Types of Reasoning

There are 3 main types of reasoning: Deductive, Inductive and Abductive.

Deductive Reasoning uses existing facts and logic to create a new perfect fact. We use this in Mathematics.

Example: An hour has 60 minutes. I did 60 minutes of walking. So I did one hour of walking.

Irregular yellow hexagon with six straight sides

Example: A hexagon is a flat shape with 6 straight sides. This flat shape has 6 straight sides. So this shape is a hexagon.

The result is certain to be true. Just what we love in mathematics.

Challenge: Think about a rule or fact you know, and try to deduce a new fact!

Inductive Reasoning uses observations to create general rules that are likely to be true. This reasoning is used a lot in Science.

Example: All rabbits we watched returned home to burrows. So (as far as we know) rabbits live in burrows.

Example: A study showed that students who didn't practice also get low exam scores. So it appears that practice is important to passing exams.

It gives us a good understanding of the world around us, and helps us master many things.

It is correct as far as we know, and can be improved when new facts come along.

Example: Europeans believed all swans were white, until explorers discovered Black Swans in Australia!

Challenge: Observe something in your day-to-day life and try to make a general rule about it.

Abductive Reasoning uses observations to reach the most likely conclusions. This reasoning is used a lot in everyday life.

Example: there are many lovely flowers in Sam's garden, so we think Sam is a good gardener.

Example: Alex is very healthy, so Alex probably has a good diet.

Example: Billy is tall and athletic, so is likely a basketball player.

Silhouette of Sherlock Holmes with a magnifying glass

This reasoning can help us make quick decisions in life. For example if we want gardening advice we can ask Sam.

Sherlock Holmes uses this type of reasoning!

But be careful not to be prejudiced. Always keep an open mind.

Challenge: Imagine you're a detective. Look around and make educated guesses about the world around you. What was the last meal in the house? Where does your pet like to sleep?

In Mathematics

Inductive: we spot a pattern (like 1, 4, 9, 16, ... looks like squares) and make a rule
Deductive: we use facts/rules to show something must be true (a proof)
Abductive: we choose the most likely explanation when we don't know everything yet (a good guess), then we check it

Example: Pattern then Proof

We might notice (inductive) that 1+3=4, 1+3+5=9, 1+3+5+7=16 ... so it looks like the sum of the first odd numbers makes a square.

Then we try to prove it (deductive) so we know it is always true.

Conclusion

Reasoning is a powerful tool that helps us explore and understand.

Type	Starts With...	Goal	Certainty
Deductive	Rules and Facts	Find a specific fact	100% Certain
Inductive	Observations	Find a general rule	Likely
Abductive	Observations	Find the best explanation	Most Likely

You don't have to remember the names, but it is good to know about the different types of reasoning and what they are good for.

There's always more to learn, and keeping an open mind is key.

Happy reasoning!