Have you ever found yourself understanding something more deeply while you're discussing it with someone else? Recently, while in a discussion with an atheist, I had several realizations that had not thoroughly come to me before - these are probably old hat to you, but to me they are not, so I shall note them down, lest I forget them.
Now to be perfectly accurate, the second aspect of this discussion is outlined in a somewhat less direct way in my book, Synergy: Science Reasons With Atheists, but the importance of the argument in discussions with atheists cannot be overstated.
As for the first aspect of the argument, reproduced below, I shall have to put it in the book soon, I think, since it is perfectly unanswerable.
To understand why these realizations work, you have to understand that empiricism, strictly defined, means "observation." If you observe something, you can empirically prove it happened. If you don't observe it, you cannot empirically prove it. You may be able to prove it through other means (logical deduction or logical induction, for example), but you can't prove it empirically because you haven't personally observed it.
Proving the existence of God.
If God is infinite, then we can prove His existence through formal logic, as Aquinas did, but we cannot empirically prove His existence, and that for two reasons:
1) While discussing the relative merits of Cantor's theory of infinite sets, the atheist claimed that he could empirically verify the theory to be true.
I pointed out that this is impossible.
We are, by definition, finite. This means our senses are finite and therefore the power of our observation is finite. So, even if we were presented with the infinite, we would be unable to observe that infinity precisely because our senses are not powerful enough to observe it.
The atheist may be able to verify that Cantor's theory is true through formal logical analysis, but he can't prove it true through empiricism because infinity is not graspable, even in principle, via the senses. After all, even the whole of the universe is not infinite, so he has no example for his senses to operate on.
And even if the universe were infinite, he still wouldn't be able to prove Cantor's theory true, because he wouldn't be able to observe its infinity. His senses are finite, and therefore incapable of taking in all that infinity comprises.
Indeed, the universe may very well be infinite, but if it is, we wouldn't be able to tell. Only our minds are able to accept the idea of infinity, our senses are unable to accept its reality. Infinity is not subject to empiricism.
Thus, because God is infinite, this conclusion would also apply to God. God could be standing right in front of us, but we wouldn't be able to empirically observe Him because our senses are too weak.
2) Empiricism cannot prove anything beyond a toy system.
It cannot work as a means of proving anything seriously complex, and for a very simple reason: strictly speaking, in order for me to be able to empirically verify something, I have to personally observe it. But because I am finite, I don't have the power to do this in any complex situation.
Consider the example of the craters on the moon. The atheist with whom I was discussing this matter claimed that these craters are empirical evidence of meteors.
Actually, these craters are empirical evidence of nothing at all.
Strictly speaking, if I am a real, full-time empiricist, unless I personally observed a meteor impacting the moon and forming a crater, I cannot say meteors form craters.
Worse, even if I did observe a meteor forming a crater, I can say only that a meteor formed the crater I just saw created, but for the millions of other craters, I cannot say that because I didn't personally see the impacts.
After all, because the formation of the other craters was unobserved by me, perhaps the other craters were formed in some way yet unknown to me. I can't know. And I can't accept your testimony about it because that would be trusting someone else's senses, which I don't know are trustworthy.
Even if you saw a crater formed in such a manner, I cannot trust your observation unless I physically saw you see the crater as it was being formed by a meteor. If you saw it, and I saw you see it, then I would empirically know that your observations were correct. In all other cases, I couldn't be sure your observations were correct.
Now, it is almost certainly the case that all those craters were in fact, formed by meteors, but I know that through formal logic, in this case, through mathematical analysis, which is purely formal logic, through induction from evidence provided by experiments which I claim are similar to meteor impact, etc. I do not know this through empirical observation.
So (as I point out in my book), when I read in a scientific journal that someone performed an experiment and I believe or otherwise accept the results of that experiment, I don't accept the results because I am an empiricist, I accept the results precisely because I'm not an empiricist.
That is, I accept the experimental results on faith. I trust the person who wrote the article, I trust the peers who reviewed the article - I trust a person or groups of persons.
Again, as I point out in the book, I could not do science without this faith. Faith is critical to scientific endeavors, for even the most strict "empiricist" has not performed all the foundational experiments in his discipline, nor has he personally created all the instruments through which the experiments were performed. Yet he should do both, in order to be sure that everything worked in the way he thinks they work.
He can't have done all this.
Even if he tried to be a strict empiricist, given the current state of knowledge, he wouldn't live long enough to discover anything really valuable.
The great irony is, that the men of Christian faith who developed the scientific method in the Middle Ages were better empiricists than today's atheists, if only because they actually did perform the foundational experiments with equipment they created themselves.
3) Empiricism is the opposite of science.
If I am strictly an empiricist, I only accept what I have experienced, I do not accept what I have not experienced. But I have not experienced the future, by definition.
So, when anyone makes a prediction about a future event, he is - by definition - not being empirical. He is rejecting empiricism in favor of faith: faith in an orderly future (which he has not yet experienced, so he can't know it is going to be reliably orderly).
A real empiricist would not make scientific hypotheses, since he would have no grounds for doing so. True, the history of his experience may so far be orderly, but he has no guarantee of the future, so forming hypotheses or, worse, attempting to test an hypothesis, is empirically absurd.
After all, the empiricist hasn't experienced the results of the test he is about to attempt, so he can't know anything about those results. The very attempt to run the test is an act of faith, not of empiricism. The consistent empiricist rejects acts of faith as unverifiable flights of fancy.
The consistent empiricist is philosophically incapable of conceiving of the future. Indeed, the word should not even appear in his vocabulary since it cannot be verified at all. The very fact that an "empiricist" conceives of the future and acts as if there is one is proof that he isn't really an empiricist.
Given these facts, empiricism is a chimera, a will-o-the-wisp, a falsehood.
There really is no such thing as empiricism nor any such thing as an empiricist.
Anyone who claims to be an empiricist is lying to himself.
He trust others, but he won't admit it.
His worldview relies on faith, a tremendous faith in other persons and their observations, in his own powers of observation, and in the future.
And that is what theology is about - faith in Persons, and therefore, faith in the future.
Insofar as we are all persons made in the image and likeness of the Persons of the Godhead, every scientist is, in his innermost being, a theologian, although he knows it not and acknowledges it not, because he has to trust persons in order to even begin his work, much less bring it to completion.