While I was still an undergraduate at the University of Waterloo, I attended a lecture by the Canadian philosopher William Hatcher detailing a logical proof of God. Having recently had something of an existential crisis, thoughts of God and spirituality were very much on my mind. Here was something that I could really sink my teeth into: in contrast to the blind dogma fed to me by the fundamentalist Christians I was hanging out with at the time, Hatcher took more of a scientific approach.
At the same time, I was taking a philosophy course on science and religion. As soon as I heard the talk, I just knew I had to write an essay on it. What I came up with, which can be found here, turned out to be rather critical. At first I was extremely impressed with the simplicity of the argument, but soon discovered the hole--detailed in the essay.
Hatcher has written others essay that attempt to apply the tools of mathematics to metaphysical problems such as "A Logical Solution to the Problem of Evil" which can be found in "Logic and Logos: Essays in Science Religion and Philosophy." While I don't believe either example is entirely successful, the approach is nonetheless greatly appreciated. Sadly, Prof. Hatcher is no longer with us and passed away in 2004. His legacy, however, is alive and well and his estate is attempting to compile his work online: http://william.hatcher.org/.
The point I wanted to make with this essay was not about God, nor about the problem of evil, it was rather about knowledge itself. I have looked at a number of other proofs of God, and while they are all interesting and ultimately quite audacious, none of them is really commensurate with more useful proofs in science and mathematics. What if certain questions, such as, "Is there a God?" simply cannot be answered?
A more obvious example would be certain more extreme claims in the interpretation of quantum mechanics such as, "The moon truly isn't there when we aren't looking at it." That is, when something is not being observed, it no longer exists. Such an assertion is clearly absurd because the only way we ascertain existence is through observation and hence, unanswerable.
Multi-valued logics have a long and somewhat chequered history, culminating in the current, slightly controversial extreme of "fuzzy logic." In fuzzy logic, it's not that there are more than two truth-values, rather truth exists on a continuum between 100% false and 100% true, but nonetheless it is in the same spirit.
My own contribution is somewhat more modest (and likely not original). I propose adding a single extra truth value, namely that something cannot be known. Here are the truth tables:
0 1 X
0 0 0 0
1 0 1 X
X 0 X X
0 1 X
0 0 1 X
1 1 1 1
X X 1 X
Here, X denotes that a proposition "cannot be known" and functions somewhat like an NaN or Inf in floating point arithmetic in the sense that once one creeps into a calculation, the tendency is for it to propogate itself throughout.
As I've gotten older, I haven't lost my interest in questions of God, metaphysics and spirituality, although I try now to take them a bit less seriously. If you want to waste a lot of time, log onto one of the discussion boards debating the existence of God. The same tired arguments are brought up again and again and the same tired counter-arguments brought up in response.
One development that interests me is the current crop of fervently atheist authors such as Richard Dawkins. Part of their argument against God and religion is that science has become so powerful in explanatory ability that faith has lost any purchase it might once have had. My own belief is the exact opposite: science and faith actually complement one another perfectly. That being said, we should guard against having a "God of the gaps" wherein we attribute to God and spirituality whatever it is that science has yet failed to conquer, hence the domain of spirituality becomes smaller and smaller. Once we acknowledge, however, that certain things cannot be known, we now have an enormous zone wherein faith and spirituality can thrive. I like to think of the boundary between the known and the unknowable as a "jumping off point."