Sound arguments are great in one way:
They have true conclusions.
But not all sound arguments are interesting arguments.
Here, for example, is a sound but uninteresting argument.
Let's take a conclusion that's fairly hard
to establish-- Fermat's last theorem.
What does it say?
It says that for no a, b, c, n greater than 2
is a to the n equal to b to the n plus c to the n.
It took many hundreds of years to prove this.
You'd think that establishing a sound argument
for this conclusion is very hard.
In fact, it's easy.
Here's a sound argument to the conclusion
that Fermat's last theorem is true.
Premise-- Fermat's last theorem is true.
Conclusion-- Fermat's last theorem is true.
The argument is valid because it's impossible
that its premise be true and its conclusion false.
The argument is sound, because as a matter of fact,
its premise is true.
But of course, you're not going to, in any interesting sense,
prove to anybody or persuade anybody
that Fermat's last theorem is true by appealing
to this argument.
Likewise, it's very easy to come up
with sound arguments for the existence
or non-existence of God.
I'm going to give you at least one in a slightly tricky way
here, because I'm not going to tell you which of two arguments
is sound.
But one of them is.
OK, first argument.
Premise-- God exists.
Conclusion-- God exists.
Second argument.
Premise-- it's not the case the God exists.
Conclusion-- it's not the case the God exists.
At least one of these arguments is sound.
If God exists, it's the first argument.
If God doesn't exist, it's the second argument.
But neither of them is very interesting,
because we're not going to persuade anybody or prove
to anybody who didn't know it already
that God exists or doesn't exist by appealing
to one of these arguments.
So good, interesting arguments have a further virtue
in addition to soundness.
That is they're potentially convincing.
Now, this depends on where you start.
Potential convincingness depends in part
on who is in a position to be convinced.
We'll define it like this.
An argument is potentially convincing for a person when,
prior to being confronted with the argument,
the person believes the premises but doesn't believe
the conclusion, and the person is in a position
to see that the argument is valid.
So if the argument is potentially convincing for you,
then because you believe the premises before being
confronted with the argument, you'll
be inclined to accept all of those premises.
And because you're in a position to see that the argument is
valid, you'll be in a position to see
that, given that the premises are true,
the conclusion, too, must be true.
So you're in a position to be persuaded
that the conclusion is true.
So take an argument that we looked at earlier.
Premise-- God exists.
Conclusion-- God exists.
This argument is not going to be potentially convincing
for anybody, because there's nobody who's
going to, prior to being confronted with this argument,
believe the premise and not believe the conclusion.
And the same could be said for other arguments that quite
routinely get made for the existence
or non-existence of God.
So for example, here's an argument that you hear.
Premise-- everything the Bible says is true.
Premise two-- the Bible says that God exists.
Conclusion-- God exists.
This may be a sound argument.
If the premises are true and the conclusion is true,
then it's a sound argument because it's also
a valid argument.
But it's not going to be potentially
convincing for any realistic person.
There's no person out there in the world
who believes that everything that the Bible says
is true-- that first premise-- and doesn't yet
believe that God exists.
You're not going to find anybody who is going to say, "Oh, yes.
Gosh.
Look, on being confronted with this argument,
I recognize that the premises are true,
and as a result of that, I've come
to believe that God exists."
The people who believe the premises
already believe the conclusion.
So we're looking for an argument that's
not like that-- an argument that can convince people.
And in particular, we're looking for an argument that
can convince a special kind of person.
We'll call this person the reasonable agnostic.
To say that the person is an agnostic
is to say that this person has yet
to come to a view about whether God exists or God doesn't
exist.
He or she is keeping an open mind
about the existence of God.
To say this person is reasonable is
to say that he or she shares all of our everyday beliefs
about things not pertaining to God,
and this person is rational in the sense
that she's able to think through arguments
and understand patterns of reasoning.
If we can come up with a sound argument that
is potentially convincing for this person,
the reasonable agnostic, then we will
have what we want-- a proof for the existence
or non-existence of God.