Key terms and concepts

Pupils in sixth year doing maths may come across counterexamples in that context. For example, one question might be:

When decoded this simply says

"For every 𝜒 where 𝜒 is a whole number 5𝜒 is greater than 4𝜒"

This is shown to be false by giving a counterexample, namely that when 𝜒=0  5𝜒 is not greater than 4𝜒

In Philosophy counterexamples were originally introduced because there were examples of them being used in other areas of the course. However, now they are primarily being treated as a standalone topic in the Arguments in Action component of the course. The 2018 Course Specification states:

—the use of counterexamples to show that a universal statement is false

In other words, if someone makes the claim that 'All birds can fly' a counterexample would be a bird that couldn't fly such as a penguin. Similarly, if someone makes the claim that 'Apart from humans no animal uses tools' a counter example would be a non-human animal that does use a tool. Presumably 'universal statement' will also include some statements of the form 'if p then q' but it would be helpful if this was clarified.

There is a difference between the mathematics example and the two philosophical examples. In maths the counterexample is found by trial and error and mathematical intuition; in the philosophical examples the counterexamples depend upon knowledge of the world. The challenge for question setters is to come up with questions about counterexamples that don't collapse into being a general knowledge quiz. This was avoided in the 2016 QP by asking:

Would giving a counter-example be an appropriate way to
challenge this argument? Explain your answer.

It should be noted that philosophy books and other sources will often talk about counterexamples in the context of showing that an argument is not valid. To do this you have to provide an argument that has the same form/structure as the one that you are trying to show is invalid but in this counterexample the premises are true and the conclusion false.The ability to do this is not a stated requirement of Higher Philosophy but such counterexamples can be considered a special case of showing that a universal statement is false. When someone is claiming that their argument is valid they are effectively claiming that all arguments that have the same form/structure will be valid, i.e. they are structured such that if their premises are true then the conclusion is necessarily true. A counterexample to this universal claim would be an example of an argument that has the same form/structure but has true premises and a false conclusion. It would be helpful if it was clarified if candidates would ever be required to apply counterexamples in this way.