Definitions of
validity:
Definition 1:
An argument is valid if the premises are
(or were) true, then the conclusion must be
true.
Definition 2: An argument
is valid if it is not possible that the premises
of the argument are true, while the conclusion
is false.
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.
