Thinking clearly is really important for programmers. ‘Ergo’s adventures in thinking’ is a an introduction to clear logical thinking, that uses poems and drawing to highlight common reasoning mistakes “logical fallacies’ for young children. It contains seven poems about Ergo (a character the reader creates), one for each day of the week. In each poem Ergo makes a thinking mistake. As the reader you must explain why Ergo is wrong each time, and draw a fun picture to go with each poem.

Use in class

Laminate the pages for photocopying or repeated use. Use the booklet for guided reading, in the book corner or for homework. Have your students read and try to understand the poems and then discuss the thinking muddle involved.

Short Notes for grown ups

This beginner’s book, explores how to avoid muddled thinking. Computer Scientist’s use logic to help understand the world. This is a part of ‘computational thinking’ and it is all about thinking clearly. It will prepare your child to solve problems by helping them think in a clear, logical way and draw correct conclusions from the information available.

The seven poems, one a day for a week, will give your child an easy and fun introduction to common logical thinking mistakes or ‘fallacies’. Each poem and related drawing activity shows, by example, one of the following common logical errors.

There are two statements about cats that do not make sense together as they contradict each other. Ergo has up to that point only seen grey cats so believes that all cats are grey. The second example shows that at least one black cat exists. The black cat means that Ergo’s original belief about all cats cannot be true. Just because you have not seen an example of something does not mean it does not exist.

The Gambler’s fallacy

Throwing a fair coin, which has not been tampered with, should always be 50/50 heads or tails. What happened before cannot affect the next toss. This is called being ‘statistically independent’. Ergo should have known that the next toss was just as likely to be a head as a tail.

The Causal fallacy

A common mistake is to think there is a link between two things, when either there is actually no link at all, or the link works the other way round. Just because Ergo sees that umbrellas and rain happen together does not show which causes the other, if at all. Getting your umbrella out will not make it rain. It is the other way round: rain may make you get an umbrella out.

Two wrongs do not make a right

Ergo thinks that because some people do bad things, it means it is ok for everyone to do bad things.  Grown-ups often use the proverb “Two wrongs don’t make a right to counter this. It does not make things better to do another wrong. This is called a ‘fallacy of relevance’.

Ergo has decided to attack the woman rather than showing that her argument is wrong, but facts about what a speaker looks like have nothing to do with whether they are right or not. This is called the Ad hominem fallacy. Facts about a speaker might be used to understand a moral issue, but only if there is a direct link between the person’s morals and what they are saying. If someone is known to lie then that might be used to help decide if they are lying now, for example.

Bandwagon fallacy

Ergo thinks that just because most people believe something, then that alone makes it true. This is also known as the ‘Bandwagon fallacy’ or Argumentum ad populum (Latin for “appeal to the people”). Sometimes the one lone voice claiming something else is true is actually right. You should ask for evidence rather than rely on what other people think.

Syllogism

Syllogism are classical logical statements that allow two facts to be joined to prove a third. Here, the person thinks he has, sadly, forgotten all those he went to school with. This is called the ‘major premise’. Ergo then says he was a classmate at school. This is the ‘minor premise’. If you combine these two premises then you can correctly logically conclude from them using a Syllogism that the person does not know Ergo. However, the conclusion only follows if the statements are actually true. If they weren’t actually at school together, or the person is mistaken and has not forgotten everyone, then the conclusion may not be true either.

It is important to make sure basic facts are true before drawing conclusions from them.

Shakespeare used fallacies based on Syllogisms to make jokes:

Flavius: Have you forgot me, sir?
Timon: Why dost ask that? I have forgot all men;
Then, if thou grant’st thou’rt a man, I have forgot thee.
(William Shakespeare, Timon of Athens, Act Four, scene 3