# 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.

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.