Testing Validity

Remember our definition of validity:
An argument is valid if and only if it is impossible for the premises to be true and the conclusion false.
There are many ways that we might test whether an individual argument is valid.

The most direct way of testing for validity is to simply describe or imagine various possibilities. If you can describe a possibility where the premises are true and the conclusion is false, you will have shown that the argument is invalid.

For example, consider the following argument:

Premise 1 If my car's battery is dead, then my car won't start.
Premise 2 My car won't start.
Conclusion Therefore, my battery is dead.
To see that this argument is invalid, we can simply imagine various other possibilities which could keep my car from starting. As someone pointed out in class, it's possible that the car has no engine. If this were true, then both of the premises would be true, but the conclusion would be false.

One other way of testing validity

As I mentioned, there are many ways you might test the validity of an argument. One way that I described in class was to test other arguments with the same form.

Validity is a “formal” property of an argument. That is, if an argument is valid, any argument with exactly the same form will also be valid.
So, one way of testing the validity of an argument is to test whether other arguments with the same form are all valid.

If you can find another argument with the same form that is clearly invalid, this shows that the original argument is also invalid.
In class, we saw that Gaunilo's objection to Anselm's Ontological Argument proceeds in exactly this way.