Critical Thinking by Example

Example 4.1: Example of a valid argument. P1: I am over 50ft tall. C: So, I am over 40ft tall. Students struggle with validity because there is a temptation to claim that an argument is invalid because it has a false premise. Notice, however, that the definition of validity specifically rejects requiring establishing the truth of the premise set: we are asked to ASSUME that the premises are true. So, to evaluate the validity of an argument requires that you sometimes let your imagination run wild. In example 4.1 we must imagine something very implausible: that the author is 50ft tall. Of course no human is that tall. But imagine someone were that tall. If someone were that tall, then it would have to be the case that he or she is over 40ft tall. That is, if the premise is true, then the conclusion must be true. Alternatively, we can see how the second definition of validity applies: if we imagine that the premise is true, then it is not possible that the conclusion is false. If someone is over 50ft tall, then it is not possible that they are not over 40ft tall. Example 4.2: Example of a invalid argument. P1: I am over 1ft tall. C: So, I am over 2ft tall. We can see why 4.2 is invalid: if the premise is true, it does not follow that the conclusion must be true. The author could be taller than 1ft and less than 2ft tall. So, the argument is invalid. Hint: not everyone is helped by this hint, but enough that it is worth saying: to judge the validity of an argument it might help to imagine an “empty universe”. Next, imagine the universe is described only in the ways that the premises say. In example 4.1, we might imagine a universe with a single person over 50ft. tall. In the second case we imagine a single person over 1ft. In this way you can focus on what is at issue: whether the conclusion must be true in your imaginary universe.