As I've mentioned before, I get lots of email from all sorts of people. Lots of it is interesting, and lots of it is stupid. This morning, when I was checking my mail, I found an email from a creationist in my mailbox, which puts forth an "proof" against atheism that I hadn't seen before. It's about as idiotic as most creationist arguments are,
but it's one that I've never seen before, and it's interesting to shred it from the viewpoint of mathematical logic.
Here's his argument:
Now to the main point, and somewhat more interesting stuff. I recently ran across a proof (perhaps not in the mathematical sense; I don't know) against atheism. Atheism, both in the forms I've encountered and in logical necessity, requires that matter/energy is eternal, since the atheist would by necessity argue against any point at which matter/energy came into existence. Nothing does not create something. For anything to be eternal and be in the present, it must by necessity have come from eternity past. However, between eternity past and the present, there is an infinite amount of time. Therefore, traveling forward from eternity past, one could never reach the present day. Therefore, atheism cannot be true, and a definite point at which matter/energy came into existence is necessary.
What's wrong with this? Where to begin?
First - this isn't an argument against atheism. This applies just as much to
THeism as it does to atheism. After all - to a theist, God has always existed. According to his argument, why would God's infinite existence not be an issue?
Second - it doesn't make any sense. This is the kind of argument that mathematicians hate, because it's a word game. This argument pretends to play with mathematical arguments - distance, infinity - but you can't express it
meaningfully in mathematics. It's got pretty much the same problem as
the good old "Zeno's paradox".
As a quick refresher, Zeno's paradox is based on division. There's tons of
statements of it. My own favorite is: You cannot be killed by an arrow fired from a bow. Why? Well, because to get from the bow to you, the arrow first has to cover half the distance from the bow to you. Then when it's done that, it needs to cover half the remaining distance. Then it needs to cover half of that remaining
distance. And so on - an infinite number of times. There's an infinite number of steps that it needs to cross to get from the bow to you. You can't take an infinite number of steps in a finite time - therefore, the arrow will never get to you.
It's not quite the same thing as this argument, but it's got the same basic flaw. It's playing games with the idea of infinity.
Third - it's got false premises: "Atheism, both in the forms I've encountered and in logical necessity, requires that matter/energy is eternal, since the atheist would by necessity argue against any point at which matter/energy came into existence." Do atheists really argue that the universe has to be infinitely old? Does it really argue that matter and energy are, by necessity eternal?
Of course not! The scientific theory about the creation of the universe - which is accepted by every atheist I've ever met (and also by most theists, including myself) is the big bang. To be a tad more precise, the big bang isn't really a single theory - it's a family of overlapping theories. According to all variants that I'm aware of, talking about "matter" and "energy" doesn't make any sense outside of our universe. Our universe wasn't made out of "matter" and "energy"; matter and energy are part of our universe. And according to most variants, time is part of our universe - talking about a time before the big bang is meaningless.
The reason for bringing the big bang into this is because in every version of
the big bang theory, matter and energy were created in the big bang. That is, they are not infinitely old - they do have a starting point - the starting point of time.
So we're basically looking at a straw-man argument, which creates a
false premise, asserts that all atheists "by logical necessity" must
accept that false premise, and then uses that false premise to put together
an argument that doesn't make any sense - and which applies as much to
his own theistic view of the universe as it does to any atheist's.
The underlying problem here is that the basic statement of the argument
is mathematically meaningless. As I said above, this is the kind of thing
mathematicians hate; it's not really an argument at all - it's built on
something entirely meaningless.
When you assert an infinite past - that is, that time extends infinitely
backwards from this point - what you're asserting is that there is no starting point. When you ask a question like "How did we get to this point, when
there's an infinite past behind us?", your question contains the implicit assumption
that there is a starting point, from which you can measure the distance between then and now. The argument is, actually, contradicting itself - both asserting that there can't be a starting point, and that there is a starting point. The contradiction between those two statements is then pulled
forward, and presented as a conclusion - as if it's a derived
contradiction, as in a proof by contradiction - when in fact, it's just
built into the faulty structure of the argument.
Reduced to simple logic, you can turn this into something like:
- A: ¬∃t0 : ∀ t: t0 < t
- B: ∃ t0: tnow - t0 = ∞
- C: ∀ i,j : ti - tj = ∞ ⇒ ¬∃ti
- B & C ⇒ ¬∃tnow.
B and C do logically imply that you can't possibly have a time
"now" if there's an infinite past. That's the conclusion of his anti-atheism
"proof". But you can't formulate that argument without having a time t0 at which the distance between "now" and t0 is infinite - and for the distance between tnow and t0 to be infinite, you need a t0 which is forbidden by statement A. The problem isn't the conclusion - the problem is in the formation of statement B.
This isn't a valid proof. Given contradictory premises, you can draw a line
of logical inference to any conclusion. But it's a meaningless exercise. The same flawed inferences can "prove" that God can't exist; or that God must exist; or that time can't exist at all; or that 1 = 2.