# Teaching my son the difference between inductive and deductive reasoning

My son has shown an increased ability to grasp complex ideas, and one that he recently brought up was logic, more specifically the difference between inductive and deductive reasoning. What would be the best way to help him grasp these concepts? I don't want to confuse him with a poor attempt at teaching on my part.

David Blomstrom's answer is detailed and deeply informative. I am going to offer something shorter - shorter only with a view to the basic explanation you need to give to your son.

▻ DEDUCTION

A deductive (or deductively valid) argument is one in which it is impossible for the conclusion to be false if the premises are true. The truth of the premises, if they are true, necessitates the truth of the conclusion. So :

Socrates is a man. All men are mortal. Therefore Socrates is mortal.

If Socrates is a man and if all men are mortal - if both premises or statements are true - it must be true that Socrates is a mortal.

An argument can be deductively valid even if the premises are not true but are merely assumed :

All cats are purple. Fido is a cat. Therefore Fido is purple.

This is a deductively valid argument because, if the premises are true then the conclusion must be true. This is still so, even though it is not actually true that all cats are purple or that Fido is a cat (Fido is a dog). It's merely the case that if the premises are true, so must the conclusion be.

▻ INDUCTION

Induction runs on probability. In an inductively strong argument, the conclusion is unlikely to be false if the premises are true.

Suppose I am presented with a bag of 100 tennis balls. I take out one ball : it is green. I take out another : it is green. This goes on, with every ball coming out green, up to the 99th ball. It is highly probable - very likely - that the final, 100th, ball will be green. It doesn't have to be. It might be blue or red. But it's a pretty safe inductive inference that the whole bag contains nothing but green tennis balls.

Or take this example :

Jack has never been known to read a physics book. Jack has never been taught physics. Jack has a physics exam tomorrow. So : Jack will fail the exam.

It's highly likely that Jack will fail the exam but there's no necessity. Jack's mother may be an extremely competent physicist whose work Jack has followed closely and intelligently even though his mother has never taught him physics and nor has anybody else.

Hope these examples help to make clear the basic difference between inductive and deductive reasoning.

Deduction begins with a look at "the big picture," then zooms in on more detailed clues before reaching a conclusion.

Induction is the opposite, using tiny pieces of evidence in an attempt to grasp the big picture.

When using sound logic, deduction is foolproof. Maybe I shouldn't say "foolproof" on a philosophy forum, but let's just say it's very accurate.

Induction, on the other hand is less reliable; a person using induction could reach an incorrect conclusion. So let's associate the word Induction with the word INdefinite or INconclusive. Since it begins with relatively small(er) clues, we might also associate it with the word INsignificant.

So we now have some basic rules:

Deduction = Big > Little; Conclusive

Induction = Little ("insignificant") > Big; Inconclusive

Then work through some exercises to reinforce the concept. You could start with some simple syllogisms, a common form of deductive reasoning in which two statements (a major premise and minor premise) reach a logical conclusion.

For example, the premise "Every A is B" could be followed by the minor premise "This C is A." So we can logically say that this C is B.

Now we can perform some simple exercises, occasionally replacing "is" with "has."

For example, we can say all mammals have hair (though some are nearly hairless); horses are mammals; therefore, horses have hair.

All metals have property X; silver is a metal; therefore, silver has property X.

Try to come up with similar examples in several categories (e.g. plants, animals, human culture, the arts, etc.)

Next, do a similar series of induction exercises...

The first bone we found in this cave represents a Neanderthal; the second bone also represents a Neanderthal; therefore, all the bones in this cave represent Neanderthals.

However, even though induction reasoning is based on facts (Neanderthal bones, in this case), it only allows us to form a theory...and that theory will be stronger if supported by a large amount and/or diversity of data or evidence.

Assuming every bone in a cave represents a Neanderthal based on just two bones would be absurd. What about bones representing the animals Neanderthals ate?

We can then fine tune our premises:

The first hominid or human bone we found represents a Neanderthal; the second hominid bone also represents a Neanderthal; therefore, it looks like all the hominid bones in this cave represent Neanderthals.

Our inductive trail grows stronger if we find a hundred Neanderthal bones.

We might then try to come up with some examples that include both deductive and inductive reasoning. For example...

DEDUCTION: All humans are/were bipedal; Neanderthals were human; therefore, Neanderthals were bipedal.

INDUCTION: This fossilized footprint was made by a bipedal creature; a second footprint was also made by a bipedal creature; therefore, the animal that made these tracks may have been a human (and possibly a Neanderthal).

INDUCTION #2a: The only human known to have migrated into the New World is our own species, Homo sapiens. This fossilized footprint was made in South America (where Neanderthals never lived); therefore, we know this track could not have been made by a Neanderthal.

INDUCTION #2b: This fossilized footprint was made in Europe (where Neanderthals evolved); therefore, it could have been made by a Neanderthal.

INDUCTION #3: This fossilized footprint has been dated to 250,000 years (when Neanderthals lived in Europe but modern humans hadn't migrated out of Africa); therefore, this footprint was probably made by a Neanderthal.

The goal of the game is to focus on topics (e.g. evolution/paleontology > Neanderthals) and try to put together a combination of deductive and inductive clues that form a "framework."

For example, we know that Neanderthals were bipedal humans ("archaic humans") that presumably evolved in Europe (300,000 years ago, I think) and apparently became extinct (about 30,000 years ago?).

We also know Neanderthals were extremely similar to modern humans. So the goal is to put together a combination of deductive/inductive clues that help us distinguish between human fossils and Neanderthal fossils, based on what we know about their morphology, the dates both groups first appeared in Europe (and when they became extinct), etc.

Stress the fact that good detectives need to do their homework in order to really use deductive/inductive reasoning effectively. If you're interested in political science, then study political science, history, psychology and philosophy in order to grasp the basics. Then you can create more effective lines of deductive/inductive reasoning.

In fact, that might be an idea for another game:

1) Choose a topic (e.g. a conspiracy theory).

2) Each player then has to create a series of deductive/inductive clues that shed light on the theory.

3) The winner is the player who either proves or disproves the theory or who can at least pronounce the theory credible or not highly credible with the least number of deductive/inductive clues.

Sorry for the wordy response, but, to summarize, make the difference between deduction and induction clear, then practice by applying each one to a variety of topics before creating "frameworks" based on series of deductive reasoning and inductive clues. Make it more fun by turning it into a game.

EDIT: I edited this to change "Sorry of the worse response" to "Sorry for the worthy response." ;)

Short is better.

DEDUCTION: the conclusion must follow from the premises. If a man is in the kitchen, and the kitchen is in the house, the man must be in the house.

INDUCTION: the conclusion may follow from the premises. If a man walks his dog on the prior 11 Thursdays, and it tomorrow is Thursday, he will likely walk his dog tomorrow.