No, definitely not. There are lots of reasons why they might change their pattern. For example,
maybe today is someone's birthday in the family and instead they're going to go out
to a restaurant for a special meal. This is what I was referring to when I said
it's possible for conclusions reached by inductive reasoning to be false. They will
only be true if the pattern continues the way we've observed, which we can never guarantee.
Let's take a moment to summarize the difference between these two types of reasoning.
If your conclusion comes from only facts, then you are using deductive reasoning. On the other side,
if your conclusion comes from observations and patterns, then you used inductive reasoning.
Let's put this new information into action with our first example problem. Our directions say,
consider each of the conclusions below. Determine if they were reached by using
deductive or inductive reasoning. There are a lot of parts here. It might help us to stay organized
if we only look at one part at a time. Part A says that a series of numbers goes one, two,
four, eight, and 16. The conclusion is that the next number will be 32.
Using that nice organizer to tell the difference between deductive and inductive reasoning,
what type of reasoning do you think was used here?
Inductive. We were given a pattern of numbers here and made an educated guess about what would
come next based on the past terms. There is no guarantee that 32 comes next. It makes sense,
but our pattern could switch up after 16. Maybe it starts going backwards and
rewinds to eight again, then four, and then two. Try Part B on your own now.
Did you catch that this conclusion came from deductive reasoning? We started with a definitive
fact, not an observation or a pattern. Go ahead and finish off Parts C and D now.
Part C says, all cell phones contain an antenna. Smartphones are cell phones. Are those facts,
or are they observations? Those are facts. So our conclusion, smartphones contain an antenna,
comes from deductive reasoning. Part D says every golden retriever that I have met likes to swim.
Well that's just one person's observation about golden retrievers. It's not a fact that all golden
retrievers ever across the whole world always like to swim. Since this is an observation,
the conclusion of, if I get a golden retriever he will like to swim, comes from inductive reasoning.
Taking time to determine if your given information is a fact pattern or observation
can be a great tool in determining if your reasoning is deductive or inductive.
We have one last problem to complete together. This one kicks it up a notch. Our directions tell
us to consider each set of information below. Draw a conclusion and classify your reasoning
as either deductive or inductive. So this time we don't have a conclusion. We have to make one.
To help you out, there are sentence starters for each of your conclusions.
Part A tells us that all numbers that are multiples of 10 end in zero.
450 ends in zero. The conclusion is that 450 is what? Can you finish the sentence?
450 is a multiple of 10. I can conclude that because it ends in zero,
and we were told that all numbers that are multiples of 10 end in zero.
That's just the first part of the problem though. We also have to classify our
reasoning as deductive or inductive. Which type of reasoning did you think we used?
Since our conclusion comes from facts, we used deductive reasoning.
How about Part B? Part B gives us a series of shapes shown below, and our conclusion
starts with the next shape will be. Examine these shapes and try to determine what will come next.
Did you notice that with each shape, the number of sides goes up by one?
The first one, a quadrilateral, has four sides. Next, the pentagon has five sides,
then six, then finally seven. It makes sense that the next would be an eight sided shape.
This is also called an octagon. Did we just use deductive or inductive reasoning?
Inductive. We noticed a pattern and made an educated guess about what will come next. We
used good reasoning ,but this pattern could throw us a curveball with the next shape.
Maybe our pattern repeats over again from the start with a four-sided polygon next. We can
never be 100% sure that our conclusions from inductive reasoning will be true.
Because inductive reasoning just follows patterns but can never guarantee that our
conclusion will be correct, we'll mostly be using deductive reasoning throughout this
course. Now you can determine a conclusion based on given
information and classify your reasoning as deductive or inductive. See you next time.