Ages 13+
Concepts & Flawed Reasoning

Ages 13+
Concepts & Flawed Reasoning

Case Study 2

Flawed Reasoning

Use these examples of flawed reasoning to introduce logical vocabulary and help your children identify flawed reasoning. More definitions and basic concepts can be found here.

The examples are based on famous example of deductive reasoning attributed to Aristotle. In the exercises, Aristotle’s example is distorted in various ways, either using false information or faulty reasoning. Challenge your children to identify exactly why these arguments fail. 

Here are some definitions of the terms used below: 

  • Premises are the statements or information on which an argument is based (in these cases, the first two lines). 

  • The conclusion (the third line in these examples) is the statement drawn from the premises.

  • When an argument is valid, that means its conclusion follows logically from its premises.

  • When an argument is sound, that means it is both valid and based on premises that are true, meaning its conclusion is also true.

These examples can help students to break up reasoning into logical steps, make the logical steps of an argument explicit to themselves, and identify where reasoning breaks down. Critical thinking must enable us to detect logical errors and to recognize whether they lead us to false conclusions. Notice, however, that flawed reasoning does not guarantee a false conclusion. 

Aristotle’s Reasoning

“All human beings are mortal.
Socrates is a human being.
Therefore, Socrates is mortal.”
The premises are true, the reasoning is valid, and the conclusion is, as a result, true.

Exercises

  1. All human beings are women.
    Socrates is a human being.
    Therefore, Socrates is a woman.

    One of the premises is false, the reasoning is valid, but the conclusion is false.

  1. Half the human race is female.
    Socrates is a human being.
    Therefore, Socrates is female.

    The premises are true, but the reasoning is invalid, and the conclusion is false.

  1. Half the human race is male.
    Socrates is a human being.
    Therefore, Socrates is male.

    The premises are true, the reasoning is invalid, but the conclusion is true.