A common criticism against the so-called New Atheists -- e.g., Richard Dawkins, Jerry Coyne, PZ Myers, Sam Harris, etc. -- is that they are philosophically naive and accept an unreflective, dogmatic scientism. Is this a fair point?

Well, there are several distinct points here, so let's take them one by one.

I don't pretend to be an expert on those guys, but I have looked at them a little bit, and the impression I have is that, yes, they are philosophically rather naive. Indeed, that's the very reason why I've never bothered to study them in depth: because, compared to the works of more erudite and sophisticated philosophers, I tend to find their work a little dissatisfying. Being charitable, I suspect that part of this is down to the fact that they're deliberately writing for a popular audience, rather than an audience of trained philosophers, and consequently need to gloss over some of the more abstruse and nit-picking details. But such an explanation can only go so far. I think it's reasonable to suppose that many of them are simply unaware that some of these arguments -- both the theistic arguments that they're criticising, and the atheistic or agnostic arguments that they're supporting -- can be developed in much stronger forms than the ones they consider. I don't say decisive forms, necessarily, but philosophically more rigorous and compelling ones than their crude caricatures would suggest.

Second, are they unreflective? No, I don't think that's fair. They've certainly thought very seriously about these issues, maybe less than professional philosophers who devote their entire working lives to them, but much more than most ordinary people.

Third, are they dogmatically scientistic? That's a hard one to decide, because I'm not quite sure what it even means. They certainly do seem to believe that the world operates in a law-governed, naturalistic way, a way that the scientific method might lead us towards an understanding of; and to feel that we have no good reason (be it a posteriori or a priori) for believing in anything supernatural over and above this. I suppose this attitude becomes dogmatic when one refuses to accept that anything even could constitute evidence against such a world-view. But I think the point that I'm sticking on is not whether there ever could be evidence against this. I am having trouble imagining what it could actually look like: but, who knows, maybe it is a possibility. Rather, my inclination is to feel that, if such evidence was to come to light, then the proper domain of scientific enquiry would simply expand to absorb it. Go back a few hundred years, and natural philosophy (i.e science) was regarded as continuous with natural theology. As Isaac Newton said in the General Scholium to his Principia, 'to treat of God from phenomena is certainly a part of natural philosophy'. And what about the advocates for Intelligent Design that these New Atheists are so bothered by? Are they being dogmatically scientistic, by trying to draw theological matters into the domain of scientific investigation (in, for what it's worth, almost exactly the same way that Newton did)?

I don't get the impression that the New Atheists are dogmatic about the particular scientific theories that they currently believe. It's in the very nature of science that its central tenets have developed gradually over time, and will continue to develop further in the future, with old and cherished theories being overturned in favour of new and better supported ones. I think its fair to say that the New Atheists are not expecting that science is about to start moving back in a theistic direction. But they don't pretend to know what direction it is going to move in: if they did, they'd already be taking it in that direction themselves. And, if the evidence was to end up leading the scientific community towards a notion of a supernatural deity, it could still qualify as science for all that. If it's dogmatically scientistic to feel that we should believe things on the basis of evidence and argument, and be willing to follow that evidence dispassionately wherever it might happen to lead, then count me in.

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