Richard Dawkins offers an argument against theism in The God Delusion. The key issue is complexity. How do we account for the complexity of the world we see around us? Not, says Dawkins, by invoking the God hypothesis, because a God would have to be at least as complex as the complexity he is invoked to explain.
But is this an argument against the existence of God, or merely a refutation of one argument for the existence of God (the argument from complexity)? If the latter, Dawkins can hardly claim to have established there is no God. Even if the argument from complexity is a poor argument for the existence of God, maybe there are better arguments? Maybe there is a God nevertheless?
But actually, Dawkins claims to have shown that God must indeed be highly improbable because, if unexplained complexity entails improbability, then God must himself be highly improbable. Indeed - God must be even more improbable than whatever complexity he is invoked to explain.
In response, theists have argued, for example, that God is simple not complex. God is a single, simple mind which can entertain complex thoughts. The mind that entertains those complex thoughts is, nevertheless, itself simple.
Rather than get into that issue, I want to raise another worry - a worry concerning Dawkins's claim that his argument is "scientific".
Is it? The key principle seems to be that if the complexity of something is explained as the deliberate creation of a mind, then that mind must contain at least as much complexity as the complexity it is supposed to explain.
This principle does seem plausible. If I deliberately fully design and then subsequently build a mousetrap, that mousetrap's structure must be fully represented in my mind (or at least in my blueprint) prior to my building it. My representation must represent each of the various parts of the trap and how they fit and work together. So my my mental or physical representation must itself have parts. It must be at least as complex as the designed trap.
But, assuming this principle is true, is it a scientific principle? Did scientists discover it to be true?
If it were a scientific, empirically established principle about representations that they are at least as complex as that which they represent, we could be sure that it would apply to physical beings like ourselves. But then why should we suppose it applies to beings that transcend the empirically observable world, such as gods? If the principle is a mere law of nature (alongside other laws, such as that every action has an equal and opposite reaction) why suppose it applies to gods?
In short, if Dawkins's principle is a scientific, empirically established principle, it seems it can't do the work Dawkins requires of it.
However, if the principle were some sort of logical and/or conceptual truth about representation, then presumably it will apply to gods too. In fact, I think Dawkins's principle, or something like it, probably is such a conceptual truth (one that e.g. Wittgenstein's picture theory of meaning articulates - Wittgenstein's theory requires a structural isomorphism between a representation and that which it represents).
But establishing such logical/conceptual truths is the business of philosophy, not science. So Dawkins' argument turns out to be a philosophical argument, not a scientific argument.
In which case, Dawkins' well-known disdain for philosophy is ironic. He's actually doing - or needs to do - philosophy here, not science...