#
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.