If you go to the right places on the Internet it is fairly easy to come across Dawkinsian atheists who claim to be empiricists. They are not empiricists, of course—most haven’t done a single basic experiment themselves, let alone all of the basic experiments—but they will certainly claim to be, if not by name. When this is pointed out to them, they will take refuge in what might be called a collective empiricism: as long as someone has empirically verified it, and it is theoretically possible to empirically verify it again, that’s OK.
Being a retreat this isn’t well thought out, of course. Why should the bare theoretical possibility of an experiment being run again make human testimony about a previous experiment more believable? Still, that’s really a minor point; this new version doesn’t do what they want it to, anyway. They are hoping to divide knowledge up into reliable knowledge and everything else. It doesn’t do anything like that; their “knowledge” is just as unreliable as every other form of knowledge they denigrate, except for the kinds it’s less reliable than. What it does do is codify the reductionism which they practice. They want life to be simple, and so they rule out, as a simple matter of choice, types of knowledge which they don’t want to deal with. In practice, those are most types of knowledge. Ironically, given the high respect in which most such people hold mathematical physics, this includes mathematics.
What they are really trying to limit knowledge is the substitute for knowledge proposed by Kant. Basically, come up with a theory and then test it against experience. According to this concept of knowledge, nothing is actually known. Things are guessed at, and the best you can do is feel reasonably confident in your guesses when applying them to the parts of life in which you have tested them before.
The curious thing about this is that not even Kant tried to limit knowledge to this; he only limited knowledge of real things to this. That is, of things which exist. He fully recognized the universal validity of logic and reason; all he doubted was noesis, that is, perception of reality. Being the end of Modern Philosophy, he doubted that the senses could be trusted at all, and so the mind could not know anything which existed outside of it. But things which do not exist, such as hypothetical statements like the theorems of mathematics, he still thought fully knowable.
The Dawkinsian reductionists have eliminated this as well. They take somewhat seriously C.S. Lewis’s argument that if reason is the product of blind material processes, there can be no reason to trust it. (They probably didn’t actually hear his version of it; the problem is fairly obvious with only a moment’s thought. Unfortunately Lewis’s conclusion was that Dawkinsian evolution is self-refuting, which is not true. Dawkinsian evolution may be true, and if it is, it is intellectual suicide, but it is not self-contradictory.)
Given this semi-radical skepticism, the modern materialist is actually abjuring all knowledge. He doesn’t deny it, he merely disavows it. He’s uninterested. He will proceed with what amounts to a betting scheme, taking the Kantian approach as simply his preferred method for dealing with what may well be an irrational universe. Trouble emerges because—having no use for it—he redefines the word “reason” to mean this sort of bet, and “reasonable” to mean betting in the same manner as him. Thus anyone who makes any sort of real knowledge claim is “irrational”. The most common knowledge claim to excite this sort of opprobrium is to claim to know that God exists, probably mainly for practical reasons—Dawkinsian Atheists tend to strongly dislike traditional morality, which they associate with Christianity for mostly historical reasons—but also because God is known entirely through means which the Dawkinsian Atheist rejects (reason and testimony).
This phenomenon also gives rise to some very strange results when applied to mathematics, which the Dawkinsian Atheist must accept, despite his obvious rejection of it, because Physics (the field of study) is dependent upon mathematics. The compromise which this sort of extreme skeptic tends to employ is absurd in the abstract, but fits with his adopted approach to life: he tests mathematical theorems experimentally. I recently saw a rather striking example of this when just such an atheist offered to experimentally prove that 2 + 2 = 4 using apples. It’s really beside the point that such a demonstration would fail using sub-atomic particles if two are electrons and two positrons; it’s actually most interesting that he doesn’t understand that 2 + 2 = 4 by definition. There are actually several definitions of the Natural Numbers, but the most common is using the piano axioms. Briefly: suppose there’s something, call it one. Suppose there’s a next number after it, call that two. Suppose there’s a next number after that, call it three. And so on. Addition is defined by succession, so 2 + 2 is 4 because the number after the number after two is called four. No other possibility is conceivable, because this is simply the definition of the successor of the successor of 2. But this is not really a thinkable thought for the Dawkinsian atheist, so he’s stuck offering to do demonstrations with apples.
Actually, he’s not quite stuck doing that; he can also ridicule people for doubting. “If you don’t think that 2 + 2 = 4, the IRS would like to talk with you,” he says, and smirks in derision. He’s not interested in the definitions of the numbers, or of what additional actually is; all he cares about is practical results, because he has disavowed knowledge in favor of a betting scheme. And he can’t know that he’s betting his soul, because he doesn’t believe he has one. Pray for them.
Incidentally, these people correspond fairly well with the men Aristotle described as wanting to be horses. Each man, as a rational creature, has a duty to the truth: to seek it out and to know it as far as it has been given to him to do. These men find that unpleasant; they wish to do only the simpler tasks of caring for the body. They want the wail of Ecclesiastes to be true: they want man to be only the cleverest of the beasts that crawls the earth. Pray for them.